Due-Window Assignment and Resource Allocation Scheduling with Truncated Learning Effect and Position-Dependent Weights

Shan-Shan Lin

doi:10.1155/2020/9260479

Abstract

This paper studies single-machine due-window assignment scheduling problems with truncated learning effect and resource allocation simultaneously. Linear and convex resource allocation functions under common due-window (CONW) assignment are considered. The goal is to find the optimal due-window starting (finishing) time, resource allocations and job sequence that minimize a weighted sum function of earliness and tardiness, due window starting time, due window size, and total resource consumption cost, where the weight is position-dependent weight. Optimality properties and polynomial time algorithms are proposed to solve these problems.

Highlights

Scheduling models and problems with learning effects and/or resource allocations have become popular topics for scheduling researchers in recent years
Lu et al [8] studied single-machine due-date assignment scheduling with learning effects and resource allocations. ey proved that several problems can be solved in polynomial time
For the scheduling criterion minimization subject to the constraint that the total resource compression criterion is less than or equal to a fixed constant, they proved that the problems can be solved in polynomial time

Summary

Introduction

Scheduling models and problems with learning effects (see Biskup [1]; Lu et al [2]; Azzouz et al [3]; Wang et al [4]) and/or resource allocations (see Shabtay and Steiner [5]; Yang et al [6]) have become popular topics for scheduling researchers in recent years. Wang and Wang [11] considered single-machine scheduling problems with learning effects and convex resource allocation function. We continue the work of Wang et al [18], i.e., we consider the due-window assignment scheduling problems with learning effect and resource allocation in the single-machine environment. E goal is to find the optimal due-window starting (finishing) time, resource allocations, and job sequence such that a sum of scheduling cost (including weighted sum function of Discrete Dynamics in Nature and Society earliness and tardiness, due window starting time, due window size, where the weight is position-dependent weight) and total resource consumption cost is minimized. (2) For the linear resource allocation, we proved that the sum of scheduling cost and total resource consumption cost can be solved in polynomial time.

Problem Formulation

Linear Resource Allocation

Convex Resource Allocation