O-Cubed Modeling and Simulator for Computational Organization Design

Computational & Mathematical Organization Theory 7, 155–176, 2001.c© 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.

O-Cubed Modeling and Simulator for ComputationalOrganization Design

KAZUNARI ISHIDAExcite Japan Co., Ltd., 20F Yebisu Garden Place Tower, 4-20-3, Ebisu, Shibuya-ku, Tokyo, 150-6020, Japanemail: [email protected]

TOSHIZUMI OHTAThe Graduate School of Information Systems, The University of Electro-Communications, 1-5-1 Choufushi,Choufugaoka, Tokyo 182-8585, Japanemail: [email protected]

Abstract

This paper discusses the development of O-cubed (operational organization oriented) modeling and a simulator forcomputational organization design. O-cubed modeling is used to describe an organization model in terms of modelsof coordination structures, tasks, and agents. The model of a coordination structure can represent not only taskdecomposition and allocation, but also choices between hierarchical management and autonomous management.The model of a task can represent the workflow within an organization. Using the O-cubed simulator, we can easilydescribe the models for coordination structure, tasks and agents, so that agents can make decisions concerningtask processing and choose coordination structures effectively. In order to show applicability of the modeling andsimulator, we describe an O-Cubed model of cooperation in a kitchen of a restaurant. The cooperation is goodexample to explain organization design, because it contains balanced elements of coordination structures, tasks,and agents. The example show that the organization models described by O-cubed modeling and the simulator arepromising models for designing organizations.

Keywords: coordination structure, task, agent, organization design, decision making, operational organizationmodel, simulator

1. Introduction

In this paper, we discuss the development of O-cubed (operational organization oriented)modeling and a simulator, which describes models of the coordination structure, tasks,and agents of an organization and incorporates organizational decision-making. We alsodiscuss which coordination structure is efficient for task processing, and when it works mosteffectively, by using an example (which employs O-cubed modeling and the simulator) ofcooperation among cooks in a restaurant kitchen.

Designing coordination structures is one of the major issues in organization design.The coordination structure defines how tasks are processed in an organization and howinteractions among agents who process the tasks are coordinated. Task decompositionand task assignment among the agents are central problems in coordination. In order to

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archive high performance of organization, we must determine how to decompose tasks oforganization into sub-tasks and how to assign the sub-tasks to agents.

Many researchers of organization design, employing mathematical and computationalmethods, have explored these problems by looking at coordination structures as structuresfor decomposing and allocating tasks among agents. For example, Malone (1987) definedfour typical coordination structures of hierarchical organization and market, and evaluatedthem based on individual decision-making. However, organization models such as Malone’s,when used for distributed artificial intelligence, do not seem to be sufficient for organizationdesign, because they do not describe organizational decision-making.

We developed O-cubed modeling, which incorporates organizational decision-making,and a simulator to describe a computational organization model for organization design.The O-cubed model is a model in which organizational decision-making processes areintegrated with individual decisions made by agents in the organization. Employing themodel, we can examine why the agents select certain coordination structure as alternativeorganization design.

In Section 2, we describe O-cubed modeling and the requirements of a computationalorganization model for organization design. In Section 3, we review computational organi-zation models with respect to O-cubed modeling. We also discuss O-cubed modeling andthe simulator, comparing them with the other approaches that are often used to describecomputational organization models. In Section 4, in order to show the simulator’s range ofavailability, we explain how to describe O-cubed model with the simulator, by modelingcooperation among cooks in the kitchen of a family restaurant. In Section 5, we discuss theresults of a simulation with O-cubed model. Section 6 concludes this paper.

2. Operational Organization Oriented Modeling for Organization Design

In order to design an organization computationally, we developed a framework for opera-tional organization oriented modeling in terms of coordination structure, task, and agent. Inthe framework, we introduce an organizational decision-making process that composes alldecision-making processes of agents in an organization, so that we can integrate the threeelements. With this O-cubed modeling, we can describe a practical organizational processfor task processing and evaluate alternative organization designs, based on organizationaldecision-making.

For effective task processing in an organization, an organization must be organized sothat its agents can process the tasks effectively by coordination. Coordination is definedas consistent cooperation among agents. To maintain this consistency, the agents mustmaintain consistency in their decisions. In order to maintain the decisions, the agents in-tegrate the decisions by the agents into consistent organizational decision, because theagents need organizational viewpoint to maintain consistency among the decisions. Co-ordination structures are important for maintaining consistency because the structuresdetermine the premises of decision-making, according to March and Simon (1958). There-fore, coordination structure, task, and agent are the primary elements for organizationdesign.

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Table 1. Required elements of O-cubed modeling for computational organization design.

