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CIFE

CENTER FOR INTEGRATED FACILITY ENGINEERING

Compensatory Negotiation for Agent-Based Project Schedule Coordination

By

Keesoo Kim Boyd C. Paulson, Jr. Charles J. Petrie, Jr. Victor R. Lesser

CIFE Working Paper #55 January, 2000

STANFORD UNIVERSITY

Copyright © 2000 by Center for Integrated Facility Engineering

If you would like to contact the authors, please write to: c/o CIFE, Civil and Environmental Engineering Dept., Stanford University Terman Engineering Center Mail Code: 4020 Stanford, CA 94305-4020

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Compensatory Negotiation for Agent-Based Project Schedule Coordination 1 Keesoo Kim

Boyd C. Paulson, Jr.

Dept. of Civil and Environmental Engineering Stanford Univ., Stanford, Calif., 94305, USA [email protected]

Dept. of Civil and Environmental Engineering Stanford Univ., Stanford, Calif., 94305, USA [email protected]

Charles J. Petrie, Jr.

Victor R. Lesser

Stanford Networking Research Center Stanford Univ., Stanford, Calif., 94305, USA [email protected]

Dept. of Computer and Information Science Univ. of Massachusetts, Amherst, Mass., 01003, USA [email protected]

Abstract Practitioners have tried to solve a project schedule coordination problem involving many subcontractors with a centralized approach, but failed to provide a cohesive solution. They have overlooked a principle that general contractors cannot coordinate subcontractors like they do their own forces. The project schedule coordination problem could be solved better by subcontractors in a distributed manner. This paper presents a formalized negotiation methodology for distributed project schedule coordination — a framework wherein a project can be rescheduled dynamically by all of the concerned project participants. The compensatory negotiation methodology is developed to allow agents to transfer utility to other agents for compensation of disadvantageous agreements through a multi-linked negotiation process. By employing software agents that are capable of compensatory negotiation, practitioners now can solve the problem and explore and exploit new opportunities an agent-based framework offers.

1. Introduction Despite the ubiquity of change in large, complex projects such as construction projects, current approaches to change coordination are mostly reactive, leading to less than optimal solutions. If, however, changes in a given schedule were coordinated prior to execution, then more optimal solutions could be explored. Many researchers have also explored causes of the changes. Discrepancies between the needed resources for tasks and the resources available to subcontractors are a major cause of change (O'Brien, 1995). The resource discrepancies occur when the timing of the tasks are not well matched with the available resources, i.e., when subcontractors have different schedule perspectives. These resource discrepancies are inevitable because there is no way to consider unknown subcontractors' available resources when the master project schedule is made. The resource model in our work is an abstract representation of a set of local resources (labor, material, equipment, etc) which subcontractors provide, not the global resource which general contractors provide. 1

The modified papers were submitted for the Fourth International Conference on Multiagent Systems (ICMAS-2000) and the Seventeenth National Conference on Artificial Intelligence (AAAI-2000).

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Soon after subcontracts made by the general contractor are awarded according to the master schedule, subcontractors are often motivated to change the master schedule because resource discrepancies cause additional costs either through relocating surplus resources or bringing in new resources. Therefore, it is easily predicted that the subcontractors may try to change the master schedule in order to accommodate their desires. Their motives for changing cause conflicts among subcontractors because any move affects the tasks of other subcontractors in tightly coupled project schedules. In most cases, these conflicts cannot easily be resolved simply by delaying the succeeding tasks since such delays would affect the resource profiles of succeeding subcontractors, which cause additional costs for the subcontractors. Task delays also could extend the project completion beyond the deadline. Therefore, there is a need to develop a coordination methodology for the subcontractors' resource-driven project schedule coordination process that ensures overall optimality.

