Unrelated parallel-machine scheduling with controllable processing times and eligibility constraints to minimize the makespan

This paper addresses the problem of scheduling jobs on unrelated parallel machines with eligibility constraints, where job-processing times are controllable through the allocation of a nonrenewable common resource, and can be modeled by a linear resource consumption function. The objective is to assign the jobs to machines and to allocate resources, so that the makespan is minimized. We provide an exact formulation of the addressed problem as a mixed integer programming model. In view of the computational complexity associated with the formulation makes it difficult for standard solvers to deal with large-sized problems in reasonable solution time, two ant-colony optimization algorithms based on distinct procedures, respectively, are also presented and analyzed. Numerical results show that both the proposed algorithms are capable of solving industrial-dimensioned problems within reasonable computation time and accuracy.