A Flow Shop Scheduling Problem with Transportation Time and Separated Setup Time of Jobs

Abstract

A flowshop scheduling problem has been one of the classical problems in production scheduling since Johnson proposed the well-known Johnson's rule in the two-stage flow-shop make-span scheduling problem. Mitten and Johnson (1959) separately gave solution algorithm of obtaining an optimal sequence for an ′n-job, 2-machine′ flow shop scheduling problem in which each job involves arbitrary time lags (start-lag, stop-lag). Also Maggu and Das (1980) gives solution algorithm of obtaining optimal sequence for a ′ n-job, 2-machine′ flow shop scheduling problem where in each job involves transportation time. Johnson (1959) presented a solution to the n-job, 2-machine flow-shop problem with an algorithm that produces an ordered sequence with minimum total elapsed time. Kim and Bobrowski (1994) present a computer simulation model for a limited machine job shop scheduling problem with sequence-dependent setup times. They study the influence of setup times and due date's information in priority rules performance for job-shop problem with setup times. S. M. Johnson (1954) presents optimal two and three stage production schedules with setup time included. Wlodzimierz Szwarc (1986) discussed the flow shop problem with time lags and separated setup times. C.T. Ng et al. (2007) presents the three-machine flow-shop scheduling problem to minimize maximum lateness with separate setup times. W. H. Yang et al. (1999) addressed a survey of scheduling research involving setup times. An overall view on set up times in sequencing problems is presented. In this paper, we addressed the three machine flow shop scheduling problem to minimize total completion time where setup times are treated as separate from processing times. Two cases are studied, taking into consideration these factors and the set up times separated from the processing times. This new algorithm provides an optimal scheduling sequence for flow-shop scheduling problems of 5-jobs on 3-machines and is proposed by using separated setup times of a job.The present paper is a modest attempt to investigate how the setup time is helpful for the production.