Coordination structure Task Agent

Horizontal division of labor Task decomposition Individual decision making

Vertical division of labor Workflow among sub-tasks Organizational decision making

Distinction between humanresources and the others

2.1. Required Elements of O-Cubed Modeling for Computational Organization Design

In an O-cubed model, we use a coordination structure like an instance of the social situationdescribed in ACTS theory (Carley and Prietula, 1994). In this theory, an organization ismodeled in terms of agents, tasks, and social situations, and the organization is described asa collection of intelligent agents who are cognitively restricted, task oriented, and sociallysituated. The tasks and social situations constrain behavior by limiting opportunities foraction and setting limits on what the agent knows and does, and therefore, on what theagent can know (Carley and Prietula, 1994).

However, we use social situations as organizational alternatives to achieve high organi-zational efficiency. Because agents in an organization can effectively cooperate each other,when they can reduce harmful interactions among them due to constraint by their socialsituation. We define the organizational alternatives as coordination structures. Changing thecoordination structures is a way to improve organizational efficiency. Therefore, we modelcoordination structures, in order to compare them in terms of organizational efficiency.The model must provide how agents in the organization selects structural alternatives forefficient organizational task processing (Table 1).

2.2. Basic Concept of O-Cubed Simulator

We next explain the operational organization oriented (O-cubed) simulator for developingan O-cubed model. To develop a model for designing organizations, balance and integra-tion among coordination structures (CS), tasks, and agents are fundamental requirements,because determining effective combinations of theses three elements is to essential fororganization design.

To examine such combinations, we defined an organizational alternative space (OAS)based on the CS, task, and agent. In this space, the agents in an organization look for possibledecisions that are sufficient to process organizational tasks effectively. The complexity of thespace depends on the tasks the organization handles. This is consistent with Simon’s (1981)observation that the apparent complexity of human behavior results not from the mechanismof reasoning, but from the task environment. Figure 1 shows a framework for a complextask, whose workflow includes many dependencies among jobs and required resources forthe jobs. Complexity of tasks leads to complex organizational behaviors in OAS.

To describe the space in a simple form, we decompose it into elements called selections ofalternatives, in terms of the decision-making of agents. Figure 2 shows four typical selections

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Figure 1. Complex task.

Figure 2. Four typical selections of alternatives.

of alternatives. The selections of jobs and resources in figure 2(a) and (b), respectively, arebasic decisions made by agents for task processing.

The selection of either autonomous or hierarchical management, as shown in figure 2(c),is an important point for organization design, although other models do not deal with this.Selecting hierarchical management enables manager agents to select an arrangement ofjobs and assign them to other agents. By combining these selections of alternatives fordecision-making, as shown in figure 2(d), we can describe the complex organizationalbehaviors in OAS.


Figure 3. Procedure of Organization Design with O-Cubed Modeling & Simulator.

The O-cubed simulator provides an easy, simple, and seamless description of the agents’decision-making and the organization, because of an embedded mechanism that providesfor alternative creation, selection, and execution (ACSE). Based on our identification ofthe decision-making process, we implement ACSE according to the following steps. Thefirst step is to create possible alternative actions based on individual and organizationalstates. The second step is to select several of the alternatives according to individual ororganizational preferences. The last step is to execute the selected alternatives. By usingACSE, we can describe the O-cubed model easily and simply, because ACSE integrates thedescriptions of coordination structures, tasks, and agents into the O-cubed model.

2.3. Flow of O-Cubed Modeling with O-Cubed Simulator

Figure 3 shows our organization design procedure with O-cubed modeling, defined inSection 2.1, and the simulator explained in Section 2.2.

First, to design an organization, an organization designer identifies the organization interms of CS, tasks, and agents according to O-cubed modeling. Second, the designer de-scribes the organization with CS, task, and agent data structures in the organizational al-ternatives space of the O-cubed simulator. Third, employing the ACSE of the O-cubedsimulator, the designer describes seamless model regarding individual decision-makingand organizational decision-making. Fourth, the designer can explore organization designs.To illustrate how to use the O-cubed simulator for describing the O-cubed model, we explainan example of O-cubed modeling in Section 4.

3. Review of Computational Organization Models and Simulators

Many researchers have developed mathematical and computational organization modelsfor designing organizations operationally. In this section, we discuss relevant research

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concerning computational organization models, and we identify some problems as theyapply to O-cubed modeling for computational organization design.

3.1. Review of Computational Organization Models

Cammarata et al. (1983) developed an air traffic control system based on cooperative dis-tributed problem solving (CDPS). In their system, all planes make flight plans under severalconstraints for maintaining safe distances from other planes and minimizing fuel consump-tion. When plans conflict, one of the planes is selected to alter its plans to resolve the conflict,the system employs centralized planning and several strategies such as shared conventionstrategy, least spatially constrained strategy, and most-knowledgeable-least-commitmentstrategy so that all planes can make efficient flight plans.

