Due-Window Assignment Methods and Scheduling with Generalized Positional-Dependent Weights

Wang, Ji-Bo; Wang, Sihan; Cao, Kaipeng; Liu, Mengqi; Jia, Xue

doi:10.1142/s0217595922500282

Asia Pac. J. Oper. Res.

2022

DOI: 10.1142/s0217595922500282

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Due-Window Assignment Methods and Scheduling with Generalized Positional-Dependent Weights

Ji-Bo Wang

Sihan Wang

Kaipeng Cao

et al.

Abstract: 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… Show more

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Cited by 6 publications

References 45 publications

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Study on Due-Date Assignment Scheduling with Setup Times and General Truncated Learning Effects

Yang

et al. 2023

Asia Pac. J. Oper. Res.

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This paper concentrates on the single-machine scheduling problem with past-sequence-dependent setup times and general truncated learning effects, where the job processing times are non-increasing function of their positions in a sequence. Under common, slack and different (unrestricted) due-date assignments, our goal is to minimize the weighted sum of number of early/tardy jobs and due-date assignment cost, where the weight is not related to the job but to a position, i.e., the position-dependent weight. Under the three due-date assignments, some optimal properties and three optimal solution algorithms are proposed to solve these problems, respectively.

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Study on Due-Date Assignment Scheduling with Setup Times and General Truncated Learning Effects

Yang

et al. 2023

Asia Pac. J. Oper. Res.

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Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Wang

2023

Mathematics

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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.

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Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing

Bai,

Wei,

et al. 2024

Mathematics

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Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.

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Due-Window Assignment Methods and Scheduling with Generalized Positional-Dependent Weights

Cited by 6 publications

References 45 publications

Study on Due-Date Assignment Scheduling with Setup Times and General Truncated Learning Effects

Study on Due-Date Assignment Scheduling with Setup Times and General Truncated Learning Effects

Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing

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