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

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.

Automated summary

This paper investigates a single machine common due-window assignment scheduling problem with position-dependent weights and resource allocations under just-in-time production. The actual processing time of a job is determined by the resource allocated to it. The resource allocation model is divided into linear and convex allocations. The goal is to find an optimal due-window location, job sequence, and resource allocation. The study proves that the minimization of weighted sum of scheduling cost and resource consumption cost can be solved in polynomial time. Furthermore, under convex resource allocation, the minimization of scheduling or resource consumption cost is solvable in polynomial time with bounded cost.