Optimization of Bonus-Penalty Structure in Flexible Resources-Constrained Project Scheduling Problems from Both Sides of the Contract

Project contractors often need to rent resources to execute their projects, and the clients often set up bonus-penalty structure (BP-structure) at the deadline of the project to encourage the contractors in fulfilling the project on time. In this paper, we introduce BP-structure and flexible resource-constraints (i.e. resource renting) into traditional RCPSP, and formulate an optimization model of BP-structure based on flexible resource-constraints from both sides of the contract. By solving the model the contractor gets optimal schedule and the client obtains optimal bonus-penalty rate (BP-rate) to a given due date. Both sides of the contract can obtain maximal incomes under the optimal schedule with the optimal BP-rate. Finally, the outcomes of the paper are illustrated by a numerical example.