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.

Some projects are often performed by many subcontractors that cooperate with each other and some of them are conducted by outsourcing them to several firms; so subcontractors carry out activities in competition. Appropriate trade-off between time and cost and achieving more benefit and cost saving are objectives of both models. In this paper, it is investigated that how different subcontractors of a project can cooperate to achieve more advantages if possible and how sub-contractors can compete to make the results better and find the optimum cost to minimize the time for each of them. The competition here does not mean eliminating a competitor, but the aim is to challenge the contractors in order to choose the best decision. The purpose of this study is to address the challenges in time and cost management and to find more profit allocation among subcontractors and fair competition for fair allocation as well. A model based on cooperative game theory in time/cost trade-off problem of projects is suggested and then a competition model among subcontractors based on non-cooperative game theory is proposed. A case study is rep-resented to comprehensively illustrate the problem, the cooperative techniques of cooperative game theory, and the payoff matrix of non-cooperative model among subcontractors. Results of the proposed model reveal that subcontractors can obtain higher profit from cooperation if pos-sible. When they outsource the project and compete with each other, they must consider the in-teraction activities and choose the best strategies for cost saving and gain more reward from the client. Moreover, it is found that some techniques such as Shapley value, Core, Max-Min Core, or Equal Profit Method (EPM) are able to fairly assign extra profit of cooperation, and using the payoff matrix, Nash equilibrium, and Nash bargaining helps to find the optimum point to mini-mize time and cost for interaction activities state.