Group Technology Scheduling with Due-Date Assignment and Controllable Processing Times

Abstract

This paper investigates common (slack) due-date assignment single-machine scheduling with controllable processing times within a group technology environment. Under linear and convex resource allocation functions, the cost function minimizes scheduling (including the weighted sum of earliness, tardiness, and due-date assignment, where the weights are position-dependent) and resource-allocation costs. Given some optimal properties of the problem, if the size of jobs in each group is identical, the optimal group sequence can be obtained via an assignment problem. We then illustrate that the problem is polynomially solvable in O(℘3) time, where ℘ is the number of jobs.

Optimal Different Due-Date Assignment Scheduling with Group Technology and Resource Allocation

“…Under different due-date assignments, they proved that some special cases of the weighted sum of the scheduling cost (including earliness, tardiness, and the due-date assignment cost) and resource-consumption-cost minimization can be solved in polynomial time. Liu and Wang [27] studied single-machine GT scheduling with resource allocation. Under common and slack due-date assignments, the objective was to minimize the weighted sum of earliness, tardiness, due-date assignment cost, and resourceconsumption cost.…”

“…Under common and slack due-date assignments, the objective was to minimize the weighted sum of earliness, tardiness, due-date assignment cost, and resourceconsumption cost. For linear and convex resource functions, Liu and Wang [27] proved that two special cases of the problem are polynomially solvable.…”

“…To the best of our knowledge, very few articles (see Chen et al [26]) have studied GT scheduling with resource allocation and different due-date assignments. We will continue the work of Liu and Wang [27] but consider different due-date assignments. First, for constant processing times, the objective is to minimize the weighted sum of earliness, tardiness, and due-date assignments cost (i.e., the scheduling cost, and the weights are position dependent (Lv and Wang [28], Wu et al [29], and Pan et al [30])).…”

Scheduling with Group Technology, Resource Allocation, and Learning Effect Simultaneously

“…Yan et al [24] studied a single-machine problem with resource allocation and deteriorating effect in group technology environment. Liu and Wang [25] and Wang and Liu [26] considered single-machine GT scheduling with resource allocation and due date assignment.…”

Two-Agent Slack Due-Date Assignment Scheduling with Resource Allocations and Deteriorating Jobs

“…One cause of the tardiness in job production involves another type of scheduling problem, namely, the just-in-time scheduling, which specifies delivery date for a job that incurs excess costs if completed earlier or later. This delivery date is also known as the due date, and familiar due dates include (a) common due date: i.e., the due date of each job is the same constant (Shabtay et al [7], Falq et al [8], Wu et al [9] and Liu and Wang [10]); (b) different due date: the opposite of common due date (Mosheiov et al [11] and Hidayat et al [12]); (c) slack due date: the due date of each job, although different, but with a common decision variable (Liu et al [13] and Liu and Jiang [14]).…”