201012 RISKFLOW Technical Report - Resilient Organisations

RISKFLOW MODEL

Technical Report

Prepared for: BRANZ

November 2020

RISKFLOW MODEL

Technical Report

BRANZ

Document reference: Final

Date of this version: December 10, 2020

Report authors: Nicola McDonald, Charlotte Brown, Alice Chang-Richards

www.me.co.nz

Disclaimer: Although every e�ort has been made to ensure accuracy and reliability of the information

contained in this report, neither Market Economics Limited nor any of its employees shall be held liable

for the information, opinions, and forecasts expressed in this report.

Contents

List of Figures iv

List of Tables v

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives of this report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 System Dynamics 2

2.1 Introduction to System Dynamics Modelling . . . . . . . . . . . . . . . . . . . . . 22.2 Casual loop diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Components of System Dynamics Models . . . . . . . . . . . . . . . . . . . . . . 3

3 Overview of RISKFLOW 5

3.1 RISKFLOW Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.1.1 Key underlying premises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.1.2 Model structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Model Dynamics and Feedbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2.1 Policy responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2.2 Ripple e�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2.3 Secondary and tertiary feedbacks . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Model Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.1 Conventions and notation used . . . . . . . . . . . . . . . . . . . . . . . . 113.3.2 Overview of computational method . . . . . . . . . . . . . . . . . . . . . . 12

3.4 Model Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Next Steps 14

References 17

A Index of names and definitions 18

A.1 Subscripts and concordances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18A.2 Stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20A.3 Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22A.4 Auxiliaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24A.5 Exogenous inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.6 Reporting module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

B Model equations 41

B.1 Stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41B.2 Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43B.3 Auxiliaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46B.4 Reporting module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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List of Figures

2.1 Example of a simple casual loop diagram and feedback loops . . . . . . . . . . . 22.2 Example of a simple stock flow diagram . . . . . . . . . . . . . . . . . . . . . . . 3

3.1 Procurement diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 Project stocks diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Policy response diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.4 Policy response and ripple e�ects diagram . . . . . . . . . . . . . . . . . . . . . 103.5 Sample user interface with selected reporting figures . . . . . . . . . . . . . . . . 13

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List of Tables

3.1 Description of subscript indices used in Model . . . . . . . . . . . . . . . . . . . . 113.1 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

A.1 Descriptions of subscripts used in Model . . . . . . . . . . . . . . . . . . . . . . . 18A.2 Client types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18A.3 Contract Organisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18A.3 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.4 Contracting Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.5 Experience categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.6 Input categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.7 Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.8 Response categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20A.9 Sector categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20A.10 Description of stocks and equation references . . . . . . . . . . . . . . . . . . . . 20A.10 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21A.11 Initial condition settings for stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 21A.11 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22A.12 Description of flows and equation references . . . . . . . . . . . . . . . . . . . . 22A.12 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A.12 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24A.13 Description of auxiliaries and equation references . . . . . . . . . . . . . . . . . . 24A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29A.13 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30A.14 Description of exogeneous constants . . . . . . . . . . . . . . . . . . . . . . . . . 31A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.14 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.15 Description of reporting module variables and equation references . . . . . . . . 39A.15 (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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1 Introduction

1.1 Background

The RISKFLOW System Dynamics Model has been constructed as part of a research projectaimed at building risk management strategies into the vertical construction sector. The primarypurpose for creating the model is to investigate the relationships between risks, risk managementand productivity in the construction sector, and how these relationships might differ betweenthe vertical and horizontal sub-sectors.

In the New Zealand economy, the construction sector faces significant operating challenges suchas volatility of demand (boom and bust cycles), shortages of skilled labour and site-specific re-quirements. Of particular concern is the vertical construction sector, which experiences produc-tivity volatility (PWC, 2016), reduced organisational resilience (Sapeciay, Wilkinson, & Costello,2017) and higher enterprise failure rates when compared to the horizontal sector. The aim of thisresearch project is to improve the productivity of the vertical construction sector through un-derstanding where enhanced risk management and organisational resilience processes may derivepositive outcomes.

The RISKFLOW model seeks to verify and validate the role of risk management and organi-sational resilience practices in productivity for the construction sector, focusing particularly onidentifying where differences exist between the horizontal and vertical sub-sectors and where im-provements can be made. Improving the stability of the vertical sub-sector, and the constructionsector as a whole, will likely contribute to overall productivity gains and improved socio-economicwell-being in New Zealand.

Development of the RISKFLOW model is the final component to the project, the initial compo-nents being interviews and surveys (Chang-Richards, Brown and Smith, 2019). The model wasbuilt using the data collected from these interviews and surveys, which draw extensively on stake-holder and expert knowledge of the construction sector, as well as literature reviews/searches.

1.2 Objectives of this report

The purpose of this report is to provide a detailed technical documentation of the RISKFLOWSystem Dynamics Model. By fully documenting all equations we intend to make the model astransparent as possible.

We are aware of construction sector productivity research, which has been built upon, but we areunaware of any research that takes our unique trans-disciplinary, mixed methods approach thatfocuses specifically on risk management and organisational resilience. Our RISKFLOW modelspecifically seeks to understand these concepts with respect to productivity within the verticaland horizontal construction sectors.

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2 System Dynamics

2.1 Introduction to System Dynamics Modelling

First developed during the 1950s primarily by Jay W. Forrester, system dynamics (SD) bringstogether ideas from control engineering (concepts of feedback and system self-regulation), cy-bernetics (the role of information in control systems) and organisational theory (mechanismsof human decision making and the structure of human organisations) (Meadows and Robinson,1985).

SD models are complex, non-linear, multi-loop feedback systems which seek to understand thefundamental idea of two-way causation or feedback in structural systems. Of particular interestare dynamic behaviour patterns generated overtime, and for what conditions the system asa whole is growing, oscillating, declining, stable or unstable, self-correcting or in equilibrium(Meadows and Robinson, 1985).

SD models are most commonly used for the purposes of general understanding, policy makingand design for aggregate systems. They can also be widely applied across disciplines and usedto address problems in urban, social and ecological systems. Through SD modelling, whichenables a greater understanding of complex feedback loops within systems, structural changesor strategies are identified as solutions to the problem.

2.2 Casual loop diagrams

Casual loop diagrams (CLDs) are typically the first step in building a SD model. CLDs are usedas a conceptual tool to identify casual relationships among variables within a system. Figure 2.1is a simple CLD showing the relationships between births, deaths and population. Variables (orfactors) and arrows (links) make up the basic components of CLDs. A variable is a situation,action, decision or condition which can influence, and can be influenced by, other variables. Theuse of an arrow indicates an association between two variables, or a change in the state of thesevariables.

Figure 2.1 Example of a simple casual loop diagram and feedback loops

The relationships between two variables can be positive or negative, depicted by either ‘+’ or‘-’ sign, where ‘+’ means a positive relationship or movement in the same direction, while ‘-’specifies a negative relationship or movement in the opposite direction. The number of births

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has a positive influence (‘+’) on population, meaning as the number of births increases, thepopulation also increases. Conversely, as the number of deaths increases, the population declines,illustrating a negative (‘-’) relationship between the two variables.

For casual loops, there are two types of feedback processes known as Reinforcing (R) andBalancing (B) feedbacks (see Figure 2.1). Reinforcing feedback loops can represent growing ordeclining movements. That is, they compound change in one direction with even more change.Balancing (or controlling) feedback loops seek stability, return to a desired level or equilibrium.

In the example presented above, the number of births has a positive relationship on populationand in turn population has a positive influence on the number of births. This casual loop isa reinforcing (R) growing feedback loop. The casual loop between deaths and population is abalancing (B) self regulating feedback loop.

SD models are made up of many feedback loops linked together.

2.3 Components of System Dynamics Models

SD models consist of three main elements: stocks (sometimes referred to as levels), flows (rates)and auxiliaries (converters).

Figure 2.2 Example of a simple stock flow diagram

Stocks are accumulated quantities, such as a stock of material or information. The value of astock at any given instant in time depends on the system’s past behaviour. Stocks will continueto exist even if all the flows in the system are bought to a halt. In Figure 2.2, ‘Rabbit Population’is the stock which at any point in time is determined by the flows. In diagrams, stocks are usuallyrepresented by rectangles.

Flows represent the changes to the stocks that occur overtime, characterised by a flow of materialor information to or from a stock. The flows in the diagram above, ‘rabbit births’ and ‘rabbitdeaths’, determine the level of the Rabbit Population (stock). Rabbit births represents a flow ofnew rabbits into the stock, increasing the rabbit population, depicted by a thick arrow enteringthe stock. Conversely, rabbit deaths represent the decline of the rabbit population whereby thethick arrow is exiting the stock. Flows represent activity or movement, in contrast to stockswhich represent the state of the system.

Auxiliary variables are other variables which are not flows and are capable of changing theirvalue instantaneously. These intermediate variables can be inserted into flow equations if desiredin order to break complex flow equation into smaller simplified components, making the modeleasier to understand. Auxiliary variables in the example above are the ‘rabbit birth rate’, ‘initialrabbit population’ and ‘average rabbit life’. These either represent components at the boundary

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of the system (parts whose value is not determined by the behaviour of the system itself) or theyrepresent parts of a system whose value can be derived from other parts of the system at anytime through some computational procedure.

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3 Overview of RISKFLOW

3.1 RISKFLOW Model

The RISKFLOW model was developed out of literature reviews, expert surveys and interviews.A brief overview of the model and key relationships is provided in this section. The full set ofequations for the model are provided in the Appendices to this report.

3.1.1 Key underlying premises

Some of the key underlying premises that underpin the model’s structure are as follows:

• The horizontal and vertical construction sectors are similar in terms of structure. Thus,while the specific parameters used to describe each sector may vary, the same types andforms of equations and relationships can be used to describe both sectors.

• Both the horizontal and vertical sectors can be described as operating at different processlevels or scales. These are:

– Project Procurement,– Project Progress/Workflow,– Organisation Scale (Head Contractors), and– Whole-of-Sector Scale

In the development of the RISKFLOW model, we have looked closely at the relationshipsoperating at each of these scales/levels, as well as key relationships operating betweenthem. In addition, both sectors are closely connected with their relevant subcontractingsector.

• As well as identifying that there will likely be differences in construction operations de-pending on the sector under consideration, it was also identified, particularly out of theinitial expert surveys, that the type of contracting model and client is important. Whererelevant, the model is also therefore constructed to allow for different parameters depend-ing on the client type (Government, Developer-to-Sell, Developer-to-Keep, One-off) andcontracting model (Build Only, Design-Build, Integrated).

• While head contractors are included ’individually’ in the model, subcontractors are treatedas a homogenous group. Any attempt to model the population of subcontractors in asimilar manner to main contracting organisations would add significant complexity to themodel. Unnecessary complexity would overshadow the principal purpose of the projectwhich is to investigate the differences between the horizontal and vertical sectors. WithinRISKFLOW we have therefore concentrated only on considering the impact of placingincreasing pressure on subcontractors in terms of the quantity of errors produced. In turnpressure arises by pushing the responsibility of fixing errors onto sub-contractors.

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3.1.2 Model structure

The basic model structure is derived from the different levels/scales in which both the horizontaland vertical sectors can be described as operating at; these are described in turn below.

Project Procurement

In the project procurement component of the model we have an exogenous time series of projectdemands (i.e. value of work to be done for each project). Assigned project start dates and projectexpected durations are also determined exogenously for each of the sectors. The model thenallocates each project to a specific client, contracting model and head contracting organisation.This allocation is stochastic for each element. In the case of clients and contracting models, thechance that a particular client/contracting model will be matched to a project is determinedby exogenously defined client and contracting model distributions for each sector. In the caseof head contractors for a project, the chance of any particular organisation being selected isimpacted by the particular procurement score given to the organisation (organisation score) (seeFigure 3.1). These scores, in turn, are impacted by the organisations, reputation, as well as thecontracting price (i.e. margins) offered by the organisation for the project.

Figure 3.1 Procurement diagram

Project Progress/Workflow

Project Progress/Workflow is modelled commencing in a stock of Original Work to Do and, asprogress is made, flows into the stock of Work Done, with progress in turn impacted by projectproductivity, and the level of effort applied (Figure 3.2).

All known system dynamics project models subsequent to Pugh-Roberts Associates original workhave modelled rework cycle (Lyneis and Ford, 2007). As such, the rework cycle is consideredto be the single most important feature in system dynamics project models. The rework cycleunderpins the structure of the RISKFLOW model and reflects the challenges which are faced bythe horizontal and vertical sectors, contributing to increased error rates and reduced productivity.

Rework is caused by errors, whereby work being done at any point in time contains mis-takes/errors. Once errors are discovered, the required rework is either pushed onto sub-contractors(pushed work), slipped from the project scope (slipped work), assigned to the responsibility ofthe head contractor to fix (assigned rework) or negotiated as new work to do under remuneration,i.e. as a variation. If the latter, this is conceptually treated as a new project thus entering thestock of Original Work to Do (Figure 3.2).

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Figure 3.2 Project stocks diagram

In the model we have focused not only on errors as being the source of project difficulties, butalso delays and changes in project scope. A change in scope occurs by increases in expectationbeyond the scope of the Original Work to Do (expectation increase). In terms of delays, thefollowing types of events that impact on project progress are considered: material delays, healthand safety delays, weather delays, contractor delays, rejected design delays, management delaysand inspection delays. The occurrence of all delay types is stochastic within the model, howeverin some cases the chance of a delay occurring is increased by organisational and project factors,such as the level of risk maturity or the pressure placed on subcontractors within the project.The length of delay should one occur, as well as the proportion of workflow impacted by thedelay are also stochastic within the model.

