Scheduling jobs under constant period-by-period resource availability to maximize project profit at a due date

In this paper, we propose a lump-sum payment model for the resource-constrained project scheduling problem, which is a generalization of the job shop scheduling problem. The model assumes that the contractor will receive the profit of each job at a predetermined project due date, while taking into account the time value of money. The contractor will then schedule the jobs with the objective of maximizing his total future net profit value at the due date. This proposed problem is nondeterministic polynomial-time (NP)-hard and mathematically formulated in this paper. Several variable neighborhood search (VNS) algorithms are developed by using insertion move and two-swap to generate various neighborhood structures, and making use of the well-known backward–forward scheduling, a proposed future profit priority rule, or a short-term VNS as the local refinement scheme (D-VNS). Forty-eight 20-job instances were generated using ProGen and optimally solved with ILOG CPLEX. The performances of these algorithms are evaluated based on the optimal schedules of the 48 test instances. Our experimental results indicate that the proposed VNS algorithms frequently obtain optimal solutions in a short computational time. For larger size problems, our experimental results also indicate that the D-VNS with forward direction movement outperforms the other VNS algorithms, as well as a genetic algorithm and a tabu search algorithm.