2. Motivation and Points of Departure Subcontractors' resource-driven project schedule coordination is not an easy task for general contractors because consideration of each subcontractor's motives generally will be unknown by general contractors in cases involving many subcontractors in complex projects. Furthermore, general contractors have little incentive to accommodate the subcontractors' motives. This coordination dilemma in current project schedule coordination stems from a mismatch between traditional centralized coordination techniques in the industry and current construction practices employing more and more subcontracting. Subcontractors are self-interested and cannot be coordinated simply by orders from general contractors, a method that used to work when the general contractors self-performed all work. When the benefits of subcontractors’ resource-driven project schedule coordination flow to subcontractors, and when general contractors are not willing to coordinate the work of subcontractors, subcontractors need to work together with minimal information sharing. A new distributed coordination methodology that allows subcontractors to evaluate the impact of their changes and make appropriate decisions based on the evaluation is, therefore, needed. In order to develop a new distributed coordination methodology, we identified the following requirements: (1) all tasks have the needed resource requirements information; (2) all subcontractors maintain the available resource profiles at the task-level; (3) additional costs are quantified sufficiently to be acceptable by all subcontractors; (4) minimal dependency information is available about other subcontractors so that they can interact with other subcontractors; (5) subcontractors should have communication channels to express their schedule perspectives to others; and (6) a conflict-resolution strategy should be devised in case of conflicts. At first, we investigated whether the current distributed frameworks in construction and AI planning research can provide theoretical foundations for satisfying the above conditions. Current distributed frameworks (Koo, 1987; Khedro et al., 1993; Gomes et al., 1994; Jin and Levitt, 1993) didn’t provide a conflict resolution strategy based on a cost model, even though some of them provide various conflict resolution strategies for interactions between participants. ProcessLink (Petrie et al., 1998) identifies dependencies among tasks and participants but does

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not specify a conflict resolution strategy. We conclude that there is a need to develop a distributed coordination methodology that included a cost model and a conflict-resolution strategy based on the cost model. We then reviewed a number of distributed coordination methodologies in Cooperative Distributed Problem Solving (CDPS) and Multi-Agent Systems (MAS) research, but we found that the research also has shortcomings in applications for project schedule coordination. First, we found that none of the papers mentioned an explicit method for the transfer of utility units (“money”) among software agents for compensation of disadvantageous agreements. Allowing the transfer of utility is very important for construction project schedule coordination. When a subcontractor wants to reschedule his/her tasks, the rescheduling has external effects on succeeding subcontractors’ resource profiles, causing external costs (Feldman, 1980) for the affected subcontractors. This is not to say that all of the external costs are negative. Some of them are positive. In case of negative external costs, the external effects destroy the Pareto optimality (Feldman, 1980) in a construction master schedule. By allowing the transfer of utility to compensate for the external costs, we reestablish the better Pareto optimality. Consequently, a new solution is “Pareto superior” (Feldman, 1980, p. 140) to the original master schedule. We will get a globally optimal schedule if all alternatives are considered. We assert that allowing the transfer of utility units for compensation would lead to individually rational and globally optimal solutions in CDPS and MAS systems. In other words, agents try to maximize their utilities while compensating other agents, which are forced to make disadvantageous agreements. Consequently, the agents find a globally optimal solution without making some other agents worse. This globally optimal solution will increase the social welfare and this social welfare will be distributed directly to agents. Many implicit mechanisms of the transfer of utility were proposed in a number of CDPS and MAS papers. However, the explicit and direct mechanism of the transfer of utility proposed in this paper is more efficient than using incentives or reward mechanisms we may find in some market-based systems (Malone, et al, 1988; Wellman, 1993; Shoham and Tanaka, 1997). Clarke tax voting mechanism (Ephrati and Rosenschein, 1996) collects taxes centrally, but provides no way to distribute the collected taxes. Unified negotiation protocol (Rosenschein and Zlotkin, 1994) does not provide an explicit way of transferring utilities, so it uses an implicit way – working together after flipping a coin. We also argue that the transfer of utility for compensation is different from payment via contracts used in many MAS research (Sandholm, 1993; Sen and Durfee, 1996), in which any profit-seeking bid from agents might prevent a system from reaching a globally optimal solution. Compromise via negotiation (Sycara, 1989) provides a way of transferring utilities between agents through a central mediator, but it is implicit and not for compensation of disadvantageous agreements. Distributed constraint satisfaction (Yokoo et al., 1992, 1998) and distributed search (Durfee and Montgomery, 1991; Sycara, et al., 1991) find a satisfactory solution that produces no disadvantageous agreement for any agent.