Organisational Scale (Head Contractors)

Each organisation may be involved in several projects, potentially simultaneously. At the organi-sation level RISKFLOW keeps track of key organisational attributes which have flow-on impactsto dynamics occurring elsewhere in the model. These attributes are:

• Public perception of each organisation’s experience, as well as their perception of each organ-isation’s reliability in terms of mistakes/delays. As identified above, these two attributestogether determine the reputation held by each organisation, which then influences thechance of winning contracts during the procurement process.

• The quantity of labour held by each organisation as well as the skill level of that labour (un-skilled, skilled, high skilled). The more unskilled the labour stock held by each organisation,the greater the chance of errors during project workflow and flow-on rework errors. Labour

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attributes also impact on the margins offered by organisations during project procurementnegotiations. That is, if an organisation has a low level of labour utilisation (i.e. not manyof the available staff are occupied in projects) the more willing the organisation will be toundertake work at lower margins.

• Financial health – The modelled financial health index of each organisation reflects therelative margins received on projects per employee. In a similar way to underutilisedlabour, the lower the financial health index, the more willing an organisation will be toaccept projects with lower margins, in order to receive some income in the door.

• Risk Maturity – In this initial version of RISKFLOW, no attempt has been made to considerhow risk maturity may evolve over time, or any levers that could be used to increaserisk maturity. We have simply included an exogenous distribution of risk maturity fororganisations within the model, with the distribution for each sector based on survey results.Also based on survey findings are the relationships between the level of risk maturity of eachorganisation and the chance of rejected design, health and safety, material and inspectiondelays, as well as the chance of project errors.

Whole-of-Sector Scale

In this first version of RISKFLOW we have concentrated at the sectoral level only for thepurposes of developing aggregate indicators. This is so comparisons can be made between thevertical and horizontal construction sectors at the whole-of-sector level. For example, indicatorsare developed for overall margins received by each sector as well as the value of total delays andtotal errors experienced within each sector.

Nevertheless, our background literature review, surveys and expert interviews highlighted somedynamics occurring at the sectoral level. These sectoral dynamics may have important implica-tions in terms of the risks faced and ultimately the levels of productivity attained by the verticaland horizontal construction sectors. For example, it is frequently highlighted that the verticalsector is particularly prone to fluctuations in project demands over time, which can result involatile workflow and input costs (including labour and sub-contracting). Although we wouldhave liked to investigate these implications further, it was determined that we did not have scopewithin this first project.

3.2 Model Dynamics and Feedbacks

In this section we describe the principal responses and feedback loops operating within RISK-FLOW. For ease of understanding these are separated into three categories (1) policy responses,(2) ripple effects and (3) secondary and tertiary feedbacks or knock-on effects.

3.2.1 Policy responses

Policy (also termed management) responses are the actions taken by project managers in attemptto bring a system (principally at the project level) into alignment with desired states. Policyresponses are negative or controlling feedbacks, in other words the more the system deviates froma desired state, the more effort is directed towards bringing the system back into alignment.

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Lyneis and Ford (2007) identified four major controlling feedbacks or actions taken by projectmanagers: (1) slip deadline, (2) work faster or harder (increase work intensity), (3) work morehours or overtime and (4) add more staff. Note that in RISKFLOW we do not model slipdeadline explicitly, instead it occurs by default, depending on the level of other responses. Inaddition to the controlling feedbacks identified by Lyneis and Ford above, we have included sup-plementary feedbacks in RISKFLOW (see Figure 3.3). In the vertical and horizontal constructionsectors it is also possible to increase work throughput by (5) adding further subcontractors oroutsourcing, along with (6) changing construction methods/cost-cutting/innovating as identifiedby Nasirzadeh et al. 2008. We have, in addition, also added the responses identified in expertinterviews of (7) pushing responsibility of work onto the client (slip scope) and (8) pushing re-sponsibility of work onto subcontractors (push work). In Lyneis and Ford, the key system statemonitored by managers when deciding to implement policy responses is the expected completiondelay. In RISKFLOW, however, managers also monitor the expected margins relative to antici-pated margins (i.e anticipated budget overruns), in addition to time overruns, when determiningthe level of policy response.

Figure 3.3 Policy response diagram

3.2.2 Ripple e�ects

Ripple effects are the primary side effects resulting from well-intentioned decisions and controlactions (policy responses) which generate undesirable and unintended consequences (Lyneis andFord, 2007). Modelling ripple effects in project dynamics captures and leverages the concept ofpolicy resistance. Lyneis and Ford (2007) identify several ripple effects associated with initialpolicy responses. Although we have been informed by this article, we have adapted these slightlyto be more in line with the expert surveys and interviews undertaken in the initial stages of theproject (see Figure 3.4).

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The principal ripple effects identified are: (1) by increasing staff and subcontractors on a jobthere will be more congestion and communication difficulties as a result, which both reduceproductivity and increases the rate of errors in work, thereby causing resistance against increasingwork output. Similarly (2) increasing overtime and work intensity of staff causes workforce fatiguewhich lowers productivity, and (3) by undertaking innovation and seeking ways to cut costs thereis also an increased chance of errors. In addition (4) by pushing more work onto subcontractors,thus increasing the pressure on subcontractors there is also an increased chance of errors, as wellas (5) increasing the chance of project delays. Furthermore (6) the chance of delays (particularlydue to health and safety incidences) is also increased by adding more pressure on staff to increasework intensity, as is (7) the chance of errors.

These ripple effects identified above typically reduce productivity or quality by increasing theerror fraction rate and rework.

Figure 3.4 Policy response and ripple e�ects diagram

3.2.3 Secondary and tertiary feedbacks

Ripple effects generate secondary and tertiary feedbacks or knock on effects. A number of thesefeedbacks operate within RISKFLOW. Many of these cross over between different scales and areonly described qualitatively here. Full equations can be found in the Appendices.

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Morale is one aspect of the system that operates between the project and organisation scales.Within a particular project, staff morale is impacted negatively by increasing fatigue as wellas project errors. Declining staff morale not only impacts on productivity within an individualproject, it also spills over into other projects held by an organisation through a process of staffmixing. Organisational morale is also a key factor in determining the leaving rate of staff. Inturn, high worker turnover will reduce the level of organisation experience which will increasethe likelihood of errors during projects.

Organisation reputation also creates important connections between the project and organisationscale, as well as procurement processes. Reputation is deemed to have two key components: per-ceived experience and perceived mistakes. While the more work that is completed on projects willadd to the perceived experience and hence reputation of an organisation, project errors and de-lays will increase the level of perceived mistakes and thereby reduce an organisation’s experience.Reputation is a key factor considered during the procurement process in determining whetherorganisations are awarded new projects. Unfortunately, organisations that do not have success inprocurement may, over time, become more desperate to win projects and undercut competitors(as they have spare labour capacity and poor financial performance) by reducing margins. Withlesser margins and contingencies at hand this can, however, lead to behaviours/responses thatonly further increase chances of errors and delays (e.g. cost-cutting, working hard) which willthen only further reduce reputation and chances of winning projects.

3.3 Model Specifics

Specific conventions and notations used in the RISKFLOW model are detailed below, as well asa brief overview of the computational method used.

3.3.1 Conventions and notation used

Stocks are in bold font, with the first letter capitalised. Auxiliary (intermediate calculation)steps are named in all lower case italics. Variables with names in all capital letters and italics areexogenous inputs. Subscripts are used to indicate the dimensionality of a variable. For example,the stock Financialhealths,co denotes the financial health index by sector (subscript ‘s’), andcontract organisation (subscript ‘co’). Full information on subscripts is provided in Table 3.1.

Table 3.1 Description of subscript indices used in Model

Subscript indices Description

ct = [Govt,DevK,DevS,OneO] Client types: see Table A.2 in Appendix A.1co = [ConOrg1, ConOrg2, ConOrg3,

..., ConOrg20] Contract Organisations: see Table A.3 in Appendix A.1cm = [BuildO,DesignB, Integr] Contracting Model: see Table A.4 in Appendix A.1exp = [UnExper, Experin,HighExp] Experience categories: see Table A.5 in Appendix A.1inp = [Labour,Materials,

Subcontractors] Input categories: see Table A.6 in Appendix A.1p = [Project1, P roject2, P roject3,

(continued on next page)

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Table 3.1 (continued)

Subscript indices Description

..., P roject100] Projects: see Table A.7 in Appendix A.1r = [Sta�ng , Subcontracting,

Overtime,Workintensity,

Costcutting, Slipscope, Pushwork] Response categories: see Table A.8 in Appendix A.1s = [Horz, V ert] Sector categories: see Table A.9 in Appendix A.1

3.3.2 Overview of computational method

The model is made up of a rate equation for each stock that expresses how the value of thatstock will change with time (known as a system of ordinary differential equations) in the form:

d

dtStock = rateofchange (3.1)

The rates of change rateofchange in this model can be (often nonlinear) functions of other stocksin the model at the current time or a past time (delays), as well as constant parameters andtime varying exogenous inputs. Due to the nonlinearity in the model, these equations cannottypically be solved explicitly to find Stock(t). However, these types of nonlinear dynamicalsystems arise almost ubiquitously in models of the real world and many methods have beendeveloped to numerically approximate the solutions (values of Stock(t)). Numerical methodsfor solving differential equations must be convergent, i.e. the numerical solution must convergeto the exact solution (the error must go to zero) as the step size �t goes to zero.

The System Dynamics software packages contain a number of built-in methods for solving models.We have chosen to use Euler’s method which transforms the rate equations for the stocks intofinite difference equations numerically approximates the solution as:

Stock(t+�t) = Stock(t) + (rateofchange)⇥�t (3.2)

Euler’s method uses a fixed time step and only one calculation (function value) is required pertime step. Additionally, it is what is known as an explicit method which means that calculatingthe value of the stocks at a time step only requires knowledge of the values at the previous timestep, as in Eq. 3.2. This simplicity does however mean that the numerical error does not decreasewith step size as quickly as some other methods, so a smaller step size is required for numericalaccuracy. We have chosen 0.1 months (approximately 3 days) as the model time step.

3.4 Model Outputs

A large number of variables are tracked by the model during a simulation over time. A varietyof measures and indicators can potentially be developed from this information, depending onhow users wish to utilise the model. Thus far a simple user interface has been developed thatdraws together some key summaries of sector and productivity information. A screen shot ofthis interface is provided below.

Page 12

Figure 3.5 Sample user interface with selected reporting figures

The first two figures in the outputs screen examine, across the whole of each sector, two keyissues relating to loss productivity, i.e. errors and delays. The value of errors is costed accordingto the amount of rework required and the resulting materials, contracting and labour requiredto undertake that rework. The value of delays, however, is calculated according to the value ofwork that is scheduled to occur but cannot due to project delays (i.e. this is not necessarilyy theactual cost experienced by the delay).

The figure on the far right tracks total productivity index over time, calculated for each of thetwo sectors. This index is, in turn, calculated by dividing the monthly value of work completedby the monthly costs incurred (labour, subcontractors, materials). The bottom middle figurealso keeps track of the average value of this productivity index over the simulation.

Finally the bottom left figure calculates the average margins received on projects, as a percentageof total project value by each sector, while the bottom right figure calculates the proportion ofsubcontractor work that is undertaken without remuneration (i.e. because sub-contractors wearthe responsibility of undertaking rework).

It should be emphasised that due to the stochastic nature of many of the components of theRISKFLOW model, the outputs will vary each time the model is run, even when initial settingsand parameters are kept constant.

Page 13

4 Next Steps

Prior to this project, the majority of system dynamics models relating to construction wereat project level. But the reality is that the construction sector is complex and projects areinextricably linked to the wider sector: the decisions and behaviours of individuals, constructioncompanies, clients, and the regulatory environment. This project is an attempt to link all thesecomplex and interconnected elements together. In particular, our focus was on how risk ismanaged in this complex environment by both vertical and horizontal construction sectors andhow this flows to sector productivity. We have also attempted to integrate behavioural elementsof risk management, which is rarely included.

Presently RISKFLOW is best viewed as a prototype model, useful for demonstrating the applica-tion of system dynamics thinking and techniques to the analysis of construction sector dynamics.Although significant effort has been undertaken, through literature reviews, surveys and expertinterviews, to develop an appropriate structure for the model, it is still the case that many ofthe function shapes and appropriate parameters are uncertain. For example, given the largebreadth of functions that needed to be developed for the model, and the desire to not makethe survey and expert interviews too onerous, it was not always possible to ask the number ofquestions that would have been required to fully understand the shapes of some functions. Thiswas especially the case for functions which had many dependent variables or relationships withother components of the model (for example the function defining project error rate). The modeldevelopment process would benefit from having a wider group of experts available to draw on inpopulation of the model functions and parameters, to help remove any distortion created by theperceptions of single individuals. We did, for example, note that the experts interviewed fromthe horizontal and vertical sectors provided vastly different parameters relating to the nature andfrequency of project delays, which may have simply been due to different understandings of thequestions rather than actual differences between the sectors. With further time and resourcesfor expert elicitation, testing and calibration, it will be possible to iron out inconsistencies anddevelop more robust parametisation of the model.

Nevertheless, the RISKFLOW prototype demonstrates the potential power of this type of mod-elling to inform policy debate within the sector, create a value case for improving risk manage-ment (for both construction companies and clients), and its potential for use as a learning toolto better understand the sector and identify and design interventions to improve outcomes of thesector.

