Incentive contract design in project management with serial tasks and uncertain completion times

Abstract

This article investigates an incentive contract design problem for a project manager who operates a project consisting of multiple tasks performed sequentially by different subcontractors in which all task completion times are uncertain and described by fuzzy variables. On the basis of an expected value criterion and a critical value criterion, two classes of fuzzy bilevel programming models are developed. In the case where the uncertain task completion times are mutually independent, each model can first be decomposed into multiple equivalent sub-models by taking advantage of the structural characteristics, and then a two-step optimization method is employed to derive the optimal incentive contract in each sub-model. In a more general case where the uncertain task completion times are correlative, the approximation approach (AA) technique is adopted first in order to evaluate the objective functions involving fuzzy parameters, which are usually difficult to convert into their crisp equivalents. Then, an AA-based hybrid genetic algorithm integrated with the golden search method and variable neighbourhood search is designed to solve the proposed fuzzy bilevel programming models. Finally, a numerical example of a construction project is conducted to demonstrate the modelling idea and the effectiveness of the proposed methods.