The system may be available with respect to the planning capability of agent. However,a model which the system has is insufficient for designing organizations because of twoproblems in regarding O-cubed modeling. First, there is no task decomposition in the model,because the task of planes (agents) is the flight from a starting airport to a destination airport,and this task cannot be decomposed. Second, because there are no sub-tasks, there is noworkflow between them. Because of these two problems, the model is not sufficient fororganization design.

Malone (1987) developed a multi-agent model of coordination structures concerning hi-erarchical organization and market with a mathematical model based on queuing theory. Inthe model, four typical coordination structures are modeled: functional hierarchy, producthierarchy, centralized market, and decentralized market. He evaluated the four coordinationstructures in terms of three cost measures: coordination cost, production cost, and vulner-ability cost. Based on the evaluation, he concluded that a promising coordination structureis decentralized market so called electronic market, when coordination cost decrease dueto development of information technology.

The mathematical model of coordination structure in the model may be good for thefirst step of organization design. However, the model is insufficient for design organizationbecause of four problems regarding O-cubed modeling. First, description of vertical divisionof labor in the model is only hierarchical contract. Agents in the model do not process tasksautonomously; instead, they process tasks based on directives of manager agents. Second,the model does not include workflow, although it includes task decomposition. Third, there isno distinction between human resources and other resources. Fourth, agents in the model donot make plans to process tasks because of the queue model; rather, they process tasks in anad-hoc manner. Because of these four problems, the model is not sufficient for organizationdesign.

Abbas and O’Hare (1997) described cooperation among intelligent agents to deal withwarehouse tasks. The warehouse model consists of strategic agents, manager agents, stackagents, unstack agents, and vehicle agents along with hierarchical management. Theyemployed AGENT0 (Torrance, 1991; Shoham, 1993) to develop the model. AGENT0was developed as a test-bed to describe cooperation agents that have mental states basedon agent-oriented programming (AOP) (Shoham, 1990). Carley et al. (1992) also de-scribe cooperation concerning warehouse task. In the warehouse model, all agents have all


capabilities to complete tasks equally. The agents can horizontally communicate the otheragents to get necessary information for its’ task completion. In order to describe cognitivemechanism of agent, they developed Plural-Soar, based on Soar (Laird et al., 1987). TheSoar has a general cognitive architecture to solve problems by searching problem space. Themodels with cognitive capabilities of agents are suitable for explore effect on organizationalefficiency when the capabilities are easily changed.

However, the model is insufficient for designing an organization because of three prob-lems in terms of regarding O-cubed modeling. First, the models do not handle hierarchicalmanagement and horizontal relationship for autonomous management simultaneously; eventhough the two management styles are important alternatives that organization must be se-lect for organizational efficiency. Second, there is only simple workflow among sub-tasksbecause of the nature of warehouse tasks. Third, the description of organizational decision-making is insufficient, because each agent makes its decisions individually with AGENT0and Plural Soar. In the next section, we will discuss the problems with the previous simulator,contrasting with the O-cubed simulator, for O-cubed modeling.

3.2. Review of Simulators for Computational Organization Model

In this section, we discuss the availability of operational organization oriented (O-cubed)modeling and simulator for computational organization modeling. We compare the O-cubedsimulator with other simulators such as AGENT0 and Plural SOAR, which are based ondecentralized artificial intelligence (DAI). Based on O-cubed modeling, we discuss thesimulators with respect to four points. The first point is the focus of decision-making of thetools. The second point is tool’s feature. The third point is characteristic of description ofdecision-making with the tools. The fourth point is applicability of the tools for developingan operational organizational model.

The decision-making of the O-cubed simulator is focused on the organizational level,whereas that of the AGENT0 and Plural SOAR is focused on the individual level.

Features of the O-cubed simulator are the organizational alternative space (OAS), whichis composed of coordination structure, task, and agent and the mechanism of alternativecreation, selection, and execution (ACSE) in Section 2.2. Features of AGENT0 are theagent’s mental state, made up of belief, commitment, and conditional action statements,and commitment rules. Features of Plural SOAR are problem space architecture, whichconsists of initial, current, and goal states, and operators to operate the space.

Because of the O-cubed simulator’s focus and features, it provides seamless descriptionthe organizational decision-making and the individual decision-making, whereas AGENT0and Plural SOAR do not. Due to the description O-cubed simulator is suitable for O-cubedmodeling defined in Section 2.1. Table 2 shows the comparison among simulators.

3.3. Summary

To summarize the problems in this research, the agents in the models do not share orga-nizational decision-making, although they make decisions individually. Due to the lack oforganizational decision-making, the three elements do not seem to be well integrated.

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Table 2. Comparison among simulators concerning organization design.