RISKFLOW could be used to analyse and interrogate a number whole of construction sectorchallenges, including:

• Procurement and contracting analysis – how do different procurement and contractingmodels affect the performance of the sector?

• Impact of improved risk management practices such as early contractor involvement, risksharing etc.

• Impact of different margins / project pricing strategies

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• Value case for improving risk management capabilities within organisations

• Labour force management evaluation

• Impact of more robust workflow pipelines

Below, we suggest some potential future applications or adaptations for the model. We have alsoidentified some potential end-users for each use type.

• Learning tool

System dynamics tools, like RISKFLOW, are ideally suited for use as learning tools. Thetracking of cause-effect relationships enables users to build system intuition. The dynamicrelationships allow for users to experiment by changing variables and experiencing theimpacts of these changes. This can a) help sector members better understand the impli-cations of their actions and b) enable researchers and regulators to better understand howthe system works as a whole and where interventions might be best made for maximumbenefit.For use as a learning tool potential improvement to the model include, further validationof model, improved user interface, user manual.Potential end-user / collaborator : MBIE endeavour project, CanConstructNZ, “will modeland report the dynamic inter-relationships of New Zealand’s infrastructure work pipeline(the proposed building, construction, and infrastructure projects) against the construc-tion sector’s capacity and capability to deliver (including procurement processes, supplychain organisations, people, and technology tools).” RISKFLOW has already started toexplore and map out many of these complex issues and could be enhanced to contributeto the project. Other potential end-users include MBIE and Construction Sector Accord,BRANZ, QuakeCentre, InfraCom, Engineering and construction management schools inNew Zealand.

• Policy analysis and evaluation

Policy analysis and evaluation is challenging in a complex sector like the constructionsector. The link between cause and effect is often unclear. System dynamics models likeRISKFLOW can provide some structure and rigour around identifying and evaluating thebest policy interventions.RISKFLOW, once validated, could be used to a) identify leverage points in the constructionsystem where policy interventions might have the biggest benefit and b) help create a valuecase for proposed policy interventions.Potential end-users: MBIE and Construction Sector Accord work on their TransformationPlan; QuakeCentre and their work on valuing the benefits of BIM; Infracom on infrastruc-ture planning.

• Organisational analysis tool

Aspects of RISKFLOW could be further developed to help individual organisations betterunderstand their business and make better risk management decisions. The scope of thistool could be quite varied but could cover financial management, project pricing, site/teammanagement approaches, project risk management approaches, and staff management. Thetool could help highlight, amongst other things, the cost (financial and wellbeing) relatedto rework and quality issues, and poor project management.Potential end-user : MBIE and Construction Sector Accord capability development pro-gramme

Page 15

• Client education tool

Throughout the project, the role of clients in project and organisational risk has beenhighlighted. There is a perception in the sector that some clients do not understand con-struction risk, and the way that projects are procured and managed unreasonably increasesthe burden of risk on the construction company and can impact the quality of the builtenvironment.Some of the thinking and modelling in RISKFLOW could be evolved to create a client toolwhich helps clients explore the pros and cons of a) different contract and procurement mod-els, b) contractor selection criteria, c) design and scope changes, etc for different projects(type, size, complexity, location, etc).Potential end-user : MBIE Construction Sector Accord construction sector capability de-velopment

Page 16

References

Chang-Richards, A., Smith, N. 2019. Building risk management strategies into the vertical con-struction sector. A preliminary report. Project LR10481, Building Research Levy 2018/2019.

Lyneis, J. M., Ford, D. N. 2007. System dynamics applied to project management: a survey,assessment, and directions for future research. System Dynamics Review: The Journal of theSystem Dynamics Society, 23(2-3), 157-189.

Maani, K. E., Cavana, R. Y. 2000. Systems Thinking and Modelling: Understanding Change andComplexity. Pearson Education.

Meadows, D., Robinson, J. M. 1985. The electronic oracle: computer models and social decisions.John Wiley & Sons.

Nasirzadeh, F., Afshar, A., Khanzadi, M., & Howick, S. 2008. Integrating system dynamicsand fuzzy logic modelling for construction risk management. Construction Management andEconomics, 26(11), 1197-1212.

PWC. 2016. Valuing the role of construction in the New Zealand economy: a report to the Con-struction Strategy Group.

Sapeciay, Z., Wilkinson, S., Costello, S. B. 2017. Building organisational resilience for the con-struction industry: New Zealand practitioners’ perspective. International Journal of DisasterResilience in the Built Environment, 8(1), 98–108.

Smith, N.J., McDonald, G.W. 2007. Ecological Footprints of New Zealand and its Regions 2003-04. Report prepared for Ministry for the Environment. Market Economics, Takapuna, Auck-land.

Smith, N.J., Zhang, Y., Cardwell, R., McDonald, G., Kim, J-H, Murray, C. 2015. Development ofa Social Accounting Framework for New Zealand. ERI Research Report 2015/01, GNS Science,Lower Hutt.

Page 17

A Index of names and

definitions

A.1 Subscripts and concordances

Most subscripts are described in Table 3.1 on page 12. However, the natural capital types, and industryand commodity groupings can vary between different model applications and are described here.

Table A.1 Descriptions of subscripts used in Model

Name Short Name Element Notation

Client types Client ct

Contract organisation ContOrg co

Contracting model ContractM cm

Experience Experience exp

Inputs Inputs inp

Project Project p

Response Response r

Sector Sector s

Table A.2 Client types

Name Description

Govt Government

DevK Developer-to-keep

DevS Developer-to-sell

Oneo Once or occasional clients

Table A.3 Contract Organisations

Name Description

ConOrg1 Contract Organisation 1




Page 18

Table A.3 (continued)

Name Description

... ...


Table A.4 Contracting Model

Name Description

BuildO Build only

DesignB Design-build

Integr Integrated

Table A.5 Experience categories

Name Description

UnExper Unexperienced

Experin Experienced

HighExp Highly experienced

Table A.6 Input categories

Name Description

Labour Labour

Materials Materials

Subcontractors Subcontractors

Table A.7 Projects

Name Description

Project1 Project 1

Project2 Project 2

Project3 Project 3

... ...

Project100 Project 100

Page 19

Table A.8 Response categories

Name Description

Sta�ng Staffing

Subcontracting Subcontracting

Overtime Overtime

WorkIntensity Work intensity

CostCutting Cost cutting

SlipScope Slip scope

PushWork Push work

Table A.9 Sector categories

Name Description

Horz Horizontal sector

V ert Vertical sector

A.2 Stocks

Table A.10 Description of stocks and equation references

Name Description Eq. ref

Budgetresponses,p,r Budget response index (B.1)

Cdelays,p Contractor delay (B.2)

Coststodates,p Costs to date (B.4)

Deadlineresponses,p,r Deadline response index (B.5)

Financialhealths,co Financial health index (B.6)

Hsdelays,p Health and safety delay (B.7)

Idelays,p Inspection delay (B.8)

Labours,co,exp Labour (B.9)

Mdelays,p Material delay (B.10)

Mgdelays,p Management delay (B.11)

Originalprojectvalues,p,co Original project value (B.12)

Originalworktodos,p Original work to do (B.13)

Perceivedexperiences,co Perceived experience (B.14)

Perceivedmistakess,co Perceived mistakes (B.15)


Page 20



Perclabutilisations,co Perceived labour utilisation (B.16)

Projectmorales,p.co Project morale (B.17)

Rddelays,p Rejected design delay (B.18)

Reworkdiscovereds,p Rework discovered (B.19)

Reworknewworktodos,p Rework and new work to do (B.20)

Riskmaturitys,co Risk maturity index (B.21)

Subcontractorreworktodos,p Sub-contractor rework to do (B.3)

Timetodates,p Time taken in project to date (B.22)

Totalcontpaidworks,p Total rework undertaken by subcontractor and paid by headcontractor to date

(B.23)

Totalcontreworks,p Total rework undertaken by subcontractor without remunera-tion to date

(B.24)

Undiscoveredreworks,p Undiscovered rework (B.25)

Wdelays,p Weather delay (B.26)

Workdones,p Work done (B.27)

Workforceenergys,p Workforceenergy index (B.28)

Table A.11 Initial condition settings for stocks

Name Notes

iBudgetresponses,p,r Set to 1 at t=0

iCdelays,p Set to 0 at t=0

iCoststodates,p Set to 0 at t=0

iDeadlineresponses,p,r Set to 1 at t=0

iIdelays,p Set to 0 at t=0

iF inancialhealths,co Set according to ratio of estimated margin per employee at t=0

iHsdelays,p Set to 0 at t=0

iLabours,co,exp Presently all organisations are allocated an equal share of the totalsector labour. In turn sector labour at t=0 is set according toinitial value of work up front multiplied by the average proportionof work value that is for labour and divided by a monthly wagerate

iMdelays,p Set to 0 at t=0

iMgdelays,p Set to 0 at t=0

iOriginalprojectvalues,co,exp Set to 0 at t=0

iOriginalworktodos,p Set to 0 at t=0


Page 21


Name Notes

iPerceivedexperiences,co Presently all organisations are allocated the same initial perceivedexperience index

iPerceivedmistakess,co Presently all organisations are allocated the same initial perceivedmistakes index

iPerclabutilisations,co Presently all organisations are allocated the same initial value of0.95

iProjectmorales,p,co Set to 0 at t=0

iRddelays,p Set to 0 at t=0

iReworkdiscovereds,p Set to 0 at t=0

iReworknewworktodos,p Set to 0 at t=0

iRiskmaturitys,co Presently all organisations are allocated a risk maturity index byrandomly selecting from a normal distribution of mean = 1 andstandard deviation = 0.167

iSubcontractorreworktodos,p Set to 0 at t=0

iT imetodates,p Set to 0 at t=0

iTotalcontpaidworks,p Set to 0 at t=0

iTotalcontreworks,p Set to 0 at t=0

iUndiscoveredreworks,p Set to 0 at t=0

iWdelays,p Set to 0 at t=0

iWorkdones,p Set to 0 at t=0

iWorkforceenergys,p Set to 1 at t=0

A.3 Flows

Table A.12 Description of flows and equation references


assignedreworks,p Rework assigned to responsibility of main contractor (B.29)

changebrindexs,p,r Change in budget response index (B.30)

changedrindexs,p,r Change in deadline response index (B.31)

chngperclabutils,co Change in perceived labour utilisation (B.90)

cins,p Inputs to contractor delays (B.32)

couts,p Outputs from contractor delays (B.34)

discoverys,p Discovery of rework (B.35)

expectationincreases,p Increase in project expectations/scope (B.36)


Page 22



experienceforgottens,co Forgetting/obsolescence of previous experience (B.37)

financialhealthhistorics,co Financial health becoming historic/obsolete (B.38)

financialhealthnews,co New inputs to financial health (B.39)

hirings,co,exp Hiring of new labour (B.40)

hsins,p Inputs to health and safety delays (B.41)

hsouts,p Outputs from health and safety delays (B.42)

iins,p Inputs to inspection delays (B.43)

increaseinfatigues,p Increase in project workforce fatigue (B.44)

iouts,p Outputs from inspection delays (B.45)

labexperienceins,co,exp Inputs to labour experience category (B.46)

labexperienceouts,co,exp Outputs from labour experience category (B.47)

leavings,co,exp Labour leaving organisation (B.48)

mgins,p Inputs to management delays (B.50)

mgouts,p Outputs from management delays (B.51)

mins,p Inputs to material delays (B.49)

moraleadjustments,p,co Adjustments to project morale (B.52)

moralemixins,p,co Inputs to project morale from within-organisation mix-ing

(B.53)

moralemixouts,p,co Outputs from project morale from within-organisationmixing

(B.54)

mouts,p Outputs from material delays (B.55)

newcontpaidworks,p New sub-contractor paid work (B.56)

newcontreworks,p New sub-contractor re-work (B.57)

newcostss,p Costs accrued (B.58)

newprojectvalues,p,co New project’s value (B.59)

newtimes,p New time taken on project (B.60)

newworks,p New project work (B.61)

paidreworks,p Rework for which head contractor will receive remuner-ation

(B.62)

problemsforgottens,co Problems in previous work forgotten (B.64)

progresss,p Progress on work (B.65)

projectrecords,co New record on projects (B.66)

pushedworks,p Rework pushed to the responsibility of subcontractors (B.63)

rdins,p Inputs to rejected design delays (B.67)

rdouts,p Outputs from rejected design delays (B.68)


Page 23



removings,co,exp Removing labour (B.69)

retirements,co,exp Labour retiring (B.70)

reworkprogresss,p Rework progress (B.71)

reworkwitherrorss,p Rework with errors (B.72)

shareprogresss,co New share of sector progress (B.73)

slippedworks,p Slipped work (B.74)

subcontractorreworks,p Contractor rework undertaken (B.33)

wins,p Inputs to weather delays (B.75)

workwitherrorss,p Work with errors (B.76)

wouts,p Outputs from weather delays (B.77)

A.4 Auxiliaries

Table A.13 Description of auxiliaries and equation references


agreedmargins,p Agreed project margin (B.78)

alphas,p Alpha parameter in the Beta distribution for errors (??)

applicablerdchances,p,ct,cm Applied rejected design chance (B.79)

assignedcontractors,p,co Assigned head contractor (B.80)

assignedcontractorhelds,p,co Assigned head contractor held over model run (B.81)

basemarginsps,p Base or default margin that applies to a given projectwithin a sector