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Another finding is that most CDPS and MAS applications employ pair-wise negotiation mechanisms that would be unsuitable for coordinating the tightly coupled project schedules. Therefore, we are trying to extend the current CDPS and MAS research to produce a globally optimal solution by allowing the transfer of utility for compensation of disadvantageous agreements and by developing a negotiation protocol suitable for coordinating the tightly coupled construction schedules; we will then use it to solve the current coordination dilemmas in the construction industry. Before discussing the extensions of the current CDPS and MAS research, we would like to introduce a new project schedule coordination domain on CDPS and MAS in the next section.

3. Project Schedule Coordination on CDPS and MAS In project organization, agents can reallocate their initially assigned resources whenever timing of the tasks is undesirable, which means that there are resource discrepancies between resource requirements and resource availability. However, this resource reallocation causes transaction costs. When they try to change the timing of their tasks instead, the changes cause external costs to succeeding agents. Therefore, agents have to evaluate the transaction costs associated with the reallocation of their resources and the external costs for changing the timing of tasks and then they make decisions. The project schedule coordination systems are new problem domains that CDPS and MAS research does not exploit. Since they still have their tasks, there will be no task allocation or reallocation problem. Since resources are already assigned to tasks, there will be no resource allocation problem. The problem they are trying to solve is rescheduling tasks through the project schedule coordination processes. In the new problem domains, tasks are different in quantities and costs so that transaction costs of resource reallocation and external costs of changed timing are greatly varied with tasks. Therefore, without an explicit method for transferring utility units (“money”), they cannot find fair deals with other agents. Imagine that a subcontractor needs to pay one million dollars to meet his/her schedule and it cost only ten thousand dollars for delaying succeeding tasks. He/she is willing to pay ten thousand dollars for the delay. This is an extreme case, but it shows how an agent transfers utility to other agents for compensation of disadvantageous agreements. Also, such potential great disparities between overall costs made the split option (Sandholm, 1993) and a coin tossing (Rosenschein and Zlotkin, 1994) not appropriate in this application. The problem of finding external costs in a distributed manner is also a major challenge when the number of tasks is huge. For example, a typical building project has several thousand tasks to be rescheduled. Furthermore, the tasks are tightly linked. It is easily assumed that no agent has complete knowledge of the whole schedule and that it is not feasible to send private information, such as resource and cost information, to one selected agent. The pair-wise negotiation process used in CDPS and MAS cannot find an external cost easily because agents need to ask other agents before making a counteroffer to the agent because agents do not know the consequences of their decision until getting the responses. Therefore, we need a multi-linked negotiation process where agents receive responses before making decisions.

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To summarize, a novel coordination methodology should be developed to allow agents to transfer utility to other agents for compensation of disadvantageous agreements through a multilinked negotiation process — a compensatory negotiation.

4. Compensatory Negotiation Methodology In this section, we formalize the utility function which agents have, the multi-linked negotiation protocol by which agents interact with other agents, and the monetary compensation strategy that agents use for evaluating and making decisions.

4.1 Utility Function A utility function produces utility units with which an agent evaluates and makes a decision. A utility is represented as a real valued number (“money”) which describes a difference between the benefits and costs of alternatives for the agent. The utility is common for all agents and is transferred between them for compensation. In our research, we quantify the utility based on resource utilization. The reasonable assumption about resource utilization is that resource discrepancy between the resource requirements and available resources causes additional costs of either relocating surplus resources or bringing in new resources. Ironically, the additional costs usually were reflected in the subcontract prices, so the additional costs serve as opportunities to find a better solution and reducing the additional costs can be regarded as benefits for the agents. If the benefit is more than the cost, the option is good. Utility = Benefit – Cost

(Equation 1)

Benefit = profit gain for the task from a possible option = {(RR – RA) – (RC– RB)} x K x A Cost

(Equation 2)

= cost incurred for succeeding tasks due to the possible option =

n −1

∑ COSTi i =1

= 0, if n = 2 n −2

= {(RC − RB ) − (RR − RA )}× K × A + ∑ COSTi

(Equation 3)

i =1

where RR is the resource requirements for a task in a given time; RC is the changed resource requirements for a task in a given time; RA is the available resources for RR; RB is the available resources for RC; K is the cost ratio for additional cost, which is input by a user; A is the unit cost for the resource. Suppose a task 1, whose resource requirement is 20 resources, is scheduled in August 2000. However, an agent A, which is assigned to the task, has 10 resources in September and October

