Single machine group scheduling jobs with resource allocations subject to unrestricted due date assignments

This paper investigates the single machine group scheduling with unrestricted (different) due date assignments and resource allocations (controllable processing times). The resource allocations mean that the actual job processing times are convex decreasing function of their consumption of resources. To solve the general problem of minimizing the weighted sum of earliness, tardiness, due date assignment cost and resource consumption cost (the weights are job-dependent weights), we propose lower and upper bounds to speed up the search process of the branch-and-bound algorithm. To solve this problem quickly and accurately, we also propose a heuristic algorithm. Computational results are tested to evaluate the performance of the algorithms.