<p style='text-indent:20px;'>In this study, we consider the resource allocation scheduling with a deterioration effect and position-dependent workloads concurrently on a single machine. The scheduler needs to find the optimal sequence and the optimal resource allocation such that a cost function is minimized. First, the focus is on minimizing the linear weighted sum of the schedule cost and resource consumption cost. Second problem is to minimize the schedule cost subject to an upper bound on the resource consumption cost. Third problem is to minimize the resource consumption cost subject to an upper bound on the schedule cost. Last problem is to find Pareto-optimal solutions for schedule cost and resource consumption cost. We proved that these problems remain polynomially solvable respectively.</p>
Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job’s actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded.
We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in [Formula: see text] time, where [Formula: see text] is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times.
<p style='text-indent:20px;'>This paper considers single-machine position-dependent weights scheduling problem with past-sequence-dependent delivery times and truncated sum-of-processing-times-based learning effect. The objective is to minimize the weighted sum of due date, and the number of early jobs and tardy jobs, where the weights are position-dependent weights. Under the common due date, slack due date and different due date assignments, the optimal properties are given, and the corresponding optimal solution algorithms are respectively proposed to obtain the optimal sequence and optimal due dates of jobs.</p>
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