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2000, respectively. The cost ratio is assumed as 20% and the unit cost is assumed as $100/resource. The succeeding task 2, whose resource requirement is 10 resources, is scheduled on September 2000. Another agent B, which is assigned to the task 2, has 10 resources in September 2000. The cost ratio is assumed as 20% and the unit cost is assumed as $50/resource. The utility of rescheduling task 1 of Agent A from August 2000 to September 2000 can be calculated as follows: Utility = Benefit – Cost ={RR –RA) – (RC–RB)} x K x A – {(RC – RB) – (RR – RA) } x K x A ={(20 – 0) – (20 – 10)} x 0.2 x 100 – {(10 – 0) – (10 – 10)}}x 0.2 x 50 = $ 200 - $ 100 = $ 100 > 0 Therefore, the utility of rescheduling task 1 of agent A from August 2000 to September 2000 is $100. However, if the unit cost of the succeeding task is $200/resource, the utility of rescheduling task 1 from August 2000 to September 2000 will be minus $200. Calculating the utility units with cooperation of other agents, an agent can make an appropriate decision quantitatively. The utility function produces utility units for agents based on the cost ratios input by users. Therefore, agents are assumed to be honest in our work. However, there are concerns about whether the users provide agents with incorrect cost ratios to take advantage of other agents. Since the same cost ratios are used to calculate both the benefit and costs, the users might take actual losses even though their agents make profitable deals. In some cases, an agent could get more profit from proceeding agents than actual costs with an incorrect cost ratio, but its calculated benefits using the same cost ratio will be much higher than the actual benefits so that other agents will also take advantage of the inflated benefits and the agent might end up with losses. We feel that more research will be needed to verify that a truth revelation is the dominating strategy in most cases. To help users to input their cost ratios, graphic user interface (GUI), as a part of our prototype system, is currently being developed employing the parameters that depict characteristics of resources, such as units, fixed/variable, timing, in/out, and upper units.

4.2 Multi-linked Negotiation Protocol For tightly coupled acyclic construction project schedules, instead of developing knowledgeable agents, we adopted the Zero-Intelligence-Plus (ZIP) agents (Cliff and Bruten, 1998), which only know users’ tasks, relationships with other tasks, and resource profiles, and have only basic reasoning capabilities. The consequence is that agents need to obtain a complete knowledge for their decisions through multi-linked negotiations where one agent negotiates with another agent, which in turn needs to negotiate with a third, and so on, until the last agent. This multi-linked negotiation is inspired by the work of Neiman and others (1994), but it is acyclic and therefore more straightforward than their protocol. For the multi-linked negotiation protocol, the recursive negotiation performatives and synchronous negotiation process are formalized in the next two sections.

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4.2.1

Recursive Negotiation Performatives

In our research, the pair-wise negotiation performatives (Chen, et al., 1999) were adopted and modified for our negotiation protocol used when one agent asks feedback and another agent gives cost response, and then the initiating agent decides and compensates the counterpart agent for its loss. For our multi-linked negotiation protocol, agents need to ask other agents before replying a cost response. Because tightly coupled network-like precedence relationships exist, performatives should be recursive, as shown in Table 1. Performatives followed Ask | Reply Reply | Accept | Reject Accept | Confirm Reject | Confirm Confirm | Turnover | Terminate Ask | Terminate NONE

Ask Reply Accept Reject Confirm Turnover Terminate

Table 1. Multi-linked negotiation performatives and expected response 4.2.2

Synchronous Negotiation Process

For our negotiation mechanism, we adopted and modified the negotiation process (Mudgal and Vassileva, 1999), which was represented in a state transition diagram. Our negotiation process is represented in a state transition diagram that includes the negotiation performatives. For the multi-linked negotiations, recursive performatives are represented as loops, as shown in Figure 1.

Turnover Confirm

Ask Ask

Confirm 1

Turnover

2 Reply

Confirm

Accept

Accept

Ask 3 Confirm

4 Reject

Reject

Reply

Figure 1. Modified state transition diagram for multi-linked negotiation The negotiation process is synchronous. Neiman and Lesser (1996) asserted that a synchronous negotiation process is superior to an asynchronous process in their cooperative repair method which was used in a tightly coupled coordination domain like ours.