Tool O-cubed simulator AGENT0 Plural SOAR

Focus of Organizational decision Individual decision-making (composing organizationaldecision making (including behavior)making individual decision

making)

Features Organizational alternative Mental state e.g. belief, Problem spaceof tool space e.g. coordination commitment architecture

structure & task e.g. initial state,goal state

Mechanism of creating, Conditional action statements, Operatorsselecting, and executing commitment rulesorganizational alternatives

Characteristics Seamless description between Patched and darned description between organizationalof description organizational decision decision making and individual decision makingof decision making and individualmaking decision making

Availability for Suitable for O-cubed modeling Unsuitable for O-cubed modeling due to hard to describedeveloping due to easy description of organizational decision making based on IndividualO-cubed model organizational decision making decision making

In developing a balanced and well-integrated organizational model, describing the or-ganizational decision-making process seems to be an essential function for planning orscheduling organizational behavior, as indicated in Section 2. Therefore, we developed anO-cubed simulator, as described in Section 2.2. In the next section, we will develop a bal-anced and well-integrated computational organization model based on our observations ofthe cooperation among cooks in a restaurant kitchen.

4. An Example of Development of O-Cubed Model

In this section, to show the applicability of the O-cubed model with O-cubed simulator,we describe an O-cubed model regarding cooperation among cooks in the kitchen of arestaurant. In the kitchen, cooks prepare customers’ orders by performing jobs in cookingplaces, such as at grills or ovens, which (to follow standard terminology in operationsmanagement) we call “shops” (figure 4).

We observed a typical restaurant called a “family restaurant” in Japan. In the kitchenof the restaurant, cooks prepare orders issued by customers, using cooking tools calledshops. Each order consists of several dishes called items. Each dish includes several typesof food. Cooking processes to make the food are standardized, and are described in amanual for the cooks to make the food. The primary goal of the cooks is to serve mealsordered by customers in the restaurant. In order to achieve the goal, cooks choose a coordi-nation structure dynamically and flexibly according to the number of orders issued by thecustomers.


Figure 4. Kitchen in a family restaurant.

The example of cooperation in the kitchen seems to be a good object for the computa-tional organization model, because the example contains balanced elements of coordinationstructures, tasks, and agents. The coordination structures consist of a horizontal divisionof labor and a vertical division of labor. The tasks have a distinction among cooks, shopsas cooking tools, and jobs as cooking processes. In addition, agents (cooks) change theircoordination structure for effective task processing to deal with tasks efficiently. Becauseof the balanced elements of coordination structures, tasks, and agents, the computationalorganization model provides a basic test-bed for business process re-engineering (BPR).

4.1. Observed Coordination Structures and Their Characteristics

We observed three different coordination structures among cooks in the restaurant. Basedon the point of view of horizontal division of labor and vertical division of labor, we callthe three coordination structures segmented CS, shared CS, and integrated CS.

In segmented CS (figure 5(a)), cooks divide shops (cooking tools) among them exclu-sively. Each cook specializes in a few types of cooking processes that the other agents donot handle. Each agent also makes his or her decisions autonomously. Because there is nooverlap in the use of shops by the agents, there is no conflict among the agents.

In shared CS (figure 5(b)), all agents share all shops. Each agent can handle any cookingprocess. Each agent makes his or her own decisions to process cooking tasks autonomously(in an ad-hoc manner). All cooking processes can be done by any agent, so shops are sharedamong the cooks. However, the possibility of conflict exists concerning the use of shopsand of the selection of cooking jobs among the cooks. Moreover, each agent must take moretime for decision-making than is needed for segmented CS, because he or she must payattention to all shops and cooking jobs.

In integrated CS (figure 5(c)), a manager cook specializes in managing other cooks. Themanager cook makes decisions concerning cooking processes and the other cooks carryout the processes. Because of the centralized decision-making by the manager cook, thereis no conflict among cooks. However, compared with the other coordination structures,organization with integrated CS loses a cooking agent. Moreover, the manager agent must

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Figure 5. Three types of coordination structure.

take more time for decision-making than the cooks in shared CS, because the agent mustgather information on all shops and cooking jobs, and must deal with combinatorial problemsamong cooking processes, cooking agents, and requisite shops.

We also observed changes in the processes from segmented CS to shared CS, and fromshared CS to integrated CS, as the number of tasks increased. The change seems to emergeso that the organization can continue to process organizational tasks effectively. To clarifywhy the change emerged, we describe CS, tasks, and an example program of agent’s ganttchart processing for task processing in the following sections.

4.2. Data Structure of O-Cubed Simulator and Modeling Coordination Structure

These coordination structures are easily described with the simulator. It employs a predicate-style data structure like prolog language because of the style’s flexibility for description.This style of data structure is well-suited to representing situations observed in the practicalworld, because all relational database systems employ the same style. When model buildersuse the simulator, they define the data structure as follows in order to make a table of thedata structure in the simulator’s database.

