Research on convex resource allocation scheduling with exponential time-dependent learning effects

This article addresses two scheduling problems with resource allocations and learning effects on a single machine, meaning the actual processing time of a job is a nonincreasing and continuous function of the total job parameter relating to the processed jobs and the amount of resource allocation. Our first problem is to find a job sequence and resource allocations that lead to a minimization of the weighted sum of total completion-time cost and total resource-consumption cost. The second problem is to minimize the total completion-time cost subject to the total resource-consumption cost is bounded. For a special case, we prove that both these problems are polynomially solvable. Generally, we propose some heuristic algorithms and a branch-and-bound algorithm to solve the problems.