Results of Parallel-Machine Scheduling Model with Maintenance Activity considering Time-Dependent Deterioration, Delivery Times, and Resource Allocation

Li Sun,Xiao-Hong Zhang,Lei Ning,You-Jin Park

doi:10.1155/2021/8826345

Abstract

This paper investigates parallel-machine scheduling models with maintenance activity, delivery times, time-dependent deterioration, and resource allocation. We consider two forms of the problem: the first is to minimize the sum of total completion times, total machine loads, the total absolute deviation of job completion times, and the total resource allocation; the second is to minimize the sum of total waiting times, total machine loads, the total absolute deviation of job waiting times, and the total resource allocation. The problems are proved to be solvable in polynomial time.

Highlights

Initiated by Vickson [1], scheduling problems with controllable processing times through resource allocation have been studied extensively by researchers since 1980
+Pδr4o􏽐blmie m1 􏽐njP i 1mG|qipjus dij,.LIRnAt,hDisMseAc|tioδn1,TwMeLin+trδo2dTuCc+e the problem to minimize the sum of total machine load, total completion times, and total absolute deviation of job completion times with resource consumption on all the machines
ALGORITHM 1: Algorithm for the problem to minimize the sum of total completion times, total machine loads, the total absolute deviation of job completion times, and the total resource allocation under linear resource consumption

Summary

Introduction

Initiated by Vickson [1], scheduling problems with controllable processing times through resource allocation have been studied extensively by researchers since 1980. Liu et al [31] consider the single-machine delivery time scheduling problem, which was introduced in Koulamas and Kyparisis [32]. We investigate parallel-machine scheduling problem with time-dependent deterioration delivery time maintenance activity and resource allocation, and some new results are given. If a job is scheduled on the jth position of machine Mi in a sequence, its actual processing time with resource consumption is as follows. |Ci[l] − Ci[k]| TC indicate the job’s total processing times and TW indicate the job’s tTLToiWM,talLa n d􏽐w􏽐mi atmi1hi t􏽐e1inLnrg tii.ol WAtastlii[mirnm].etaWsh,ceheisdnti.ueeend.,oylotoeafTdthLCei(uT loaMa􏽐ndLdmi o)1Ff􏽐emisnnr agi lc􏽐[Ch4mii i][nl,reL]wiM,e awii.nbeidly.l, try to find the optimal job sequence, the optimal DMA, and the optimal resource consumption on parallel-machine schedule such that the following cost functions are minimized:. See Ma et al [36]

Cases with Linear Resource Consumption Function

Conclusions