Project scheduling to minimize the makespan under flexible resource profiles and marginal diminishing returns of the resource

A standard approach to project scheduling that tackles the problem of minimizing the makespan under variable resource profiles is the Flexible Resource-Constrained Project Scheduling Problem (FRCPSP). This approach traditionally considers constant marginal returns from increasing the allocation of a particular resource, whereas in practice, project and operational managers are often faced with diminishing marginal returns. This work is the first to integrate these two interrelated aspects of resource allocation (flexible profiles and diminishing marginal returns) in order to determine the optimal resource allocation and project scheduling that will minimize the project makespan. This paper develops a mixed-integer linear programming model to obtain an optimal solution of the FRCPSP assuming diminishing marginal returns as the resource allocations are increased. In addition, to solve medium-sized instances of the problem, a heuristic algorithm based on relaxation of this mixed-integer programming model is presented. Through a series of computational tests, we further show that the average deviation in the makespan between the two strategies (optimal vs. heuristic solution) does not exceed 5%.