Scheduling Using “Activity-Based Modeling”

Reggie Davidrajuh

Department of Electrical and Computer Engineering

University of Stavanger

Stavanger, Norway

reggie.davidrajuh@uis.no

Abstract— this paper presents an interesting approach known as

“activity-based modeling (ABM)” for scheduling activities or

operations in discrete-event based dynamic systems (DEDS). In

this paper, firstly, ABM is introduced. Secondly, a new tool is

known as GPenSIM is introduced; GPenSIM is developed for

modeling and simulation of DEDS using the activity-based

modeling approach; GPenSIM is based on Petri Nets. Thirdly,

through a case study, this paper shows the effectiveness of

activity-based modeling over the traditional “resource-based

modeling” approach. The usefulness and uniqueness of this paper

is the introduction of activity-based modeling and its application

on the development of GPenSIM, and also the “proof-of-concept”

- a scheduling example – is presented in the case study.

Keywords-Discrete Event Dynamic Systems (DEDS); Petri net;

Modeling and Simulation; Scheduling; activity-based modeling

(ABM); GPenSIM

I. INTRODUCTION

This paper presents an interesting approach for scheduling of activities or operations in discrete event dynamic systems (DEDS); the approach is known as “activity-based modeling (ABM)”. The alternative and traditional approach known as the “resource-based modeling” is the default approach for scheduling (and for general modeling and simulation) of DEDS; this is because, in a real-life DEDS environment, it is the resources (robots, machines, humans, computers, etc.) that are visible and tangible, whereas activities are generally intangible and sometimes invisible e.g. electronic activities. The resources are also the most expensive elements and the investors try to get their money back (return on investment - ROI) faster; thus, the goals of the approaches become optimal use of the resources rather than optimal execution of the activities.

In this paper: the next section (section-II) briefly introduces “activity-based modeling”. Section-III presents a brief introduction to “Petri nets” which is the basis for the new tool GPenSIM; GPenSIM is also briefly introduced in this section. Section-IV presents a case study as a proof-of-concept on the effectiveness of activity-based modeling over the traditional resource-based modeling approach.

II. ACTIVITY-BASED MODELING

Activity-based Modeling (ABM) is well known among the transportation and logistics modeling community. Outside this community - among the greater modeling and simulation community - ABM is an unknown phenomenon; it is the

“resource-based modeling” and “resource-based view” that is mostly used. This is because, in engineering environment, resources are expensive and the investors always think about getting a quick return-on-investment (ROI) they spent on the resources. In addition, humans are used to think “geometrically”, focusing mainly on the elements they see and taking into consideration of how these elements are connected together. Thus, resource-based modeling is the default approach for developing a model of a DEDS model.

A few literature studies that deal with “activity-based modeling” are on transportation and logistics area; e.g. Lawton (1997), Bowman and Ben-Akiva (2000), Wang and Cheng (2000), Witlox and Tindemans (2004); However, there are a few studies that uses activity-based modeling in production systems and manufacturing area: e.g. Tatsiopoulos and Panayiotou (2000), Spedding and Sun (1999).

III. SYSTEM SPECIFICATION OF SCHEDULING

Scheduling is a typical problem in DEDS and it is well researched. The core of the problem is the optimal allocation of systems resources so as to perform all the required activities. The optimal allocation of systems resources generally refers to minimization of costs and the time to complete the activities. Typical DEDS where scheduling take place often are the computer multitasking environment, flexible manufacturing systems, and of course, logistics.

The first step in solving a scheduling problem is to provide a system specification using a suitable tool, so that there will be no ambiguity about the problem. Literature review provides efficient specifications based on Petri nets (e.g. Hruz and Zhou, 2007); in this paper (section-III-B) a new system specification of scheduling problem is given, according to which GPenSIM is designed.

A. Place/Transition Petri nets

Ever since its inception in 1960s, Petri nets have been used

as a primary tool for modeling and simulation; this is because

of Petri net’s characteristics such as simple mathematical

model, visual (graphical) language, yet clear and simple

semantics [1]. P/T Petri net (aka Ordinary Petri net) is defined

as follows [1]: Definition 1.1: Petri net is defined by the quintuple:

PN = (P, T, A, W, M0)

Where:

2011 International Conference on Computer Applications and Industrial Electronics (ICCAIE 2011)

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• P is the set of places; places are passive elements like conveyor belts, input and output buffers, etc;

• T is the set of transitions; transitions are active elements like machines, humans, robots, CPUs, etc;

• A is the set of directed arcs; an arc connects either a place to transitions or a transition to places;

• W is the set of weights of the arcs, and

• M0 is the number of tokens initially in places.