(B.82)

basemarginspcms,p,ct,cm Base or default margin that applies to a given projectwithin a sector given the client and contracting model

(B.83)

basepushworkrts,p Default proportion of work that will be pushed ontosub-contractors

(??)

cdchances,p Chance of contractor delay (B.84)

cddurationselectors,p Duration of contractor delay (B.85)

cdelaymaxs,p Adjusted proportion of project impacted by contractordelay

(B.86)

cdproportionselectors,p Proportion of project work impacted by contractor delay (B.87)

cdselectors,p Randomly generated number that will determinewhether there is a contractor delay

(B.88)

chancebyclientcontracts,p,ct,cm Chance of project scope change for given client type andcontracting model

(B.89)


Page 24



clientacceptrateps,p,ct,cm Proportion of rework for which client accepts responsi-bility

(B.91)

clientselectors,p Randomly generated number used for selecting clienttype for each project

(B.92)

completiondates,p Identification of date work completed (B.93)

contractordelays,p Initialising contractor delay (B.94)

contractorselectors,p Randomly generated number used for selecting maincontractor for each project

(B.97)

contractselectors,p,ct Randomly generated number used for selecting contracttype for each project

(B.98)

costcuttingindexs,p Cost-cutting index (B.99)

costoverrunindex1s,p Cost overrun index (B.101)

costsremainings,p Expected costs remaining (B.102)

desiredbrindexs,p,r Desired budget response index (B.103)

desireddrindexs,p,r Desired deadline response (B.104)

delaytime Delay time (??)

easeofmovementcommunications,p Ease of movement and communication (B.105)

e↵ectbrindex s,p,r Effect on budget response index (B.106)

e↵ectdrindex s,p,r Effect on deadline response index (B.107)

e↵ortapplieds,p,inp Effort applied (B.108)

e↵ortcontingencyrates,p Contingency rate adjustment for effort applied (B.109)

errormodes,p Mode in Beta distribution of error rate (B.110)

errorrates,p Proportion of work progress containing errors (B.112)

estimatedtotalprojectcostss,p Estimated total project costs (B.113)

estimatedtotalprojectdurations,p Estimated total project duration (B.114)

expectedbudgetoverrunindexs,p Expected budget overrun index when using default sec-tor margin rate

(B.115)

expectede↵ortapplieds,p,inp Expected effort applied (B.116)

expectedmarginandconts,p,co Expected margin and contingency rate (B.117)

expectedmonthlycostss,p,inp Expected monthly costs (B.118)

expectedtimeoverrunindexs,p Expected time overrun index (B.119)

experienceops,p,co Overall experience of each head contractor if working ona project

(B.121)

experienceps,p Experience of head contractor applicable to project (B.120)

fhhorizontalco Financial health of horizontal organisations (B.122)

fhverticalco Financial health of vertical organisations (B.123)


Page 25



financialhealthscores,co Financial health score (B.124)

healthsafetydelays,p Initialising health and safety delay (B.125)

heldmargino↵ereds,p,co Margin offered held over model run (B.126)

heldreputations,p,co Reputation held over model run (B.127)

hsalphas,p Alpha parameter in Beta distribution of health andsafety delay chance

(B.128)

hsdelaychances,p Randomly generated number used to determine whetherthere is a health and safety delay

(B.129)

hsdelaymaxs,p Adjusted proportion of project impacted by health andsafety delay

(B.130)

hsdurationselectors,p Health and safety delay duration (B.131)

hsmodes,p Mode in Beta distribution determining chance of healthand safety delay

(B.132)

hsproportionselectors,p Proportion of project impacted by health and safety de-lay should it occur

(B.133)

hsselector Randomly generated number that will determinewhether there is a health and safety delay

(B.134)

idurationselectors,p Inspection delay duration (B.135)

inspectiondelays,p Initialising inspection delay (B.136)

inspectiondelaychances,p Chance of inspection delay (B.137)

iproportionselectors,p Proportion of project impacted by inspection delayshould it occur

(B.138)

iselector Randomly generated number that will determinewhether there is an inspection delay

(B.139)

knownworktodos,p Known work to do (B.140)

labourcostss,p Labour costs (B.141)

labourutilisationrts,co Organisation labour utilisation rate (B.142)

laggedcds,p Lagged contractor delay (B.143)

laggedhss,p Lagged health and safety delay (B.144)

laggedids,p Lagged inspection delay (B.145)

laggedknownworktodos,p Lagged known work to do (B.146)

laggedmds,p Lagged material delay (B.147)

laggedmgds,p Lagged management delay (B.148)

laggedprojectbyccmos,p,ct,cm,co Lagged project by client, contracting model and organ-isation

(B.149)

laggedrds,p Lagged rejected design delay (B.150)

laggedtotaldelays,p,inp Lagged total delay (B.151)


Page 26



laggedundisreworks,p Lagged undiscovered rework (B.152)

laggedweathers,p Lagged weather delay (B.153)

managementdelays,p Initialising management delay (B.154)

managementdelaychances,p Chance of management delay (B.155)

marginandcontperemployees,co Margin and contingency per employee (B.156)

margino↵ereds,p,ct,cm,co Margin offered (B.157)

margino↵eredccs,p,ct,cm,co Margin offered (set to zero for non-applicable clienttypes)

(B.158)

marginweightcs,p,ct Weight given to margins/price during procurement (setto zero for non-applicable client types)

(B.159)

materialcostss,p Material costs (B.160)

materialdelays,p Initialising material delay (B.161)

materialdelaychances,p Chance of material delay (B.162)

maxfinancialhealths Maximum financial health score for sector (??)

maxhsandms,p Proportion of project delayed by either health and safetyor material delays

(B.163)

maxiandmgs,p Proportion of project delayed by either inspection ormanagement delays

(B.164)

maxidelays,p Adjusted proportion of project impacted by inspectiondelay

(B.165)

maximgcs,p Proportion of project delayed by either contractor, in-spection or management delays

(B.166)

maxrdandws,p Proportion of project delayed by either rejected designor weather delays

(B.167)

maxrdwhsms,p Proportion of project delayed by either rejected design,weather, health and safety or material delays

(B.168)

maxvclients,ct Maximum of number range allocated to client (B.169)

maxvcontracts,ct,cm Maximum of number range allocated to a contractingmodel

(B.170)

maxvcontractors,p,co Maximum of number range allocated to head contract-ing organisation

(??)

mddurationselectors,p Material delay duration (??)

mdelaymaxs,p Adjusted proportion of project impacted by material de-lay

(??)

mdproportionselectors,p Proportion of project impacted by material delay shouldit occur

(??)

mdselectors,p Randomly generated number that will determinewhether there is a material delay

(??)


Page 27



meanfatigueexperiences,p Average of workforce experience and energy (??)

mgdelaymaxs,p Adjusted proportion of project impacted by manage-ment delay

(??)

mgdurationselectors,p Management delay duration (??)

mgproportionselectors,p Proportion of project impacted by management delayshould it occur

(??)

mgselectors,p Randomly generated number that will determinewhether there is a management delay

(??)

minvclients,ct Minimum of number range allocated to client (B.171)

minvcontracts,ct,cm Minimum of number range allocated to a contractingmodel

(B.172)

minvcontractors,p,co Minimum of number range allocated to a head contract-ing organisation

(B.173)

moraleimpactss,p,co Morale impacts (B.174)

neededlabours,co Needed labour (B.175)

newworkshares,p New work share (B.176)

newworkshocks,p,ct,cm,co Initialisation of new project work (B.177)

nondelayede↵orts,p,inp Project effort not accounting for any project delays (B.178)

nondelayedprogresss,p Project progress not accounting for any project delays (B.179)

nondelayedsta�ndex s,p Staff index not accounting for any project delays (B.180)

nondelayedsubcontractorindexs,p Sub-contractor index, not accounting for any projectdealys

(B.181)

organisationcompletionscores,co Organisations’ completion on time score (B.182)

organisationexperiences,co Organisations’ total experience (B.183)

organisationexperiencees,co,exp Organisations’ weighted experience (B.184)

organisationmorales,co Organisations’ morale (B.185)

organisationscores,p,co Organisations’ perceived score in project procurement (B.186)

organisationscore1s,p,co Organisations’ re-based score in project procurement (B.187)

overtimeindexs,p Overtime index (B.188)

overworkindexs,p Overwork index (B.189)

productivitys,p,inp Project productivity index (rate of progress given effortapplied)

(B.190)

progressbycontractors,p,co Head contractor project progress (B.191)

projectbyccmos,p,ct,cm,co Project by client, contracting model and contracting or-ganisation

(B.192)

projectcompletionscores,p,co Project completion on time score (B.193)


Page 28



projectdemandsbyclients,p,ct Project demands by client (excluding margins) (B.194)

projectdemandsexclmarginss,p Project demands excluding default margins (B.195)

projectsbyclientandcontracts,p,ct,cm Project demands by client and contracting model (ex-cluding margins)

(B.196)

pushedworkrates,p Proportion of rework pushed onto subcontractors (B.197)

ratiomaterialstoworks,p Ratio of material costs to work costs (B.198)

ratiounpaidtopaids,p Ratio of unpaid work to paid work for subcontractors (B.199)

rddurationselectors,p Rejected design delay duration (B.204)

rddelaymaxs,p Adjusted proportion of project impacted by rejected de-sign delay

(B.200)

rdproportionselectors,p Proportion of project impacted by rejected design delayshould it occur

(B.205)

rdselectors,p Randomly generated number that will determinewhether there is a rejected design delay

(B.206)

reallocatablesta↵ s,p,inp Staff that can be reallocated (B.207)

rejecteddesigns,p Initialising rejected design delay (B.208)

reputations,ct,co Reputation of a contracting organisation as perceivedby a client

(B.209)

reputationcs,p,ct,co Reputation of a contracting organisation as perceivedby a client for project procurement

(B.210)

reputationweightcs,p,ct Weight given to reputation in selecting among potentialhead contracting organisations, given project client

(B.211)

riskmaturityops,p,co Risk maturity applied to project management, given ap-plicable contracting organisation

(B.212)

riskmaturityps,p Overall risk maturity applied to project management (B.213)

scopechangeselectors,p Randomly generated number used to determine whetherthere will be a client-initiated change in project scope

(B.214)

scopeproportionselectors,p Randomly generated number used to determine scopechange proportion

(B.111)

selectedclients,p,ct Client responsible for project demand (B.215)

selectedcontracts,ct,p,cm Selected contracting model used for a project (B.216)

selectedcontractors,p,ct,co Head contracting organisation selected to undertakeproject

(B.217)

selectedmargincs,p,co Margins applied in contracting given selected head con-tractor

(B.219)

selectedmargino↵ereds,p,co Margins offered given project client and contractingmodel

(B.220)

selectedprojectmorales,p Project morale given head contracting organisation (B.221)


Page 29



selectedrdchances,p Chance of rejected design delay (B.222)

selectedreputations,p,co Perceived reputation of potential contractors, given theproject client

(B.223)

selectedscopechangechances,p Chance of client-initiated change in project scope (B.224)

sharelabours,co,exp Share of organisation’s labour that is in an experienceclass

(B.225)

slipscoperates,p Proportion of project rework that is avoided or slippedfrom project scope

(B.226)

sta�ndex s,p Staff effort index (B.227)

sta�ndexadjusteds,p Staff effort index adjusted for delays (B.228)

sta↵shares,p,co Share of organisation’s staff working on project (B.229)

subcontractorcostss,p Subcontractor costs (B.230)

subcontractorindexs,p Subcontractor effort index (B.231)

subcontractorindexadjusteds,p Subcontractor effort index adjusted for project delays (B.232)

subcontractorpressures,p Pressure on subcontractors (B.95)

subcontractorreworkprogresss,p Progress by subcontractors on rework (B.96)

surplusonprojectss,p,co Surplus on projects (B.233)

timeoverrunindex1s,p time overrun index (B.234)

totaldelays,p Total proportion of project impacted by delays of alltypes

(B.235)

totalorge↵orts,p,co Total organisation effort (B.236)

totalweightedmorales,co Total weighted morale (B.237)

utilisedlabouros,co Organisations’ utilised labour across all projects (B.238)

utilisedlabourpos,p,co Labour utilised in a project (B.239)

wdelaymaxs,p Adjusted proportion of project impacted by weather de-lay

(B.240)

wdurationselectors,p Weather delay duration (B.241)

weatherdelays,p Initialising weather delay (B.242)

weightedmorales,p,co Weighted morale (B.243)

weightedsta↵subcontractorindex s,p Weighted index of staff and subcontractors (B.244)

workintensityindexs, p Work intensity index (B.245)

wproportionselectors,p Proportion of project impacted by weather delay shouldit occur

(B.246)

wselectors,p Randomly generated number that will determinewhether there is a weather delay

(B.247)

Page 30

A.5 Exogenous inputs

Table A.14 Description of exogeneous constants

Name Description

AV ERAGELABOURCOSTs Average monthly labour costs per employee

Estimated from Statistics New Zealand’s Average HourlyEarnings by Industry for the Construction sector

AV GLEAV INGRATEs Average labour leaving rate

Set at 8 percent per annum as survey indicated 6-8 percent.