\def Prop(〈Atrb-1〉, 〈Atrb-2〉, .., 〈Atrb-I〉 , .., 〈Atrb-N〉)

When an instance of the data structure is made, the instance is stored and managed on thetable. The Prop is an identifier of a predicate or a name of the table. 〈Atrb-I〉 is an attribute inthe I-th slot in the predicate. The data structure in the predicate is stored on the simulator’sdatabase, which records the predicate declarations in a model program. The attribute cancontain three types of data, i.e., symbol, number, and list, like the prolog language.

Based on the data structure form and coordination structure definition for O-Cubed mod-eling from Table 1 in Section 2, three types of coordination structures, that are segmentedCS, shared CS, and integrated CS, can be described in terms of horizontal and verticaldivisions of labor. The horizontal division of labor is described as the availability of a shop,i.e., ShopAvailability (〈Shop〉, 〈Agent〉), where 〈Shop〉 is the name of a shop and 〈Agent〉is the name of an agent using that shop. The vertical division of labor is described as the


Figure 6. Matrixes of Resource Availability and Management Relations.

relationship between a manager and a cooking agent, i.e., ManagementRelation (〈Worker〉,〈Coordinator〉), where 〈Worker〉 is the name of a worker agent, and 〈Coordinator〉 is thename of the agent coordinating the worker agents.

Introducing a resource availability matrix and a management relation matrix (figure 6),we can represent the three types of coordination structures in terms of two aspects ofdivision of labor. In this figure, a circle in (A1,S1) indicates that agent-1 can use shop-1(ShopAvailability (Agnt-1, Shop-1)). A circle in (M1,W1) indicates that agent-1 manageshimself or herself (ManagementRelation (Agent-1, Agent-1)). A circle in (M2,W3) indicatesthat agent-2 manages agent-3 (ManagementRelation (Agent-3, Agent-2)).

Figure 7 describes the three types of coordinated structures with a resource availabil-ity matrix and a management relation matrix. For the segmented CS in (a), the resourceavailability (RA) matrix indicates that each agent uses his or her shops exclusively. Themanagement relations (MR) matrix shows the autonomous decision-making of agents asdiagonal elements. For the shared coordinated structure in (b), the RA matrix indicates thatall agents share all shops. The MR matrix shows autonomous decision-making of agents asdiagonal elements, which is similar to segmented CS.

For integrated CS in (c), the RA matrix indicates that all cooking agents can use all shopsexcept one, and that the manager agent uses only that one shop. The MR matrix shows thatthe manager agent manages the other agents.

4.3. Modeling Tasks

The tasks in a cooking process have basic characteristics in an actual organization. Thecharacteristics are distinction among jobs, machines for processing the jobs, and agents

Figure 7. Matrixes of Resource Availability and Management Relations.

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Figure 8. Menu and Cooking process.

who use the machines. Figure 8 shows an example of a menu and the cooking processesthat describe the tasks in a kitchen. The relationship between an order and an item representsthe relationship between a task and a sub-task. Jobs and the processing time chart representprocesses for completing the jobs. Shops represent machines for processing the jobs. Agentsuse the shops according to the coordination structure they choose.

The menu of a family restaurant includes several lunches. Each lunch consists of severaldishes. The lunch that a customer orders is defined as an “order”. The component dishes ofthe lunch are defined as “items”. The cooking process for making each dish is defined as a“job”. The relationship between the orders, items, and jobs is shown in figure 9.

Based on the relationships, data structures for orders, items, and jobs are respectivelydefined as OrderData (〈Order〉, 〈Item〉), ItemData (〈Item〉, 〈Job〉), JobData (〈Job〉, 〈Step〉,〈Time〉).

The menu and cooking processes in figure 8 can be described as shown in figure 10, basedon the relationships between orders, items, and jobs in figure 9. These predicate instancesare stored on a blackboard as a menu database.

Based on the definition of the data structure of the menu, slips of order, items, and jobs,which are issued according to the arrival of a customer’s order, are defined respectively

Figure 9. Relation among Order, Item, and Job.


Figure 10. Menu-Cooking process database.

as ORDER (〈Order〉, 〈Oidx〉, 〈TimeStamp〉), ITEM (〈Item〉, 〈Iidx〉, 〈Oidx〉, 〈TimeStamp〉),JOB (〈Job〉, 〈Jidx〉, 〈Shop〉, 〈Iidx〉, 〈TimeStamp〉, 〈Next〉, 〈Who〉).

4.4. Describing Scheduling Procedure in Terms of Organizational and AgentDecision-Making Processes

Depending on organizational conditions, agents may make decisions individually or orga-nizationally. The two types of decision-making processes must be described in the sameprogram, in order to develop a basic model enabling self-selection of coordination struc-ture. The O-Cubed simulator provides an ACSE rule template to describe organizationaland individual decision-making in the same manner. The template is presented by Ishida(1996) in detail.

