Client Perspective Based Multimode Project Payment Scheduling Problem and Its Heuristic Algorithm

This article involves the multimode project payment scheduling problem where activities can be performed with several discrete modes and the objective is to maximize the net present value (NPV) of the client. The assumptions are identified and the notations are defined at first. Then, the optimization model of the problem is constructed and its strong NP-hardness is proved by simplifying it to the subproblem of the discrete time/cost tradeoff problem. On the basis of the characteristic of the problem, a special heuristic algorithm composed of two modules is developed. Through the iteration between the two modules, the heuristic can find the desirable solution for the problem. The heuristic is tested on a data set consisting of 40 instances generated randomly. On the basis of the results obtained, the following conclusions can be drawn: All the instances can be solved within 24.63 seconds; the relative deviation of the objective function value from its upper bound is not greater than 8.24%; the NPV of the client decreases with the increase of the payment number, the interest rate per period, the profit margin of the contractor, or the payment proportion.