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4.3 Monetary Compensation Strategy In our research, agents are located in the middle of the continuum between pure cooperative agents and pure self-interested agents. They are cooperative in terms of rescheduling their tasks as long as their costs are compensated, but they become self-interested in terms of asking other agents to reschedule their tasks as long as their benefits are more than compensation for other agents. We found that these agents’ characteristics rooted from the characteristics of construction projects where agents are closely coupled and precedence relationships between their tasks are dominant. The agents are cooperative while they wait for their turns and become self-interested at their turns. It is obvious that every agent will have its fair turn in our work. In the agent-based project schedule coordination framework, two strategies exist for the two types of agent models: the self-interested initiating agent and the cooperative responding agent. Agents can play both roles, depending on their position in the negotiation process. For representation of the monetary compensation strategy, we adopt the form of the event/response list (Chan, et al, 1999) to describe the algorithms the agents use, as shown in Table 2. Event initiator Initiate Turnover

Initiating agent

Receive message EstimateBenefit Ask

Receive response CompareBC 1. Accept

Receive response 2. Reject

Receive response Turnover

Responding / Initiating agent

Receive message EstimateCost Ask Receive response AccumulateCost Reply Receive decision Accept Receive response Confirm Receive decision Reject Receive response Confirm Receive message EstimateBenefit : :

Last Responding agent

Receive message EstimateCost Reply

Receive decision Confirm

Receive response Confirm : : : : Terminate

Table 2. Event/response list

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When the Turnover message is initiated by the system, the initiating agent sends the Ask message to the responding agents to reply their costs after it calculates the benefit of its change using the EstimateBenefit module (see Algorithm 1). RC and RB are calculated by agents. Algorithm 1: EstimateBenefit 1: K ßcost ratio from file 2: A ß unit price from file 3: RR ß resource requirements for a task in a given time 4: RA ß available resources in a given time 5: B ß {(RR – RA) – (RC – RB)} x K x A After calculating their costs using the EstimateCost module (see Algorithm 2), the responding agents also send the Ask messages to other responding agents to reply their costs recursively until there is no responding agent. Algorithm 2: EstimateCost (task n) 1: if n = 2, C ß 0 else 1: K ßcost ratio from file 2: A ß unit price from file 3: RR ß resource requirements for a task in a given time 4: RA ß available resources in a given time 5: C ß {(RC – RB) – (RR – RA) } x K x A 6: n ß n - 1 The responding agents send the Reply message with their costs to the asked agents that will accumulate the costs to their own costs using the AccumulateCost module (see Algorithm 3) and send the Reply message recursively up to the initiating agent. Algorithm 3: AccumulateCost 1: C’ ß cost response from responding agents 2: C ß C + C’ After getting all cost responses, the initiating agent compares the benefit and cost of its change using the CompareBC module (see Algorithm 4) and makes a decision whether it changes the schedule or keeps its schedule based on the comparison. Algorithm 4: CompareBC 1: U ß B – C 2: if U > 0 then Accept 3: else Reject When the agent decides to change its schedule, it sends the Accept messages with compensation to the responding agents that will send the Accept messages recursively to the last agent. The last agent, then, sends the Confirm message to the sent agents that send the Confirm messages recursively to the initiating agent. The Reject and Confirm processes will be the same

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processes as the Accept and Confirm processes. The initiating agent iterates these processes until there is no task left. Then the initiating agent sends the Turnover message to the responding agents according to the order specified in the project master schedule. The relationship information between agents is kept within the individual agents. The responding agent changes its role into that of the initiating agent. The aforementioned processes will be repeated with another agent until no agent is left. After exploring their alternatives, the last agent sends the Terminate message to the system. Since the project schedule coordination based on the above processes is NP-complete, an approximation is needed. In our work, it is reasonably assumed that an initiating agent takes only benefit value (Equation 2) when cost value (Equation 3) is negative (-) value, which means that the option is mutually beneficial for both initiating agent and responding agents. In that case, the initiating agent does not need to compensate responding agents. This assumption allows the self-interested initiating agent to consider only alternatives that produce positive (+) benefits. That means that they will ignore indifferent alternatives that produce zero (0) or negative (-) benefits. The assumption also restricts the cooperative responding agents’ roles as giving feedback only without exploring any alternative. This approximation considerably reduces the number of alternatives that agents should consider while ensuring the quality of the solution. The unexplored alternatives by the initiating agents will be explored by succeeding agents in our work. The succeeding agents explore feasible alternatives, which produce positive (+) benefits, for both ways: forward processes with succeeding tasks and backward processes with proceeding tasks in the project master schedule. Every agent has an equal opportunity to explore all feasible alternatives for their tasks. Eventually all feasible alternatives are explored and an individually rational and globally optimal solution will be found. To summarize, using the aforementioned compensatory negotiation methodology, agents can calculate utility with utility function, can explore feasible alternatives with cooperation of other agents by the multi-linked negotiation protocol, evaluate the impact of their alternatives based on the monetary compensation strategy, and make appropriate decisions based on the evaluation. When the decisions affect other agents’ tasks, agents transfer utility for compensation of other agents that are forced to make disadvantageous agreements, and, as a result, agents cooperatively find a globally optimal solution in a distributed manner.