The ACSE rule template creates all alternatives that satisfy the constraints of variablesin the template by referring to instances of the predicate on the simulator’s database thatare defined by a model builder. The variables play a key role in creating alternatives. Eachvariable is prefixed by “$”. The variable satisfaction is that all variables in the conditionpart of the rule template are consistently bound to attributes in instances of the predicate.

The template is similar to the production rule of a production system. However, the ruletemplate has a nest syntax that the production system does not have. This extension is a keyfactor for easy and simple description of an agent’s decision-making and the interactionsamong the agents.

The template shown in figure 11 consists of argument variables (ARGS), a loop controller(LC), a condition part (CP), a nested-condition part (NCP), an alternative selection controller(ASC), an operation part (OP), and a nested operation part (NOP).

The ARGS are variables of the template. The LC is a termination condition of the tem-plate. The function of the controller is similar to that of a while-loop in C language. TheCP consists of a combination of data structures for creating alternatives and restriction.The NCP in the CP works to restrict the creation of alternatives. The ASCE selects cer-tain alternatives among those created by the condition part. The OP works to execute the

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Figure 11. A rule template for ACSE mechanism.

alternatives selected by the ASC. In the NOP, some nested rule templates can be written fora nest structure in the program.

When an agent processes tasks, the jobs that compose the tasks must be scheduled wellto enable efficient task processing. The agent makes schedules for task processing by otheragents, using Gantt-chart processing. Figure 12 shows a program for Gantt-chart processing.The program makes the fastest schedule for processing tasks based on the coordinationstructure. The coordination structure is described by the predicates, ManagementRelationand ShopAvailability, defined in Section 4.2 for vertical and horizontal division of labor.

In the template, TIME (〈Time〉) represents the current time of the model, @set ($Var1,$Var2) is a function for binding an attribute bound by $Var2 to $Var1, JOB (〈Jidx〉, 〈Shop〉,〈Time〉) is a predicate of the job, as explained in Section 4.3, and {WHILE, COND (#equal($fg, NO))} is a loop controller. #equal ($fg, NO) is a comparison function. When a valuebound to $fg is NO, #equal returns true. Otherwise, the it returns false. The loop controller

Figure 12. An example of Gantt-chart processing for making schedules.


continues executing the template until the return value becomes false. For example, the loopcontroller indicates that the template is being applied while $fg is bound to NO. The symbol∧ negates statements enclosed by brackets. The comparison function #range ($Var1, $Var2,$Var3) returns true when a value bound to $Var2 is both greater than a value bound to $Var1and less than a value bound to $Var3. If a comparison function returns true, ACSE passesthe pattern matching of the template. Otherwise, ACSE fails it.

ACSE enables the rule templates to obtain the fastest time for each job, automati-cally checking all inconsistencies between previously confirmed schedules and temporaryschedules.

4.5. Summary

In this section, we discussed an example of cooperation among cooks in a restaurant kitchento show the applicability of the O-cubed simulator. The example of cooperation seems tobe a good object for the computational organization model due to example of balancedmodels of coordination structures, tasks, and agents. Employing the O-cubed simulator, wecan easily describe the example.

5. Running the O-Cubed Model with the O-Cubed Simulator

In this section, we explain the parameters of the O-cubed model, show the results of oursimulation, discuss the results, and clarify the logic of the model. We also discuss problemswith the O-cubed simulator.

5.1. Model Parameters

The model includes the five scheduling parameters listed in Table 3. They depend on thecoordination structure defined in Section 4.1. Search time is the time required to recognizejobs that are neither scheduled nor processed, as well as the availability of shops and agentsthat depend on the previous schedule and corodination structure. The search time requiredfor agents with a segmented CS is smaller than that for agents with a shared CS. This isbecause agents with a shared CS must recognize all shops, while agents with a segmentedCS only must recognize part of the shops. The search time required for agents with a sharedCS is in turn smaller than that for agents with an integrated CS, because a managementagent with an integrated CS must consider all kitchen conditions.

Maximum number of jobs to schedule at once is a parameter for an integrated CS. Dueto the lack of hierarchical management, agents with segmented and shared CSs pick upa job to schedule. Maximum number of job arrangements and scheduling time per jobare also parameters for an integrated CS, because agents with this CS must consider jobarrangements, while agents with the other CSs only pick up jobs.

Recognition ratio for others’ schedules is a parameter for a shared CS, because agentswith this CS may conflict with each other, but agents with other CSs do not have anyconflicts.

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Table 3. Parameters of the O-cubed model.

Search time 0.5 1.3 2.4

Maximum number of jobs to schedule at once 1 1 500

Maximum number of job arrangements 1 1 3

Scheduling time per job more than two none none 0.4

Recognition ratio for schedules of others none 0.8 none

In Table 3 the values for each cell are determined by our observations of the kitchendescribed in Section 4.1. Cells containing “none” indicate that the parameter has no effecton the CS due to the structural characteristics, as described in Section 4.1.

