Multi-mode project payment scheduling problems with bonus–penalty structure

This paper involves the multi-mode project payment scheduling problem with bonus–penalty structure where activities can be performed with several modes and a bonus–penalty structure exists at the deadline of the project. In the problem the decisions on when to schedule events and payments, the magnitude of each payment, and the performing mode of each activity need to be optimized. A two-module simulated annealing heuristic is proposed to solve the mixed integer non-linear programming models for the contractor and the client, and a satisfactory solution, which consists of payment event set, event schedule, and payment amount set, may be found through iterations between the heuristic’s two modules. The profits of the two parties of the contract are changed significantly by the bonus–penalty structure and the structure may be considered as a coordination mechanism essentially, which may enhance the flexibility of payment scheduling and be helpful for the two parties to get more profits from the project. Through solving and analyzing an instance the insight that the bonus–penalty structure may advance the project completion effectively and improve the profits of the two parties in the meantime can be obtained.