An equitable approach to the payment scheduling problem in project management

This study reports on a new approach to the payment scheduling problem. In this approach, the amount and timing of the payments made by the client and received by the contractor are determined so as to achieve an equitable solution. An equitable solution is defined as one where both the contractor and the client deviate from their respective ideal solutions by an equal percentage. The ideal solutions for the contractor and the client result from having a lump sum payment at the start and end of the project respectively. A double loop genetic algorithm is proposed to solve for an equitable solution. The outer loop represents the client and the inner loop the contractor. The inner loop corresponds to a multi-mode resource constrained project scheduling problem with the objective of maximizing the contractor's net present value for a given payment distribution. When searching for an equitable solution, information flows between the outer and inner loops regarding the payment distribution over the event nodes and the timing of these payments. An example problem is solved and analyzed. A set of 93 problems from the literature are solved and some computational results are reported. 1. THE PROBLEM DEFINITION A review of the project management and scheduling literature reveals that a considerable amount of effort has been spent on the resource constrained project scheduling problem (RCPSP) with the objective of minimizing the makespan (Özdamar and Ulusoy, 1995; Kolisch and Padman, 1998). It is only relatively recently that financial considerations attract increasing attention although the first attempts for modelling financial aspects of project management appeared rather early (Russell, 1970). Financial aspects of project management have been included in the problem formulation through the use of the maximization of the net present value (NPV) objective which includes both the negative (disbursement) and the positive (receipt) cash flows throughout the project. A recent review of project network models with discounted cash flows is given by Herroelen et al. (1997). The problem treated in this paper can be considered as an extension of the payment scheduling problem. The payment scheduling problem considers the amount and timing of the