5.2. Results of Simulation with the O-Cubed Model

The relative efficiency of coordination structures is compared in terms of task processingtime, because this is an important concern for customer satisfaction. Figure 13 shows theresults of a simulation with the O-cubed model described in Section 4. The y-axis is therelative efficiency among the three coordination structures. The relative efficiency of eachcoordination structure is calculated as Ecs = (Tmin/Tcs) ∗ 100, where Tmin is the minimumtime among the average task processing times with coordination structures, and Tcs is theaverage task processing time with the coordination structure. The x-axis is the load, whichindicates how many orders appear in a simulation.

The figure explains why the observed changing process emerges (depending on thenumber of tasks), in terms of task processing time. The results show that the cooks weobserved seem to select the best way to change the coordination structure to effectivelyprocess tasks and quickly serve meals to customers. We can successfully explain theobserved changing process of coordinated structures cited in Section 4.1, based on thenumber of tasks and the average task processing time, using O-cubed modeling andsimulation.

Figure 13. Relative efficiency and load.


5.3. Identifying Characteristics of Coordination Structures

To enable discussion of the simulation results shown in figure 13, we illustrate the relativesensitivity of the increase in task processing time with load (figure 14). The sensitivity ofeach coordination structure Scs is defined as Scs = Tmax/D, where Tmax is the maximumvalue of the increase in task processing time, and D is the increase in load.

Based on figure 14, if the load is low (4–7), the sensitivity of a segmented CS to changesin load is low. However, if the load is moderate to high (7–34), the sensitivity is high. On theother hand, the sensitivities of a shared CS and an integrated CS are high when the load islow (4–7). However, if the load is moderate to high, the sensitivities are low. These resultsindicate that there is a lot of idle time among agents in a segmented CS when the load is notlow, due to the inflexible use of segmented resources that are shops in the segmented CS.

In comparing between a shared CS and an integrated CS when the load is low (7–13),the sensitivity of an integrated CS is higher. However, when the load is moderate to high(16–34) the sensitivity of a shared CS is higher, except in the range of 19–25. These resultsindicate that a shared CS suffers from increasing conflicts among agents when the load ishigh.

Figure 15 shows a comparison among CSs for the relative variance in task processingtime. The variance Vcs is calculated as follows: RVcs = Vcs/Vmax, where Vcs is the variancein task processing time for fifty simulations with a CS, and Vmax is the biggest variancevalue among them.

Figure 14. Relative sensitivity and load.

Figure 15. Relative variance and load.

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Figure 16. Logic of O-cubed model.

The results show that the variance for an integrated CS is lower than that of the otherCSs, due to its hierarchical management. However, if failures occur frequently, the variancemight tend to be high. The high variance for a segmented CS is due to inflexible use ofsegmented resources when the load is moderate to high. Conflicts between agents in a sharedCS result in a high variance for its task processing time.

Figure 16 summarizes the logic of the O-cubed model based on the results shown infigures 14 and 15. A segmented CS, shared CS, and integrated CS have negative effectdrivers for relative efficiency, such as idle time, conflict, and scheduling time, respectively.A segmented CS produces idle time due to inflexible use of segmented resources andautonomous management. A shared CS leads to conflicts among agents, since they shareresources and manage autonomously. An integrated CS consumes scheduling time becausea management agent must make decisions on task processing by other agents. Based onthe results from figures 14 and 15 and considering the negative effect drivers for relativeefficiency, an increase in load has a bigger effect on idle time than on conflict, and it has asmaller effect on scheduling time.

In the simulation, we did not model task-processing failures, due to the routine natureof tasks in the example of a kitchen in a family restaurant. If we consider an example that


includes non-routine tasks, we should model failures. This would lead to changes in orderamong the CSs regarding relative efficiency. The effect of failures on scheduling time maybe the largest among the negative effect drivers, due to the vulnerability of hierarchicalmanagement to uncertainty in cases of failure.

5.4. Effect of Search Time on CS Efficiency

Correcting information concerning unprocessed jobs, planned schedules, shop status, andagent status is a necessary activity for agents before scheduling or decision-making. Searchtime, as shown in Table 2, is a parameter that describes the time spent to correct informationin a certain CS. In the table, we set the values for search time based on the characteristicsof the CSs and on our observations.

In this section, to explore the effect of search time on the relative efficiency of the CSs,we assume that all CSs require the same search time to correct information for decision-making. Figure 17 shows a comparison among CSs when the load level is 4. The y-axis isthe relative efficiency, which is calculated in the same way as for figure 13. The x-axis isthe search time.

