A fuzzy leader-follower game approach to interaction of project client and multiple contractors in time/cost trade-off problem

Abstract

In recent years, clients often employ multiple contractors to implement different activities of the projects. Each contractor manages and implements a subset of activities according to the deter-mined schedule and payments. In this situation, time/cost trade-off problem becomes a distributed decision making problem in which the client, as leader, and the contractors, as followers, pursue their own objectives. We establish a multi-objective, bi-level distributed programming model based on fuzzy mathematical programming for this time/cost trade-off problem. The model is then developed for three common behaviors of client i.e. profit seeking, minimization of project time, as well as combination of profit seeking and minimization of project time behaviors. As the solution approaches, we propose transformation method based on Karush-Kuhn-Tucker condi-tions projects to transform bi-level programming problem to a single level one. Numerical results reveal that the client’s behaviors have measurable impact on time and cost of activities performed by contractors. Moreover, we found that when the client does not have complete information about the contractors’ financial situations, the client should make trade-off between his confidence level and his profit.

Keywords

• Bi-level distributed program-ming problem
• Project client
• Project contractors
• Leader-follower interaction