AV GMARGINCONTSHs Average margin and contingency share of project costs

Set at 11.5 percent for horizontal and 7.5 percent for verti-cal, derived from sector survey

BASEMARGINs,ct,cm Average margin and contingency added to project price,

given type of client and contracting model

Derived from expert elicitation of the adjustments thatwould be made within each sector to a base margin depend-ing on client and contract type and checking that overallsector average margins equate to those derived from thesector survey

BASEREJECTEDDESIGNCHANCEs,ct,cm Average or default chance of a rejected design delay per

project

Set at 1 for all client and contract types for the horizontalsector. Set at 1 for build-only and integrated contracts (allclient types) and 0.5 for design-build contracts (all clienttypes) for the vertical sector. Based on expert elicitation

BASESLIPSCOPERTs Proportion of discovered project errors that are pushed onto

clients

Derived from expert elicitation

BRCHPs,r Budget response change parameter

CDALPHAs Alpha parameter in beta distribution that determines dura-

tion of subcontractor delays

Set at 1.2 for both sectors, based on expert elicitation

CDBASECHANCEs Average or default chance of subcontractor delay per month

Set at 0.9 for horizontal and 0.063 for vertical, based onexpert elicitation

CDBETAs Beta parameter in Beta distribution that determines dura-

tion of subcontractor delays

Set at 40 for horizontal and 20 for vertical, based on expertelicitation

CLIENTACCEPTRATEct,cm Proportion of discovered rework for which client will accept

responsibility


Page 31


Name Description


CLIENTSHAREDEMANDSs,ct Share of project demands by client type

For horizontal 0.7 is allocated to government/public clients,0.15 to developers who keep and 0.15 to developers who on-sell. These shares were derived from expert elicitation. Forthe vertical sector 0.4 is allocated to government/publicclients and 0.2 shares are allocated to each of the remain-ing three client types. These shares were informed by in-spection of Figure 21 in https://www.pwc.co.nz/pdfs/CSG-PwC-Value-of-Construction-Sector-NZ.pdf

CONTTOLABRTs,inp Ratio of contractor costs to labour costs per unit of work

done

set to 1 for labour and materials and 0.75 for subcontractors- derived from expert elicitation results for vertical sector

CONTRACTSHAREDEMANDSs,ct,cm Share of client project demands allocated to contracting

model


CPALPHAs Alpha parameter in beta distribution that selects proportion

of project work impacted by contractor delay

Assumed to be 2 for both sectors

CPBETAs Beta parameter in beta distribution that selects proportion

of project work impacted by contractor delay


CWEIGHTs Weight given to movement/communication in productivity

function

Determined through expert elicitation

DESIREDLABUTILISATIONRATE Desired labour utilisation rate

Assumed to be 95 percent

DRWEIGHTs,r Weight given to deadline response index in determining in-

tensity of management response

Determined from expert elecitation

DRCHPs,r Deadline response change parameter

Assumed to be 3 for staffing and work intensity (both sec-tors) and 2 otherwise (both sectors)

EFORGETRATEs Years over which experience is forgotten

Set at 5 years for horizontal, 3 years for vertical based onexpert elicitation

ERRORBASEMODEs,cm Typical proportion of total work done that needs to be re-

worked

Determined from expert elicitation


Page 32


Name Description

EXPECTEDDURATIONs,p Expected duration of projects

A sample of 100 projects over the last 7 years was de-rived using the Pacifecon database, with adjustments forincreased frequency of projects in the earlier years of thedatabase as indicated by Statistics New Zealand’s buildingconsent data. The expected duration of each project wasderived by applying a rate of work completed by monthto the project value. We applied the same average rate asused by Pacificon, but this rate was randomly varied amongprojects based on a normal distribution

EXPECTEDINPUTSHs,inp Expected share of project costs allocated to input type


EWEIGHTs Weight given to workforce energy in productivity function


FHCONSTANTs Financial health constant in function that determines mar-

gin offered


FHPARAMETERs Financial health parameter in function that determines

margin offered


FLOWONFACTORs Rate at which rework causes additional rework

Assumed to be 0.2

HIRINGLAGs Lag between identifying needs for new labour and finding

new labour

Derived from expert elicitation of average times to fill eachexperience category and weighting by proportion of labourin each category. Just under one month for horizontal andless than 2 weeks for vertical.

HSBASEMODEs Default or base mode in Beta distribution function that de-

termines chance of health and safety delay

Assumed to be 0.9 for horizontal and 0.0042 for vertical,based on expert elicitation

HSBETAs Beta parameter in Beta distribution function that deter-

mines chance of health and safety delay

Set as 2 for horizontal and 10 for vertical, based on expertelicitation

HSDALPHAs Alpha parameter in Beta distribution function that deter-

mines duration of health and safety delays

Set as 3 for both sectors, based on expert elicitation

HSDBETAs Beta parameter in Beta distribution function that deter-

mines duration of health and safety delays


Page 33


Name Description

Set as 5 for both sectors, based on expert elicitation

HSDSHIFTs Shift parameter in function that determines duration of

health and safety delays

Set as 0.23 for both sectors, based on expert elicitation

IBASECHANCEs Default or base chance of inspection delay per month

Set as 0.9 for horizontal and 0.0066 for vertical, based onexpert elicitation

IDALPHAs Alpha parameter in Beta distribution function that deter-

mines the duration of inspection delays


IDBETAs Alpha parameter in Beta distribution function that deter-

mines the duration of inspection delays


IFINANCIALHEALTHs,co Initial financial health index

All organisations are allocated an average sector financialhealth index for t=0

ILABOURs,co,exp Initial labour

Total number of initial employees in each sector are esti-mated based on total value of all projects in first month,and assuming 95 percent of staff will be occupied by theseprojects. Employees in each sector are then allocated tocontracting organisations assuming all organisations withineach sector are the same size. Employees in each organisa-tion are then split among experience categories using theaverage industry proportions derived from expert elicitation

IPALPHAs Alpha parameter in Beta distribution function that deter-

mines the proportion of work impacted by inspection delays


IPBETAs Beta parameter in Beta distribution function that deter-

mines the proportion of work impacted by inspection delays


INTENSITY APPLYinp Scalar that determines whether an input type is impacted

by increased work intensity

By definition, set to 1 for labour inputs and 0 for otherinput types

IPERCLABUTILISATIONs,co Initial perceived labour utilisation

Set at 0.95 for all organisations

IPERCEIV EDEXPERIENCEs,co Initial perceived experience

All organisations allocated an average sector experience att=0


Page 34


Name Description

IPERCEIV EDMISTAKESs,co Initial perceived mistakes

All organisations allocated an average sector mistake his-tory at t=0

IRISKMATURITYs,co Initial risk maturity

Survey generally indicated a normal distribution. Risk ma-turity index for each organisation is randomly selected froma normal distribution (changes each simulation) with mean1 and standard deviation 0.167

LEAV INGPARAMETER Parameter in function that determines rate of employees

leaving

Set to 4

LEXPERIENCEWEIGHTexp Relative weight of an experience class in determining or-

ganisation experience

Derived so that weighted average labour experience in baseyear equals 1

LUCONSTANTs Labour utilisation constant in function that determines

margin offered


LUPARAMETERs Labour utilisation parameter in function that determines

margin offered


LABPROGRESSRATEexp Rate of progression of labour between experience classes

Set according to definitions of experience categories

MARGINWEIGHTs,ct Weight given to margins offered in awarding projects


MAXBRr Maximum deadline response index

Assumed to range between 1.3 and 5

MAXDRr Maximum deadline response index

Assumed to range between 1.3 and 5

MBASECHANGEs Base or default chance of material delays

Based on expert elicitation

MDALPHAs Alpha parameter in beta distribution function that deter-

mines duration of material delays


MDBETAs Beta parameter in beta distribution function that deter-

mines duration of material delays


MFORGETRATEs Years over which mistakes are forgotten


Page 35


Name Description

Set at five years for horizontal and three years for verticalbased on expert elicitation.

MGBASECHANCEs Base or default chance of management delays

Assumed to be 0.1 for both sectors

MGDALPHAs Alpha parameter in beta distribution function that deter-

mines duration of management delays


MGDBETAs Beta parameter in beta distribution function that deter-

mines duration of management delays


MGPALPHAs Alpha parameter in beta distribution function that deter-

mines proportion of work impacted by management delays


MGPBETAs Beta parameter in beta distribution function that deter-

mines proportion of work impacted by management delays


MISTAKESWEIGHTs Weight given to mistakes in evaluating an organisations’

experience


MPALPHAs Alpha parameter in beta distribution function that deter-

mines proportion of work impacted by material delays


MPBETAs Beta parameter in beta distribution function that deter-

mines proportion of work impacted by material delays


MWEIGHTs Weight given to morale in productivity function


NEV ERFIXEDREWORKRTs Share of errors that are never corrected

10 percent for vertical sector and 5 percent for horizontalsector. Shares were derived from expert elicitation

NEWLABSHs,exp Share of new labour hired that belongs to each experience

class

For horizontal sector unexperienced is 0.15, experienced0.35 and highly experienced 0.5. For vertical 0.6 is unexpe-rienced, 0.3 experienced and 0.1 highly experienced. Shareswere derived from expert elicitation

OECONSTANTs Organisation experience constant in function determining

margin offered



Page 36


Name Description

OEPARAMETERs Organisation experience parameter in function determining

margin offered


OV ERTIMEAPPLYinp Scalar that determines whether an input type is impacted

by increased overtime

By definition, set to 1 for labour inputs and 0 for otherinput types

PCSCALARs Scalar for workforce communication in productivity func-

tion


PCSHIFTs Shift parameter for workforce communication in productiv-

ity function


PESCALARs Scalar for workforce energy in productivity function


PESHIFTs Shift parameter for workforce energy in productivity func-

tion


PMSCALARs Scalar for workforce morale in productivity function


PMSHIFTs Shift parameter for workforce morale in productivity func-

tion


PROJECTDEMANDSs,p Value of projects demanded by all clients

A sample of 100 projects over the last 7 years was de-rived using the Pacifecon database, with adjustments forincreased frequency of projects in the earlier years of thedatabase as indicated by Statistics New Zealand’s buildingconsent database. All projects were also rebased to con-stant dollar terms (i.e. inflation costs removed)

PROJECTSTARTs,p Month of project work commencement

A sample of 100 projects over the last 7 years was de-rived using the Pacifecon database, with adjustments forincreased frequency of projects in the earlier years of thedatabase as indicated by building consent database.

PUSHWORKRTs Proportion of discovered rework that is pushed onto sub-

contractors


RDDALPHAs Alpha parameter in beta distribution function that deter-

mines duration of rejected design delays


Page 37


Name Description


RDDBETAs Beta parameter in beta distribution function that deter-

mines duration of rejected design delays


RDPALPHAs Alpha parameter in beta distribution function that deter-

mines proportion of work imapcted by rejected design delays


RDPBETAs Beta parameter in beta distribution function that deter-

mines proportion of work impacted by rejected design delays


REMOV INGLAG Time to adjust workforce down if in excess of demand

Set at 3 months based on results from expert elicitation forvertical sector

REPUTATIONWEIGHTs,ct Weight given to reputation in awarding projects


RETIREMENTRATEs,exp Proportion of labour that leaves organisation due to retire-

ment or leaving sector


RMPARAMETERs Parameter in function that adjusts typical error rate for

projects according to risk maturity


SCOPECHANGECHANCEs,ct,cm Chance of scope change per project

Assumed to be 1.2 for both sectors

SHAREMATERIALSSAV EDs Share of materials that can be saved and reused during re-

work

30 percent for the vertical sector and 0.05 percent for thehorizontal sector, based on expert elicitation

STAFFAPPLYinp Scalar that determines whether an input relates to staffing

By definition set to 1 for labour inputs and 0 for other inputtypes

SUBCONTRACTORAPPLYinp Scalar that determines whether an input relates to staffing

By definition set to 1 for subcontractors and 0 for otherinput types

TIMEIRRELEV ANT Time for historic financial health score to become irrelevant

Assumed to be 6 months

TIMETOREALLOCATELABOURs,inp Time to reallocate inputs to another project


Page 38


Name Description

Based on expert elicitation one week for labour in the hor-izontal sector and one month for labour in the vertical sec-tor. For sub-contractor inputs, a time of one week is as-sumed while for material inputs the time is zero

WDMEANs Mean in normal distribution function that determines du-

ration of weather delays

Set as 5 days for horizontal sector and one day for verticalsector, based on expert elicitation

WDSTDEVs Standard deviation in normal distribution function that de-

termines duration of weather delays

Set as 1.5 days for horizontal sector and 0.1 days for verticalsector

WEATHERDELAY CHANCEs Base or default chance of weather delays per month

Set at 1 for horizontal sector and zero for vertical sector,based on expert elicitation

WPALPHAs Alpha parameter in beta distribution function that deter-

mines proportion of work impacted by weather delays


WPBETAs Beta parameter in beta distribution function that deter-

mines proportion of work impacted by weather delays


A.6 Reporting module

Table A.15 Description of reporting module variables and equation references


completedcostss,p Rate at which total costs incurred by main contractingorganisation for undertaking project increases

(B.248)

completedprojects,p Rate of project completion (B.249)

completedworkdones,p Rate of work completion (B.250)

Comworkdones,p Total value of completed work (B.251)

Compprojectcostss,p Total costs incurred by main contracting organisationfor undertaking project

(B.252)

Compprojectvalueincmarginss,p Total value of completed project including margins (B.253)

cumulativeproductivityindexs Average productivity index over all projects (B.254)

delayvalueexclmarginss,p Value of project delays excluding margins (B.255)

heldmargino↵eredspos,p,co Margin offered for project (B.256)