P/T Petri nets have some limitations. One of the limitations is ‘homogenous’ tokens: let’s say that the tokens inside a place represent resources; then in P/T Petri nets, all these resources are of the same type and cannot be differentiated. Another limitation of P/T Petri net is that it is not possible impose additional logical functions (‘firing conditions’) for a transition to fulfill. Colored Petri nets (CPN) [5], or better - Petri net Interpreted for Control (PIC) [4] removes these limitations.

B. Petri Net Interpreted for Scheduling (PNS)

A new definition is given below for specifying scheduling

problems using Petri Nets.

Definition 1.2: A Petri net interpreted for Scheduling

consists of three parts:

PNS = (PN, SE, CE) Where,

• The first part PN defines the graph theoretic structure

– the ordinary Petri Net, defined by the definition 1.1,

consisting of a set of passive elements called places,

a set of active elements called transitions, a set of

bipartite arcs with arc weights connecting places and

transitions, and a set of initial markings;

• The second part SE is the extension for System

Resources; System resources will not appear in the

Petri Net model, as they are managed in background

by the system; SE consists of the following elements:

SE = (R, Ω, o, t, X, Y),

Where,

• R is the set of systems resources, R = R1,

R2,… , Rn

• Ω is the set of operations executable by all

the systems resources, Ω = ω1, ω2,…, ωm

• o is the partitioning of the operations into

subsets that can be executable by the

individual resources, o: R →2Ω

• t is the set of timing that are taken for

operations, t: R× Ω →N+

• X and Y are the set of input and output

servers that feed material into the resources

and remove worked parts from the

resources;

• The third part CE is the color extension; CE has

many functions such as overloading tokens with data

to differentiate one token from another, and mapping

transitions to logic functions;

CE = (C, ψ),

Where,

• C: M → c1, c2, … is a function mapping the set of

tokens onto a set of value assignments (colors) to

enable them carry W-I-P with them.

• ψ: T → LOG is the set of logical conditions for firing

(firing conditions), and for executing resource

manipulation commands such as request for resource,

resource usage, and release of resource after usage.

C. GPenSIM: A new tool for modeling and simulation of

DEDS

As a tool for modeling and simulation of DEDS, GPenSIM must provide robust support for resource usage, as resources are one of the primary elements of any DEDS. Since GPenSIM is based on Petri net, it was obvious to represent resources as tokens, as it was the widespread practice; however, it was found out the representing resources in the model (and thus giving explicit visibility to it – a resource-based modeling approach) produces bulky Petri net models. Alternatively (and untraditionally), GPenSIM also supports representing resources as variables in programming code (soft-coding, as opposed to hardwiring); by this approach (activity-based modeling), resources are not shown in the model and kept in the background and they are managed by the system. For this approach – giving visibility to activities and managing resources in background – a load of built-in functions must be provided for manipulating resources (request, usage, release, mutual-exclusion, semaphore, priority, accounting, etc.).

GPenSIM is developed by the author of this paper [3]. The reason for developing GPenSIM is two-folded:

• For basic users: to provide a tool that is easy to understand and easy to use, even for users with minimal mathematical and programming skills;

• For advanced users: allow seamless integration of models made with GPenSIM with the other toolboxes that are readily available on the MATLAB platform; allow easy extension of GPenSIM functions.

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IV. CASE STUDY

Figure 1 shows a Flexible Manufacturing Cell (FMC) facility at the Narvik Institute of Technology, Norway. The FMC facility consists of a Mori Seiki CNC Vertical Machining Center (VMC), a Mori Seiki CNC Horizontal Machining Center (HMC) and an ABB IRB2000 robot for moving parts from point-2-pint (ROBOT), a conveyor belt for input of raw materials (IN) and a conveyor belt for output of machined parts (OUT). Let us assume a much simplified set of operational specifications of the machining parts at the FMC facility:

1. To start a cycle, raw material must be available on the incoming conveyor belt, and the robot is also available

2. The robot moves a raw material from the conveyor belt and loads into VMC or HMC according to the machining program specification

3. When the machining is complete at a machining center (HMC or VMC), the robot unloads the work piece from the machine and either loads the piece into the other machine (HMC or VMC) if more machining is needed or put it on to the output conveyor belt if machining is complete

4. Both CNC machines provide just two types of operations; HMC can do chipping or grinding, whereas VMC can do drilling and boring.

Fig. 1: Flexible Manufacturing Cell at Narvik Institute of Technology, Norway

A. System Specification

With the descriptions given above, the scheduling system specification of the FMC can be put forward as follows:

R = HMC, VMC, ROBOT, X,Y

Ω = ΩHMC U ΩVMC U ΩROBOT

Where,

ΩHMC = Grind(ω1), Chip(ω2)

ΩVMC = Drill(ω3), Bore(ω4)

ΩROBOT = XH(ω5), XV(ω6), HV(ω7), VH(ω8), HY(ω9), VY(ω10).