Based on these results, when the search time is 0.1, there is little difference among CSsin terms of relative efficiency, although a segmented CS is slightly more efficiency. Whenthe search time is 0.5 or 0.9, a shared CS is the most efficient of the CSs. When the searchtime is longer than 1.3, an integrated CS is the most efficient. This figure shows the sametendency as figure 13, i.e., when value along the x-axis increases, the most efficient CSchanges from segmented to shared, and then from shared to integrated.

Figure 18 shows the relative sensitivity to changes in search time. The sensitivity iscalculated in the same way as for figure 14. Based on these results, a segmented CS isalways the most sensitive of the CSs. An integrated CS has the lowest sensitivity, exceptfor changes in search time between 0.1 and 0.5. Figure 19 shows a comparison in terms ofabsolute variance. The increase in variance of processing time is largest for a segmentedCS. The variance for an integrated CS does not seem to be influenced by increases in searchtime.

Figure 17. Relative efficiency and search time.

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Figure 18. Relative sensitivity and search time.

Figure 19. Variance and search time.

5.5. Implications Derived from the Simulation Results

The results of the simulation show the important function of a coordinator in a rapidlychanging environment, because an Integrated CS can most successfully deal with the varioustypes of jobs in a high-loading environment, as shown in figure 13. For example, in processesof free software development, a coordinator has the important role of integrating the workof beta-testers in the software development community. The beta-testers do various types ofwork such as finding bugs in the software, fixing the bugs, and proposing ideas to improvethe software. Without a coordinator, free software development could not be successful dueto the lack of integration of all this work.

The autonomous behaviors of intelligent agents can be emphasized to explain the ef-ficiency of processes. The inefficiency of a segmented CS except at low loads seems toillustrate the disadvantages of bureaucracy or traditional software development. The effi-ciency of a shared CS relative to a segmented CS shows the advantage of flexible cooperationwithout central regulations. A shared CS may be an example of the CS that is used in freesoftware development. However, the processes do not work efficiently without a coordinatorin a high-loading environment.

The efficiency of an integrated CS for high loading shows that a central integration ofinformation leads to high performance when a central decision-maker with high compu-tation and communication ability can rapidly and completely integrate information. Anintegrated CS can work efficiently due to a coordinator’s expertise concerning softwaredevelopment.


5.6. Combinatorial Problems for an O-Cubed Simulator

Due to the features of the O-cubed simulator explained in Section 2.2, coordination struc-tures, tasks, and agents can easily be described in an organizational alternative space (OAS).The OAS is fully examined by the mechanism of alternative creation, selection, and execu-tion (ACSE).

However, implementing planning capability in organizational decision-making inherentlyleads to combinatorial problems among jobs, shops, and agents. When we examine allareas of the OAS, we suffer from an explosion of computation time and space. In theO-cubed model, we assume that human beings consider only several alternatives due totheir limitations in calculation capability. Based on this assumption, we can avoid theexplosion by simplifying the problems, as shown by the parameters concerning maximumnumber of jobs to schedule at once and maximum number of job arrangements in Table 3.As a result, the agent only has to consider several alternative schedules within the totalspace of schedules, as is the case in bounded rational situations.

5.7. Summary

We have discussed the simulation results for cooperation among cooks in a restaurantkitchen. Employing the O-cubed simulator, we can easily simulate this example andsuccessfully explain the observed changing process of coordinated structures cited inSection 4.1. This is based on the number of tasks and the average task processing time,using O-cubed modeling and simulation.

6. Conclusion

In this paper, we develop O-Cubed modeling and simulator in order to implement a balancedand integrated model of organizational decision-making in terms of coordination structure,task, and agent. The balanced model enables researchers to explore organization design,which had not been successfully done with models that were not balanced integrated well.

To show the applicability of O-cubed modeling and the simulator, we used it to describe acomputational organization model of the cooperation among cooks in a restaurant kitchen.The model and simulator showed the effects of changing the coordination structure, asobserved in an actual kitchen.

Using the O-cubed simulator, we were able to develop the computational organizationmodel easily. As shown by this example, the simulator can be an effective tool for developingcomputational organization models and for exploring organization design.

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Kazunari Ishida received the B. Eng. from the Toyohashi University of Technology in 1993, and the M. Eng.and D. Eng. from the University of Electro-Communications in 1995 and 1998, respectively. He is currently asoftware engineer of Excite Japan Co., Ltd. He has been working on development of application on the Internet.He also has continued working on an operational organization model, a computer simulation and a visualizationof concepts based on terminology.

Toshizumi Ohta received the B. Eng., M. Eng., and D. Eng from the Tokyo Institute of Technology in 1970, 1972,and 1977, respectively. He is currently a professor of the Graduate School of Information Systems, the Universityof Electro-Communications, Tokyo. He has been working for an organization theory and information systems forsociety. He recently initiated an encyclopedia of social informatics on the Internet as a cyber commons.

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O-Cubed Modeling and Simulator for Computational Organization Design