5. Case Example In this section we present a concrete example of how a transfer of utility allows self-interested agents to be more cooperative in finding a globally optimal solution, which is also a Pareto optimal solution. We give a detailed explanation of how to find a globally optimal solution based on local resource constraints through the compensatory negotiation. As shown in Figure 2, the simplified master schedule of Inverted Roofing and Cladding tasks of the Durand Centre project (O’Brien, 1998) is introduced to illustrate our compensatory negotiation methodology.

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(Early Start)

Work Description Inverted Roofing Cladding

Jan

Feb 1

Mar 2 1

Apr 3 2

May 4 3

Jun 5 4

Jul 6 5

Aug

Sep

Oct

Nov

6

Figure 2. Master construction schedule w/unlimited resources Suppose these tasks are awarded to two subcontractors, Roofers, Inc. (“Roofers”) and Cladders, Inc. (“Cladders”), respectively. However, although the chosen subcontractors have their corresponding resource supplies, they have different resource profiles from the resource requirements for the tasks. Therefore, their bid prices are set at the more expansive projected cost, which is calculated based on the needed resources for the tasks, rather than estimated cost, which is calculated based on their available resources. The difference leaves room for them to improve. Table 3 shows the resource profiles and cost information of Roofer and Cladders. For the sake of simplicity, the cost ratio of the Roofers and Cladders is assumed as 20% in the case example. The unit costs of resources for Roofers and Cladders are $50 and $8, respectively.

Inverted Roofing Needed Resource Available Resource Estimated Cost Projected Cost

Jan

Cladding Needed Resource Available Resource Estimated Cost Projected Cost

Jan

Feb 10 5 250 550

Mar 10 5 250 550

Apr 10 5 250 550

May 10 5 250 550

Jun 10 10 500 500

Jul 10 10 500 500

Aug

Feb

Mar 10 10 80 80

Apr 10 10 80 80

May 10 10 80 80

Jun 10 5 40 88

Jul 10 5 40 88

Aug 10 10 80 80

10 500

(Unit in price: 1,000 dollars) Sep Oct Nov Total 60 10 60 500 3000 3200 Sep

Oct

Nov

Total 60 60 480 496

10 80

Table 3. Estimated and projected costs for Cladders In order to find a global solution in a distributed manner, the local optimal schedule should be identified. Using linear programming, the subcontractors can easily find their local optimal schedules, as shown in Figure 3. Local optimal schedule Inverted Roofing Cladding

J

F

M

A

1

M 2

1

2

3

J 3

J 4 4

A 5 5

S 6 6

O

N

Figure 3. Subcontractors’ local optimal schedule w/limited resources When the subcontractors made their local optimal schedules, schedule conflicts occur from March to September between subcontractors because cladding tasks cannot start before roofing tasks are finished. Our research resolves these schedule conflicts with the compensatory negotiation processes that allow the transfer of utility between subcontractors.

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The utility of task 1 of Roofers is = Benefit – Cost ={{RR – RA) – (RC – RB)} x K x A – {(RC – RB) – (RR – RA)} x K x A} x $1000 ={{(10 – 5) – (5 – 5)} x 0.2 x 50 – {(10 – 0) – (10 – 10)}}x 0.2 x 8} x $1000 = $ 50,000 - $ 16,000 = $ 34,000 > 0 Therefore, task 1 of Roofers will be changed to the local optimal schedule. Then, Roofers transfer $16,000 to Cladders for their loss due to the schedule change. Roofers still gain a profit of $34,000. Through the compensatory negotiation process including Cladders’ own coordination, all tasks can be scheduled optimally in a distributed manner. The final schedule is shown in Figure 4 and the analysis of the case example is summarized in Table 4. Work Description Inverted Roofing Cladding