Activities ΩHMC and ΩVMC are the main activities. Though activities ΩROBOT play auxiliary role, without these activities work pieces cannot be fed into the machines. For example, operation ω5 moves a work piece from input server X to HMC; operation ω7 moves a work piece from HMC to VMC; operation ω10 moves a work piece from VMC into output server Y.

Figure 2 shows the Petri net model of the FMC facility, obtained by resource-based modeling. The impression that we get from the model is that it resembles the physical set of the machine elements shown in figure 1; thus the Petri net model emphasizes the resources (machine elements) than the activities.

IN2HMC IN2VMC

HMC VMC

VMC2HMC

HMC2VMC

HMC2OUT VMC2OUT

pIN

pROBOT

pOUT

pVMC_AVpHMC_AV

Fig. 2: The Petri net model of the FMC obtained by “resource-based modeling”

Figure 3 shows the Petri net model obtained by the activity-based modeling. This model follows the operational specifications (activities) of the machining parts at the FMC facility. This model does not resemble the physical set of the machine elements as shown in figure 1.

Comparing the two Petri net models shown in figure 2 and 3, it is obvious that the model obtained by “activity-based modeling” is much simpler one. This is because, in resource-

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based v modeling, the machine elements (such as HMC, VMC, ROBOT) are to attributed with semaphores to highlight their nature of mutual exclusion (only one user at a time), and ROBOT in the center has to identified with number of instances (scaling) of it. In addition, the robot that takes the central position in the resource-based modeling is completely missing in the activity-based modeling, as the robot does not add value to the production – it merely helps the movement of materials between the machining elements.

In activity-based modeling, we emphasize activities only and the resources that are being used for the activities are being kept in background; resources, if available, are available from “the system” whenever they are needed; “mutual inclusion” property of the resources and the number of their instances are maintained by the system and not visible in the model. Owing to the simplicity of the activity-based modeling, the Petri model is much simplified: while the number of transactions remains the same (8 transactions) in both models, the number of places is reduced by 1 whereas the number of arcs goes down from 34 to just 14. It is must emphasized that the number of arcs is reduced by 58%, thus for a large example consisting of many machine elements, the simplification obtained by activity-based modeling will be decisive.

Fig. 3: The Petri net model of the FMC obtained by “activity-based modeling”

B. Representing Resource using GPenSIM

DEDS possess active elements such as machines, passive elements such as buffers, as well as resources. Resources (e.g. machine operators, work stations) limit utilization of systems, hence are the reasons for bottle necks in systems. In addition to resources, we need mechanisms to change the priorities (of the transitions) in order to avoid e.g. starvation and aging of competing entities [9].

As mentioned in the introduction, the scope of this paper is GPenSIM’s two approaches for representing resources in Petri net models:

1) Resource-based modeling: resources are represented as elements (e.g. as tokens) in the Petri net model; this means all the resources are ‘hard-wired’ into the Petri net model

2) Activity-based modeling: resources are not shown (not visible) in the Petri net model; they are programmed as variables in the program code (‘soft-coding’).

For the latter approach, GPenSIM provides the following functionality:

i) Declaring resources,

ii) Utilizing resources (functions for requesting (reserving), allocating, and releasing resources),

iii) Declaring Priorities of different transitions,

iv) Changing priorities of transitions: functions for increasing or decreasing priority of a transition, and comparing priorities of transitions, and

v) Reporting resource usage: new print functions that show total resource usage, idle time, etc.

The following fundamental assumption was made in realizing the additional functions for resource modeling:

A resource is a ‘critical section’ meaning a resource can be used by only one consumer at a time; this means, resources posses ‘mutual exclusion’ property.

(Though a resource can be used by only one consumer at a time, a consumer can use as many resource as it wants, limited only by availability).

V. CONCLUSION

This paper presents a new approach for modeling scheduling problems, namely activity-based modeling.

Figures 2 and 3 summarize the advantages and disadvantages of the two approaches. The activity-based modeling approach definitely reduces the model size of the

Petri net: if there are m numbers of activities and n numbers of resources, then the model by activity-based modeling

generally takes O(m) number of transitions, O(m) number of

places and O(m) number of arcs; resource-based modeling

generally takes O(m*n) number of transitions, O(m*n)

number of places and O(mn) number of arcs; Though reduction in the number of elements in a model itself is an advantage, there will be additional benefits due to the size reduction such as ease of programming, ease of extending the model, debugging the model, etc.

However, the model by resource-based modeling approach explicitly resembles the physical system (or rather the topology of connections between the elements in the physical system); this is a distinct advantage of using resource-based modeling approach. The model by activity-based modeling approach looks completely different from the actual physical system set-up.

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