A Branch-and-Bound Algorithm for Two-Stage Production-Sequencing Problems

Abstract

This paper presents an algorithm for determining an optimum solution to a two-stage production sequencing problem with these characteristics: There are n jobs to be sequenced in a two-stage production environment; each production stage is equipped with a single facility; jobs to be sequenced are subject to due-date constraints; facilities in both stages require setup prior to processing each job; setup times in both stages are sequence dependent, and setup cost is assumed to be directly proportional to setup time; and the optimal solution is one that minimizes the total setup cost (of stages I and II) without violating job-due dates. The algorithm employs controlled enumeration through branch-and-bound procedures, together with feasibility tests.

An efficient heuristic for scheduling batches of parts in a flexible flow system

“…This SDST problem is combinatorial in nature and difficult to solve efficiently for largescale applications (Uskup and Smith 1975;Srikar and Ghosh 1986). Given this acknowledged complexity of the batch-scheduling problem for FMSs, it would appear that there is scope for the development of heuristic algorithms to provide adequate and acceptable solutions.…”

“…Uskup and Smith (1975) address the two-machine problem; they minimize total flow time, subject to due-date constraints. A simplifying assumption that they use is that both setup and processing associated with a job in machine 2 cannot start until its processing is completed in machine 1.…”

“…There are several reasons for selecting this optimizing objective. First, there exists a large body of flow-shop research literature (though these studies have addressed types of problems that are different from the one considered here) that has used the minimization of makespan as a performance measure (e.g., Johnson 1954;Gupta 1977;Uskup and Smith 1975;Srikar and Ghosh 1986). Second, Suri and Whitney (1984) have identified production time as an important performance criterion in the second level of decision making (corresponding to the planning stage) for FMSs.…”

Flowshop scheduling research after five decades

“…As a result of the consideration of several objective functions and various heuristic approaches, we witnessed the expansion of efforts to solve flowshop problems with separable setups which could be either sequence independent or sequence dependent (see the reviews by Allahverdi et al (1999) and Cheng et al (2000)). While such problems were identified as early as 1969 and some solution techniques were developed around that time (see Corwin (1969), Corwin and Esogbue (1974), Gupta (1969aGupta ( , 1975 and Uskup and Smith (1975) for such early efforts), the developments in the fourth decade are significant.…”

An approximate solution of the flow-shop problem with sequence dependent setup times

“…G. Uskup and S. B. Spencer [8] offered a branch and bound algorithm to solve the two machine case with due dates. Their objective was to minimize total setup costs assuming their proportionality to the setup times.…”