Parallel machines scheduling with deterioration effects and resource allocations

This article studies multi-objective scheduling problems involving deterioration effects and resource allocations simultaneously on an unrelated parallel-machine setting. The linear and convex resource consumption models are examined, respectively. We aim to find the optimal resource allocation and the optimal job sequence to minimize the cost function including the total completion time, the total machine load, the total absolute differences in completion times and the resource allocation and the cost function including the total waiting time, the total absolute differences in waiting times, and the resource allocation, respectively. We develop polynomial time algorithms for all the problems studied.