Scheduling linearly deteriorating jobs on parallel machines: a simulated annealing approach

Scheduling deteriorating jobs on parallel machines is an NP-hard problem, for which heuristics would be the first solution option. Two variants of linearly deteriorating jobs are considered. The first is that with simple linear deterioration, i.e. where there is a deterioration rate only, which is meaningful only if the jobs are assumed to be available at a positive time t(0). In the second variant, there is a basic processing time and a deterioration rate and all jobs are available at time t = 0. In both cases, we seek to minimize the makespan. Starting from simple heuristics, both steepest descent search and simulated annealing are designed and implemented to arrive at optimal or near-optimal solutions. Computational results for randomly generated problem instances with different job/machine combinations are presented.