Jan

Feb

Mar

Apr

1

May 2

Jun 3

1

Jul 4 2

Aug 5 3

Sep 6 4

Oct

Nov

5

6

Figure 4. Coordinated schedule w/limited resources

Before negotiation After negotiation Analysis

Estimated (A) Projected (B) Revised (C) Final after compensation (D) D/B Savings

Roofer (1) 3,000 3,200 3,000 3,096 96.8% 3.2%

Cladder (2) 480 496 544 448 90.3% 9.7%

(Unit: $1,000) Total (3) 3,480 3,696 3,544 3,544 95.9% 4.1%

Table 4. Analysis of compensatory negotiation To summarize, the total cost was projected as $3,696,000 (B3). After the compensatory negotiation process, the total cost was revised to $3,544,000 (D3) — a 4.1% cost reduction. Without allowing the transfer of utility, self-interested Cladders would not cooperate with Roofers in spite of a better result — $448,000 (D2) and 9.7% cost reduction — because their actual revised cost, $544,000 (C2), is more than their projected cost, $496,000 (B2). We may notice that the total cost after compensation (D3) in a distributed manner is the same as the total cost (C3) without allowing the transfer of utility by a central controller. The reason is that the compensatory negotiation process finds a globally optimal solution at first and then compensates for any loss.

6. Conclusions and Future Work In the construction industry, there is a need to develop a new distributed coordination methodology that allows subcontractors to dynamically reschedule a project based on their resource profiles. The original objective of this research was to propose a distributed project

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schedule coordination framework for the subcontractors by applying the current distributed coordination methodologies developed for the software agents in CDPS and MAS research. However, we found that none of the CDPS and MAS papers mentioned an explicit method for transferring utility units (“money”) among software agents for compensation of disadvantageous agreements. Another shortcoming is that most CDPS and MAS research employs pair-wise negotiation mechanisms, which would be unsuitable for coordinating the tightly coupled construction schedules. After considering different characteristics between project schedule coordination and CDPS and MAS research, a new problem domain, which consists of agents that are trying to utilize their resources as much as possible, is introduced. We conclude that allowing the transfer of utility units for compensation would lead to individually rational and globally optimal solutions in agent-based project schedule coordination domains. In order to allow agents to transfer utility to other agents for compensation of disadvantageous agreements, this paper presented a novel compensatory negotiation methodology consisting of a utility function, a multi-linked negotiation process, and a monetary compensation strategy, which leads to an individually and globally optimal solution. The case example shows the significance of the methodology. However, the compensatory negotiation methodology cannot be applied directly to distributed coordination of subcontractors because subcontractors cannot give timely feedback to other subcontractors such as software agents normally can, which is the basis of the multi-linked negotiation process. Therefore, we are currently developing an agent-based project schedule coordination framework based on the compensatory negotiation methodology proposed in this paper, which provides the subcontractors with software assistants that evaluate the impact of the changes, simulates decisions in lieu of subcontractors, and advises human subcontractors. The negotiation methodology and an agent-based framework will be tested and verified by developing a multi-agent prototype system on top of the ProcessLink agent-based system developed by one of authors at the Center for Design Research of Stanford University. ProcessLink already includes distributed functionality for interleaving replanning, rescheduling, and redesign. The prototype system will provide a foundation for facilitating collaboration among project participants over the Internet. The negotiation methodology for coordinating subcontractors may also be extended to electronic supply-chain issues.

7. Acknowledgement We would like to thank Professor Raymond Levitt and Professor Martin Fischer of Stanford University, Civil and Environmental Engineering Department, and Professor Yan Jin of the University of Southern California, Aerospace and Mechanical Engineering Department, for their support of this research. Funding has been provided by the Center for Integrated Facility Engineering (CIFE) of Stanford University. Dr. Lesser’s contributions to this work was supported by the National Science Foundation under Grant No. IIS-9812755 and by the Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory, Air Force Materiel Command, USAF, under agreement number

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F30602-99-2-0525. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the author(s) and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the National Science Foundation. Defense Advanced Research Projects Agency (DARPA), the Air Force Research Laboratory, or the U.S. Government.

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