Page 39



marginsreceiveds Actual margins received on all projects (B.257)

monthlyproductivityindexs Monthly productivity index (B.258)

newdelayss New delays (B.259)

newerrorss New errors (B.260)

newprojectcostss,p New project costs (B.4)

newprojectvalueincmarginss,p New project values including margins (B.261)

newworkdones,p New work done (B.262)

Projectcostss,p Project costs (B.263)

projectmarginss,p Project margins (B.264)

Projectvalueincmarginss,p Product value including margins (B.265)

subcontractorupaidtopaids Ratio of subcontractor unpaid to paid work (B.266)

Totaldelayss Total delays (B.267)

Totalerrorss Total errors (B.268)

Totalworkdones,p Total work done (B.269)

workdoneexclmarginss,p Work done excluding margins (B.270)

workerrorss,p Work with errors (B.271)

Page 40

B Model equations

B.1 Stocks

d

dt

�Budgetresponses,p,r

�= changebrindexs,p,r (B.1)

d

dt

�Cdelays,p

�= (cins,p � couts,p) (B.2)

d

dt(Contractorreworktodos,p) = (pushedworks,p � contractorreworks,p) (B.3)

d

dt(Coststodates,p) = newcostss,p (B.4)

d

dt

�Deadlineresponses,p,r

�= changedrindexs,p,r (B.5)

d

dt(Financialhealths,co) = (financialhealthnews,co � financialhealthhistorics,co) (B.6)

d

dt

�Hsdelays,p

�= (hsins,p � hsouts,p) (B.7)

d

dt

�Idelays,p

�= (iins,p � iouts,p) (B.8)

d

dt(Labours,p) = (labexperienceins,co,exp + hirings,co,exp � labexperienceouts,co,exp

� retirements,co,exp � leavings,co,exp � removings,co,exp) (B.9)

d

dt

�Mdelays,p

�= (mins,p �mouts,p) (B.10)

d

dt

�Mgdelays,p

�= (mgins,p �mgouts,p) (B.11)

d

dt

�Originalprojectvalues,p,co

�= newprojectvalues,p (B.12)

d

dt

�Originalworktodos,p

�= (newworks,p + paidreworks,p � progresss,p � workwitherrorss,p)

(B.13)

Page 41

d

dt

�Perceivedexperiences,co

�= (shareprogresss,co � experienceforgottens,co) (B.14)

d

dt(Perceivedmistakess,co) = (projectrecords,co � problemsforgottens,co) (B.15)

d

dt(Perclabutilisations,co) = chngperclabutils,co (B.16)

d

dt

�Projectmorales,p,co

�= (moraleadjustments,p,co +moralemixins,p,co �moralemixouts,p,co)

(B.17)

d

dt

�Rddelays,co

�= (rdins,p � rdouts,p) (B.18)

d

dt(Reworkdonediscovereds,p) = (discoverys,p � assignedreworks,p � slippedworks,p

� pushedworks,p � paidreworks,p) (B.19)

d

dt(Reworknewworktodos,p) = (assignedreworks,p + expectationincreases,p

� reworkwitherrorss,p � reworkprogresss,p) (B.20)

d

dt

�Riskmaturitys,p

�= 0 (B.21)

d

dt(Timetodates,p) = newtimes,p (B.22)

d

dt

�Totalcontpaidworks,p

�= newcontpaidworks,p (B.23)

d

dt(Totalcontreworks,p) = newcontreworks,p (B.24)

d

dt(Undiscoveredreworks,p) = (workwitherrorss,p + reworkwitherrorss,p � discoverys,p) (B.25)

d

dt

�Wdelays,co

�= (wins,p � wouts,p) (B.26)

d

dt(Workdones,p) = (progresss,p + reworkprogresss,p + contractorreworks,p) (B.27)

d

dt

�Workforceenergys,co

�= increaseinfatigues,p (B.28)

Page 42

B.2 Flows

assignedreworks,p = Reworkdiscovereds,p

✓1

TIMESTEP

◆[1� slipscoperates,p � pushedworkrates,p

�X

ct,cm

(clientacceptrateps,p,ct,cm)] (1 + FLOWONFACTORs) (B.29)

changebrindexs,p,r =(desiredbrindexs,p,r � Budgetresponses,p,r)

ADJUSTBRTIME(B.30)

changedrindexs,p,r =(desireddrindexs,p,r � Deadlineresponses,p,r)

ADJUSTDRTIME(B.31)

cins,p =contractordelays,pTIMESTEP

(B.32)

contractorreworks,p = contractorreworkprogresss,p (B.33)

couts,p =laggedcds,p

TIMESTEP(B.34)

discoverys,p = laggedundisreworks,p (B.35)

expectationincreases,p =8>>>>>>>>>><

>>>>>>>>>>:

errorproportionselector ⇥P

co Originalprojectvalues,p,co for scopechangeselectors,p

(EXPECTEDINPUTSHs,Labour

hselectedscopechangechances,pEXPECTEDDURATIONs,p

⇥ timestepi

+EXPECTEDINPUTSHs,Subcontractors & Originalworktodos,p � 1

⇥CONTTOLABRTs,Subcontractors)

0 otherwise(B.36)

experienceforgottens,co =Perceivedexperiences,co

EFORGETRATEs(B.37)

financialhealthhistorics,co =Financialhealths,co

TIMEIRRELEV ANT(B.38)

financialhealthnews,co = marginandcontperemployees,o (B.39)

hirings,co,exp = max✓neededlabours,coHIRINGLAGs

⇥NEWLABSHs,exp , 0

◆(B.40)

Page 43

hsins,p =healthsafetydelays,p

TIMESTEP(B.41)

hsouts,p =laggedhss,p

TIMESTEP(B.42)

iins,p =insepectiondelays,p

TIMESTEP(B.43)

increaseinfatigues,p =(overworkindexs,p � Workforceenergys,p)

TIMETOMAXFATIGUE(B.44)

iouts,p =laggedids,ptimestep

(B.45)

labexperienceins,co,UnExper = 0

labexperienceins,co,Experin = labexperienceouts,co,UnExpr

labexperienceins,co,HighExp = labexperienceouts,co,Experin (B.46)

labexperienceouts,co,exp = Labours,co,exp ⇥ LABPROGRESSRATEexp (B.47)

leavings,co,exp =

"AV GLEAV INGRATEs

✓1

organisationmorales,co

◆LEAV INGPARAMETER#⇥ Labours,co,exp

(B.48)

mins,p =materialdelays,pTIMESTEP

(B.49)

mgins,p =managementdelays,p

TIMESTEP(B.50)

mgouts,p =laggedmgds,pTIMESTEP

(B.51)

moraleadjustments,p,co =

8>><

>>:

assignedcontractorhelds,p,co

TIMESTEP for TIME = PROJECTSTARTs,p

⇣(moraleimpactss,p,co�Projectmorales,p,co)

TIMETOADJUSTMORALE

⌘otherwise

(B.52)

moralemixins,p,co = Projectmorales,p,co ⇥ STAFFMIXINGRATE ⇥ organisationmorales,co(B.53)

moralemixouts,p,co = Projectmorales,p,co ⇥ STAFFMIXINGRATE (B.54)

mouts,p =laggedmds,pTIMESTEP

(B.55)

Page 44

newcontpaidworks,p =

8<

:0 for knownworktodos,p 0

e↵ortapplieds,p,Subcontractors otherwise(B.56)

newcontreworks,p = pushedworks,p (B.57)

newcostss,p = labourcostss,p + subcontractorcostss,p +materialcostss,p (B.58)

newprojectvalues,p,co

=

8>>>>>>>>><

>>>>>>>>>:

Pct,cm

" (projectbyclientcontractandcontractors,p,ct,cm,co

� Originalprojectvalues,p,co)TIMESTEP

#for

Pct,cm(projectbyclientcontract

andcontractors,p,ct,cm,co)

> Originalprojectvalues,p,co0 otherwise

(B.59)

newtimes,p =

8<

:1 for knownworktodos,p > 0

0 otherwise(B.60)

newworks,p

=

hPct,cm,co(newworkshocks,p,ct,cm,co)EXPECTEDINPUTSHs,Labour +

Pct,cm,co(newworkshocks,p,ct,cm,co)

⇥ EXPECTEDINPUTSHs,Subcontractors ⇥ CONTTOLABRTs,Subcontractors

i

TIMESTEP(B.61)

paidreworks,p =

✓Reworkdiscovereds,p

TIMESTEP

◆ X

ct,cm

(clientacceptrateps,p,ct,cm) (B.62)

pushedworks,p =


TIMESTEP

◆pushedworkrate (B.63)

problemsforgottens,co =1

time+

(Perceivedmistakess,co � 1)

MFORGETRATEs(B.64)

progresss,p = newworkshares,p�e↵ortapplieds,p,Labour ⇥ productivitys,p,Labour

+e↵ortapplieds,p,Subcontractors ⇥ productivitys,p,Subcontractors

�

�workwitherrorss,p (B.65)

Page 45

projectrecords,co =organisationcompletionscores,co

TIMESTEP(B.66)

rdins,p =rejecteddesigns,p

TIMESTEP(B.67)

rdouts,p =laggedrds,p

TIMESTEP(B.68)

removings,co,exp =

8<

:0 for neededlabours,co � 0

�neededlabours,co ⇥ sharelabours,co,exp

REMOV INGLAG otherwise(B.69)

retirements,co,exp = Labours,co,exp ⇥RETIREMENTRATEs,exp (B.70)

reworkprogresss,p = (1� newworkshares,p)�e↵ortapplieds,p,Labour ⇥ productivitys,p,Labour

+ e↵ortapplieds,p,Subcontractors ⇥ productivitys,p,Subcontractors

�

�reworkwitherrorss,p (B.71)

reworkwitherrorss,p =�productivitys,p,Labour ⇥ e↵ortapplieds,p,Labour + productivitys,p,Subcontractors

⇥ e↵ortapplieds,p,Subcontractors

� �1� newworkshares,p

�⇥ errorrates,p (B.72)

shareprogresss,co =

Pp(progressbycontractors,p,co)P

p,co(progressbycontractors,p,co)(B.73)

slippedworks,p =


TIMESTEP

◆slipscoperates,p (B.74)

wins,p =weatherdelay

TIMESTEP(B.75)

workwitherrorss,p =�productivitys,p,Labour ⇥ e↵ortapplieds,p,Labour + productivitys,p,Subcontractors

⇥ e↵ortapplieds,p,Subcontractors

�newworkshare errorrates,p (B.76)

wouts,p =laggedweathers,pTIMESTEP

(B.77)

B.3 Auxiliaries

agreedmargins,p =X

co

(selectedmargincs,p,co) (B.78)

applicablerdchances,p,ct,cm = selectedcontracts,ct,p,cm ⇥BASEREJECTEDDESIGNCHANCEs,ct,cm

⇥ selectedclients,p,ct (B.79)

Page 46

assignedcontractors,p,co =

8<

:0 for

Pct,cm(projectbyclientcontractandcontractors,p,ct,cm,co) = 0

1 otherwise(B.80)

assignedcontractorhelds,p,co =

8>>><

>>>:

0 for TIME < PROJECTSTARTs,p

HISTORY (assignedcontractor,

PROJECTSTARTs,p) otherwise(B.81)

basemarginsps,p =X

ct,cm

basemarginspcms,p,ct,cm (B.82)

basemarginspcms,p,ct,cm = BASEMARGINs,ct,cm ⇥ selectedcontracts,ct,p,cm ⇥ selectedclients,p,ct(B.83)

cdchances,p = CDBASECHANCEs ⇥ [MAX(2, contractorpressures,p)]CDCHANCEPs (B.84)

cddurationselectors,p ⇠ Beta(CDALPHAs , CDBETAs)EXPECTEDDURATIONs,p (B.85)

cdelaymaxs,p =

8<

:1 for Cdelays,p > 1

Cdelays,p otherwise(B.86)

cdproportionselectors,p ⇠ Beta(CPALPHAs , CPBETAs) (B.87)

cdselectors,p ⇠ unif(0, 1) (B.88)

chancebyclientcontracts,p,ct,cm = SCOPECHANGECHANCEs,ct,cm ⇥ selectedclients,p,ct

⇥ selectedcontracts,ct,p,cm (B.89)

chngperclabutils,co =(labourutilisationrt� Perclabutilisations,co)

TIMEADJUSTPERC(B.90)

clientacceptrateps,p,ct,cm = CLIENTACCEPTRATEs,ct,cm ⇥ selectedcontracts,ct,p,cm ⇥ selectedclients,p,ct(B.91)

clientselectors,p ⇠ unif(0, 1) (B.92)

completiondates,p =

8>>><

>>>:

1 for laggedknownworktodos,p > 0

& knownworktodos,p = 0

0 otherwise

(B.93)

Page 47

contractordelays,p =

8><

>:

cdproportionselectors,p for cdselectors,p cdchances,p time & knownworktodos,p > 0.1

0 otherwise(B.94)

contractorpressures,p

=

8<

:1 for ratiounpaidtopaid < CONTCONTINGRT

e[5⇥(ratiounpaidtopaid�CONTCONTINGRT )] otherwise(B.95)

contractorreworkprogresss,p =

8>>><

>>>:

0 for Contractorreworktodos,p = 0

e↵ortapplieds,p,Subcontractors

⇥CONTREWORKPROGRESSRTs,p otherwise

(B.96)

contractorselectors,p ⇠ unif(0, 1) (B.97)

contractselectors,p,ct ⇠ unif(0, 1) (B.98)

costcuttingindexs,p = Deadlineresponses,p,Costcutting ⇥DRWEIGHTs,Costcutting

+ Budgetresponses,p,Costcutting

�1�DRWEIGHTs,Costcutting

�(B.99)

costcuttingpscalars,p =

8<

:1 for costcuttingindexs,p < 1

(costcuttingindex1s,p � 1)CSCALARs + 1 otherwise(B.100)

costoverrunindex1s,p =

8><

>:

1 forP

co(Originalprojectvalues,p,co) = 0estimatedtotalprojectcostss,p

Pco

�Originalprojectvalues,p,co

� otherwise

(B.101)

costsremainings,p =knownworktodos,p⇣

EXPECTEDINPUTSHs,Labour + EXPECTEDINPUTSHs,Subcontractors

⇥ CONTTOLABRTs,Subcontractors

⌘

(B.102)

desiredbrindexs,p,r =

8<


min(MAXBRr, Budgetresponses,p,r ⇥ e↵ectbrindexs,p.r ) otherwise(B.103)

desireddrindexs,p,r =

8<


min(MAXDRr, (Deadlineresponses,p,r ⇥ e↵ectdrindexs,p,r ) otherwise(B.104)

Page 48

easeofmovementcommunications,p

=

8<

:1 for weightedsta↵subcontractorindex < 1

1weightedsta↵subcontractorindex1.5 otherwise

(B.105)

e↵ectbrindex s,p,r = expectedbudgetoverrunindexBRCHP s,rs,p (B.106)

e↵ectdrindex s,p,r = expectedtimeoverrunindexDRCHP s,rs,p (B.107)

e↵ortapplieds,p,inp =expectede↵ortapplieds,p,Labour ⇥ sta�ndexadjusteds,p ⇥ STAFFAPPLYinp⇥overtimeindexs,p ⇥OV ERTIMEAPPLYinp⇥workintensityindexs,p ⇥ INTENSITY APPLYinp

+ expectede↵ortapplieds,p,Subcontractors⇥subcontractorindexadjusteds,p ⇥ SUBCONTRACTORAPPLYinp (B.108)

e↵ortcontingencyrates,p = 0.03�riskmaturityp3s,p

�(B.109)

errormodes,p =selectederrorbasemodes,p ⇥"

1

riskmaturitypRMPARAMETERss,p

#⇥

mean✓meanfatigueexperiences,p ,

1

workintensityindexs,p⇥ 0.5 + subcontractorpressures,p ⇥ 0.5

◆�2

⇥ easeofmovementcommunication�2s,p ⇥ costcuttingindex3

s,p (B.110)

errorproportionselectors,p ⇠ Beta(2, 20) (B.111)

errorrates,p ⇠ Beta(alpha, 20) (B.112)

estimatedtotalprojectcostss,p = Coststodates,p + costsremainings,p (B.113)

estimatedtotalprojectdurations,p = Timetodates,p +knownworktodos,p

nondelayedprogresss,p(B.114)

expectedbudgetoverrunindexs,p =

8>>>>>>>>>>>><

>>>>>>>>>>>>:

costoverrunindex1s,p for estimatedtotalprojectcostss,p

>P

co(Originalprojectvalues,p,co)

⇥(1 + basemarginsp)

costoverrunindex1 for estimatedtotalprojectcosts

<P

co(Originalprojectvalues,p,co)

1 otherwise(B.115)

expectede↵ortapplieds,p,inp =

✓ Pco Originalprojectvalues,p,co

[EXPECTEDDURATIONs,p(1� e↵ortcontingencyrates,p)]

◆

⇥ EXPECTEDINPUTSHs,inp ⇥ CONTTOLABRTs,inp (B.116)

Page 49

expectedmarginandconts,p,co =

8>>>>>><

>>>>>>:

selectedmargincs,p,co

⇥ Originalprojectvalues,p,co

EXPECTEDDURATIONs,pfor TIME PROJECTSTARTs,p

+EXPECTEDDURATIONs,p

0 otherwise(B.117)

expectedmonthlycostss,p,inp =

X

co

Originalprojectvalues,p,co

!EXPECTEDINPUTSHs,inp

EXPECTEDDURATIONs,p

(B.118)

expectedtimeoverrunindexs,p = timeoverrunindex1s,p (B.119)

experienceps,p =X

co

experienceops,p,co (B.120)

experienceops,p.co = organisationexperiences,co ⇥ assignedcontractorhelds,p,co (B.121)

fhhorizontalco = Financialhealthhorz,co (B.122)

fhverticalco = Financialhealthvert,co (B.123)

financialhealthscores,co =Financialhealths,co

maxfinancialhealths

(B.124)

healthsafetydelays,p =

8>>><

>>>:

hsproportionselectors,p for hsselectors,p hsdelaychances,p time

& (knownworktodos,p > 0.1)

0 otherwise(B.125)

heldmargino↵ereds,p,co = HISTORY (selectedmargino↵ereds,p,co TIME � delaytime) (B.126)

heldreputations,p,co = HISTORY (selectedreputations,p,co, T IME � delaytime) (B.127)

hsalphas,p =(HSBETAs ⇥ 2hsmodes,p + 1)

(1� hsmodes,p)(B.128)

hsdelaychances,p ⇠ Beta(hsalphas,p, 30) (B.129)

hsdelaymaxs,p =

8<

:1 for Hsdelays,p > 1

Hsdelays,p otherwise(B.130)

hsdurationselectors,p ⇠ Beta(HSDALPHAs, HSDBETAs)HSDSHIFTs (B.131)

Page 50

hsmodes,p = HSBASEMODEs

0.5

✓1

riskmaturityp

◆+ 0.5

✓1

workintensityindex

◆�4(B.132)

hsproportionselectors,p ⇠ Beta(20, 3) (B.133)

hsselectors,p ⇠ unif(0, 1) (B.134)

idurationselectors,p ⇠ Beta(IDALPHAs, IDBETAs) (B.135)

insepectiondelays,p =

8>>><

>>>:

iproportionselectors,p for iselectors,p inspectiondelaychances,p ⇥ time

& knownworktodos,p > 0.1

0 otherwise(B.136)

inspectiondelaychances,p = IBASECHANCEs ⇥1

riskmaturityps,p(B.137)

iproportionselectors,p ⇠ Beta(IPALPHAs, IPBETAs) (B.138)

iselectors,p ⇠ unif(0, 1) (B.139)

knownworktodos,p = Originalworktodos,p + Reworknewworktodos,p (B.140)

labourcostss,p = (sta�ndexs,p � reallocatablesta↵ s,p,Labour) overtimeindexs,p ⇥ expectedmonthlycostss,p,Labour

(B.141)

labourutilisationrts,co =utilisedlabouros,coPexp(Labours,co,exp)

(B.142)

laggedcds,p = DELAY (contractordelays,p, cddurationselectors,p) (B.143)

laggedhss,p = DELAY (healthsafetydelays,p , hsdurationselectors,p) (B.144)

laggedids,p = DELAY (inspectiondelays,p, idurationselectors,p) (B.145)

laggedknownworktodos,p = DELAY (knownworktodos,p, T IMESTEP ) (B.146)

laggedmds,p = DELAY (materialdelays,p,mddurationselectors,p) (B.147)

laggedmgds,p = DELAY (managementdelays,p, mgdurationselectors,p) (B.148)

laggedprojectbyclientcontractandcontractors,p,ct,cm,co = DELAY (projectbyclientcontractandcontractors,p,ct,cm,co, T IMESTEP )(B.149)

laggedrds,p = DELAY (rejecteddesigns,p, rddurationselectors,p) (B.150)

Page 51

laggedtotaldelays,p,inp = DELAY (totaldelays,p, T IMETOREALLOCATELABOURs,inp) (B.151)

laggedundisreworks,p =

8>>>>>><

>>>>>>:

0 for Undiscoveredreworks,p

NEV ERFIXEDREWORKRTs

reworkwitherrorss,p(t� 0.25) otherwise

+workwitherrorss,p(t� 0.25)

(B.152)

laggedweathers,p = DELAY (weatherdelays,p, wdurationselectors,p) (B.153)

managementdelays,p =

8>>>>>><

>>>>>>:

mgproportionselectors,p for mgselectors,p managementdelaychances,p ⇥ time


0 otherwise

(B.154)

managementdelaychances,p =MGBASECHANCEs


marginandcontperemployees,co =

Pp expectedmarginandconts,p,co +

Pp surplusonprojectss,p,coP

exp Labours,co,exp

!

(B.156)

margino↵ereds,p,ct,cm =BASEMARGINs,ct,cm

+ organisationexepriences,co ⇥OEPARAMETERs +OECONSTANTs

+ financialhealthscores,co ⇥ FHPARAMETERs + FHCONSTANTs

+ PercLabUtilisations,co +⇥LUPARAMETERs + LUCONSTANTs

(B.157)

margino↵eredccs,p,ct,cm,co = margino↵ereds,p,ct,cm,co ⇥ selectedclients,p,ct ⇥ selectedcontracts,ct,p,cm(B.158)

marginweightcs,p,ct =MARGINWEIGHTs,ct ⇥ selectedclients,p,ct (B.159)

materialcostss,p = ratiomaterialstoworks,p

"(progresss,p + workwitherrorss,p)

+ (reworkprogresss,p + reworkwitherrorss,p)(1� SHAREMATERIALSSAV EDs)

#(B.160)

materialdelays,p =

8>>><

>>>:

mdproportionselectors,p for mdselectors,p MBASECHANGEs time


0 otherwise(B.161)

Page 52

materialdelaychances,p = MBASECHANCEs ⇥1


maxhsandms,p = max(Hsdelays,p,Mdelays,p) (B.163)

maxiandmgs,p = max(Idelays,p, Mgdelays,p) (B.164)

maxidelays,p =

8<

:1 for Idelays,p > 1

Idelays,p otherwise(B.165)

maximgcs,p = max(Cdelays,p,maxiandmgs,p) (B.166)

maxrdandws,p = max(Rddelays,p,Wdelays,p) (B.167)

maxrdwhsms,p = max(maxrdandws,p,maxhsandms,p) (B.168)

maxvclients,ct = minvclients,ct + CLIENTSHAREDEMANDSs,ct (B.169)

maxvcontracts,ct,cm = minvcontracts,ct,cm + CONTRACTSHAREDEMANDSs,ct,cm (B.170)

minvclients,Govt = 0

minvclients,DevK = CLIENTSHAREDEMANDSs,Govt

minvclients,DevS = CLIENTSHAREDEMANDSs,Govt + CLIENTSHAREDEMANDSs,DevK

minvclients,Oneo = CLIENTSHAREDEMANDSs,Govt + CLIENTSHAREDEMANDSs,DevK

+ CLIENTSHAREDEMANDSs,DevS (B.171)

minvcontracts,ct,BuildO = 0

minvcontracts,ct,DesignB = CONTRACTSHAREDEMANDSs,ct,BuildO

minvcontracts,ct,Integr = CONTRACTSHAREDEMANDSs,ct,BuildO

+ CONTRACTSHAREDEMANDSs,ct,DesignB (B.172)

minvcontractors,p,1 = 0

minvcontractors,p,2 = organisationscore1s,p,1

minvcontractors,p,3 = organisationscore1s,p,1 + organisationscore1s,p,2

... (B.173)

moraleimpactss,p,co = overworkindexs,p ⇥ assignedcontractorhelds,p,co (B.174)

Page 53

neededlabours,co = utilisedlabouros,co �DESIREDLABUTILISATIONRT

X

exp

Labours,co,exp

!

