Common due-window assignment and minmax scheduling with resource allocation and group technology on a single machine. Issue 11 (2nd November 2022) - Ren, Junfeng; Yang, Yang
Abstract : This article considers the minmax common due-window assignment in group scheduling with resource allocation on a single machine. In this problem, jobs are partitioned into groups. In a group, all jobs are processed contiguously, and a common due-window is assigned to them. First, a case with constant processing times is examined. The objective is to minimize the sum of the maximal costs arising from the common due-window among the jobs in each group. This problem is proved to be polynomially solvable. Next, the problem is extended to the case that includes resource allocation. The processing time of each job is considered as either a linear or a convex function of the quantity of resource allocation. The objective function considers the total resource-consumption cost and sum of the maximal costs. For the special case of group-position-dependent penalties, polynomial-time solutions are presented.