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This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a continuous bivariate non-increasing convex function involving position and resource allocation. Only the slack due-window assignment method will be used. Two linear combination problems concerning position-dependent effects and resource allocation will be studied, in which the machine requires multiple maintenance activities. We present the optimal properties or design optimal algorithms to minimise the combination of the makespan, the total completion time and the total absolute deviation of completion time and to minimise the combination of the total costs of tardiness, the slack due date, the earliness cost, and the resource amount. Finally, we also consider the bi-criteria scheduling problem with nonmaintenance activities to minimise the combination of the total resource allocation cost, the weighted number of tardy jobs, and slack due-window assignment costs. A pseudo-polynomial time algorithm is designed to solve the bi-criteria scheduling problem.

Single-machine slack due-window assignment scheduling with multiple maintenance activities and position-and-resource-dependent processing times