(B.175)

newworkshares,p =Originalworktodos,p

(Originalworktodos,p + Reworknewworktodos,p)(B.176)

newworkshocks,p,ct,cm,co =8>>><

>>>:

projectbyclientcontractandcontractors,p,ct,cm,co for projectbyclientcontractandcontractors,p,ct,cm,co

> laggedprojectbyclientcontractandcontractors,p,ct,cm,co

0 otherwise(B.177)

nondelayede↵orts,p,inp =expectede↵ortapplieds,p,Labour ⇥ nondelayedsta�ndex s,p ⇥ STAFFAPPLYinp⇥overtimeindexs,p ⇥OV ERTIMEAPPLYinp⇥workintensityindexs,p ⇥ INTENSITY APPLYinp

+ expectede↵ortapplieds,p,Subcontractors⇥nondelayedsubcontractorindexs,p ⇥ SUBCONTRACTORAPPLYinp

(B.178)

nondelayedprogresss,p = (1� workwitherrorss,p)⇥ (nondelayede↵orts,p,Labour ⇥ productivitys,p,Labour

+ nondelayede↵orts,p,Subcontractors ⇥ productivitys,p,Subcontractors) (B.179)

nondelayedsta�ndex s,p = Deadlineresponses,p,Sta�ng (B.180)

nondelayedsubcontractorindexs,p = Deadlineresponses,p,Subcontracting (B.181)

organisationcompletionscores,co =

8<

:1 for

Pp assignedcontractorhelds,p,co = 0

Pp projectcompletionscores,p,coPp assignedcontractorhelds,p,co

otherwise(B.182)

organisationexperiences,co =X

exp

organisationexperiencees,co,exp (B.183)

organisationexperiencees,co,exp = LEXPERIENCEWEIGHTexp ⇥ sharelabour (B.184)

organisationmorales,co =

8<

:1 for totalweightedmorales,co = 0

totalweightedmorales,co otherwise(B.185)

organisationscores,p,co =heldreputations,p,co ⇥X

ct

reputationweightcs,p,ct

+

✓1

heldmargino↵ereds,p,co

◆X

co

marginweightcs,p,co (B.186)

Page 54

organisationscore1s,p,co =organisationscores,p,coPco organisationscores,p,co

(B.187)

overtimeindexs,p =Deadlineresponses,p,Overtime ⇥DRWEIGHTs,Overtime

+ Budgetresponses,p,Overtime(1�DRWEIGHTs,Overtime) (B.188)

overworkindexs,p =max

1 , 1�

overtimeindexs,p + workintensityindexs,p

2� 1

�3!(B.189)

productivitys,p,inp = costcuttingpscalars,p ⇥ STAFFAPPLYinp⇥[(easeofmovementcommunications,p ⇥ PCSCALARs + PCSHIFTs)CWEIGHTs

+ (Workforceenergys,p ⇥ PESCALARs + PESHIFTs)EWEIGHTs

+ (selectedprojectmorales,p ⇥ PMSCALARs + PMSHIFTs)MWEIGHTs]

+ costcuttingpscalars,p ⇥ SUBCONTRACTORAPPLYinp⇥[(easeofmovementcommunications,p ⇥ PCSCALARs + PCSHIFTs)CWEIGHTs

+ 1⇥ EWEIGHTs

+ 1⇥MWEIGHTs]

(B.190)

progressbycontractors,p,co = progresss,p ⇥ assignedcontractorhelds,p,co (B.191)

projectbyclientcontractandcontractors,p,ct,cm,co = projectsbyclientandcontracts,p,ct,cm ⇥ selectedcontractors,p,ct,co(B.192)

projectcompletionscores,p,co =8>>><

>>>:

0 for assignedcontractorhelds,p,co = 0

1 for completiondates,p = 0

1expectedtimeoverrunindexs,p

otherwise

(B.193)

projectdemandsbyclients,p,ct = projectdemandsexclmarginss,p ⇥ selectedclients,p,ct (B.194)

projectdemandsexclmarginss,p = PROJECTDEMANDSs,p (1�AV GMARGINCONTSHs)(B.195)

projectsbyclientandcontracts,p,ct,cm = projectdemandsbyclients,p,ct ⇥ selectedcontracts,ct,p,cm (B.196)

pushedworkrates,p =PUSHWORKRATEs

✓1

riskmaturityps,p

◆hDeadlineresponses,p,Pushwork ⇥DRWEIGHTs,Pushwork

+ Budgetresponses,p,Pushwork(1�DRWEIGHTs,Pushwork)i

(B.197)

ratiomaterialstoworks,p =

EXPECTEDINPUTSHs,Materials

EXPECTEDINPUTSHs,Labour + EXPECTEDINPUTSHs,Subcontractors ⇥ CONTTOLABRTs,Subcontractors

(B.198)

Page 55

ratiounpaidtopaids,p =Totalcontreworks,p

Totalcontpaidworks,p

(B.199)

rddelaymaxs,p =

8<

:1 for Rddelays,p > 1

Rddelays,p otherwise(B.200)

rddalphaselecteds,p =X

ct,cm

RDDALPHAs,ct,cm ⇥ selectedclients,p,ct ⇥ selectedcontracts,p,ct,cm

(B.201)

rddbetaaselecteds,p =X

ct,cm

RDDBETAs,ct,cm ⇥ selectedclients,p,ct ⇥ selectedcontracts,p,ct,cm (B.202)

rddscalarselecteds,p =X

ct,cm

RDDSCALARs,ct,cm ⇥ selectedclients,p,ct ⇥ selectedcontracts,p,ct,cm

(B.203)

rddurationselectors,p ⇠ Beta(rddalphaselecteds,p, rddbetaselecteds,p)EXPECTEDDURATIONs,p ⇥ rddscalarselecteds,p(B.204)

rdproportionselectors,p ⇠ Beta(RDPALPHAs, RDPBETAs) (B.205)

rdselectors,p ⇠ unif(0, 1) (B.206)

reallocatablesta↵ s,p,inp =

8<

:totaldelays,p for laggedtotaldelays,p > totaldelays,p

laggedtotaldelays,p otherwise(B.207)

rejecteddesigns,p =

8>>><

>>>:

rdproportionselectors,p for rdselectors,p selectedrdchances,pEXPECTEDDURATIONs,p

time

& (knownworktodos,p > 0.1)

0 otherwise(B.208)

reputations,ct,co =Perceivedexperiences,co ⇥OEXPERIENCEWEIGHTs

+ Perceivedmistakess,co ⇥MISTAKESWEIGHTs (B.209)

reputationcs,p,ct,co = reputations,ct,co ⇥ selectedclients,p,ct (B.210)

reputationweightcs,p,ct = selectedclients,p,ct ⇥REPUTATIONWEIGHTs,ct (B.211)

riskmaturityops,p = Riskmaturitys,co

8<

:0 for Originalprojectvalues,p,co < 0.1

1 otherwise(B.212)

Page 56

riskmaturityps,p =

8<

:0 for

Pco(riskmaturityops,p,co) = 0

Pco(riskmaturityops,p,co) otherwise

(B.213)

scopechangeselectors,p ⇠ unif(0, 1) (B.214)

selectedclients,p,ct =

8><

>:

1 for maxvclients,ct > clientselectors,p � minvclients,ct

0 otherwise(B.215)

selectedcontracts,p,cm =

8>>><

>>>:

1 for contractselectors,p,ct � minvcontracts,ct,cm

& contractselectors,p,ct < maxvcontracts,ct,cm

0 otherwise

(B.216)

selectedcontractors,p,ct,cm =

8>>><

>>>:

1 for contractorselectors,p � minvcontractors,p,co

& contractorselectors,p < maxvcontractors,p,co

0 otherwise

(B.217)

selectederrorbasemodes,p =X

ct,cm

(ERRORBASEMODEs,cm ⇥ selectedcontracts,ct,p,cm ⇥ selectedclients,p,ct)

(B.218)

selectedmargincs,p,co = selectedmargino↵ereds,p,co ⇥ assignedcontractorhelds,p,co (B.219)

selectedmargino↵ereds,p,co =X

ct,cm

(margino↵eredccs,p,ct,cm,co) (B.220)

selectedprojectmorales,p =X

co

(Projectmorales,p,co) (B.221)

selectedrdchances,p =X

ct,cm

(applicablerdchances,p,ct,cm)1


selectedreputations,p,co =X

ct

(reputationcs,p,ct,co) (B.223)

selectedscopechangechances,p =X

ct,cm

(chancebyclientcontracts,p,ct,cm) (B.224)

sharelabours,co,exp =Labours,co,expP

exp(Labours,co,exp)(B.225)

Page 57

slipscoperates,p =BASESLIPSCOPERTs

✓1

riskmaturityps,p

◆⇥

hDeadlineresponses,p,Slipscope ⇥DRWEIGHTs,Slipscope

+ Budgetresponses,p,Slipscope(1�DRWEIGHTs,Slipscope)i

(B.226)

sta�ndex s,p = Deadlineresponses,p,Sta�ng (B.227)

sta�ndexadjusteds,p = sta�ndexs,p(1� totaldelays,p) (B.228)

sta↵shares,p,co =totalorge↵orts,p,coPp(totalorge↵orts,p,co)

(B.229)

subcontractorcostss,p =�subcontractorindexs,p � reallocatablesta↵ s,p,Subcontractors

�⇥

expectedmonthlycostss,p,Subcontractors (B.230)

subcontractorindexs,p = Deadlineresponses,p,subcontracting (B.231)

subcontractorindexadjusteds,p = subcontractorindex(1� totaldelays,p) (B.232)

surplusonprojectss,p,co =

8>>>>>>>>>><

>>>>>>>>>>:

0 for knownworktodos,p 0

�newcostss,p ⇥ assignedcontractorhelds,p,co for TIME > PROJECTSTARTs,p

+EXPECTEDDURATIONs,p

hPinp expectedmonthlycostss,p,inp otherwise

� newcostss,piassignedcontractorhelds,p,co

(B.233)

timeoverrunindex1s,p =

8>>>>>><

>>>>>>:

estimatedtotalprojectdurations,p

EXPECTEDDURATIONs,pfor EXPECTEDDURATIONs,p <

estimatedtotalprojectdurations,p <

EXPECTEDDURATIONs,p(1� e↵ortcontingencyrates,p)

1 otherwise(B.234)

totaldelays,p = max(maximgcs,p,maxrdwhsms,p) (B.235)

totalorge↵orts,p,co = expectede↵ortapplieds,p,Labour ⇥ sta�ndexadjusteds,p ⇥ assignedcontractorhelds,p,co(B.236)

totalweightedmorales,co =X

p

(weightedmorales,p,co) (B.237)

utilisedlabouros,co =X

p

(utilisedlabourpos,p,co) (B.238)

Page 58

utilisedlabourpos,p,co =

✓expectedmonthlycostss,p,Labour ⇥ sta�ndex s,p

AV ERAGELABOURCOSTs

◆assignedcontractorheld

(B.239)

wdelaymaxs,p =

8<

:1 for Wdelays,p > 1

Wdelays,p otherwise(B.240)

wdurationselectors,p ⇠ N(WDMEANs, WDSTDEVs) (B.241)

weatherdelays,p =

8>>><

>>>:

wproportionselector for wselector WEATHERDELAY CHANCEs ⇥ time

& knownworktodo > 0.1

0 otherwise(B.242)

weightedmorales,p,co = Projectmorales,p,co ⇥ sta↵shares,p.co (B.243)

weightedsta↵subcontractorindex s,p = sta�ndexadjusteds,p⇥EXPECTEDINPUTSHs,Labour

(EXPECTEDINPUTSHs,Labour + EXPECTEDINPUTSHs,Subcontractors ⇥ CONTTOLABRTs,Subcontractors)

+ subcontractorindexadjusted⇥ EXPECTEDINPUTSHs,Subcontractors⇥CONTTOLABRTs,Subcontractors

(EXPECTEDINPUTSHs,Labour + EXPECTEDINPUTSHs,Subcontractors ⇥ CONTTOLABRTs,Subcontractors)(B.244)

workintensityindexs,p =Deadlineresponses,p,Workintensity ⇥DRWEIGHTs,Workintensity

+ Budgetresponses,p,Workintensity(1�DRWEIGHTs,Workintensity)(B.245)

wproportionselectors,p ⇠ Beta(WPAPLHAs, WPBETAs) (B.246)

wselectors,p ⇠ unif(0, 1) (B.247)

B.4 Reporting module

completedcostss,p =

8<

:

Prjectcostss,p

TIMESTEP for knownworktodos,p = 0

0 otherwise(B.248)

completedprojects,p =

8<

:

Projectvalueincmarginss,p

TIMESTEP for knownworktodos,p = 0

0 otherwise(B.249)

completedworkdones,p =

8<

:

Totalworkdonestime for knownworktodos,p = 0

0 otherwise(B.250)

Page 59

d

dt(Comworkdones,p) = completedworkdones,p (B.251)

d

dt

�Compprojectcostss,p

�= completedcostss,p (B.252)

d

dt

�Compprojectvalueincmarginss,p

�= completedprojects,p (B.253)

cumulativeproductivityindexs =

8<

:0 for

Pp(Compprojectcostss,p = 0)

Pp(Comworkdones,p)P

p(Compprojectcostss,p)otherwise

(B.254)

delayvalueexclmarginss,p = totaldelays,p ⇥X

co

(Originalprojectvalues,p,co) (B.255)

heldmargino↵eredspos,p,co = heldmargino↵ereds,p ⇥X

ct

(selectedcontractors,p,ct,co) (B.256)

marginsreceiveds =

8<

:0 for

Pp(Compprojectvalueincmarginss,p = 0)

1�P

p(Compprojectcostss,p)Pp(Compprojectvalueincmarginss,p)

otherwise(B.257)

monthlyproductivityindexs =

8<

:0 for

Pp(newcostss,p = 0)

Pp(workdoneexclmarginss,p)P

p(newcostss,p)otherwise

(B.258)

newdelayss =X

p

(delayvalueexclmarginss,p) (B.259)

newerrorss =X

p

(workerrorss,p) (B.260)

newprojectvalueincmarginss,p =X

ct,cm,co

(projectbyclientcontractandcontractors,p,ct,cm,co)

⇥h1 +

X

co

(heldmargino↵eredspos,p,co)i

(B.261)

newworkdones,p = workdoneexclmarginss,p (B.262)

d

dt

�Projectcostss,p

�= (newprojectcostss,p � completedcostss,p) (B.263)

Page 60

projectmarginss,p =

8<

:0 for Compprojectvalueincmarginss,p = 0

1�Compprojectcostss,p

Compprojectvalueincmarginss,potherwise

(B.264)

d

dt

�Projectvalueincmarginss,p

�= (newprojectvalueincmarginss,p � completedprojects,p) (B.265)

subcontractorunpaidtopaids =

8<

:0 for

Pp(Totalcontpaidworks,p) = 0

Pp(Totalcontreworks,p)P

p(Totalcontpaidworks,p)otherwise

(B.266)

d

dt(Totaldelayss) = newdelayss (B.267)

d

dt(Totalerrorss) = newerrorss (B.268)

d

dt(Totalworkdones) = (newworkdones,p � completedworkdones,p) (B.269)

workdoneexclmarginss,p =

(reworkprogresss,p + progresss,p)


workerrorss,p =

(workwitherrorss,p + reworkwitherrorss,p)


Page 61

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201012 RISKFLOW Technical Report - Resilient Organisations