Research problems

2006 Discrete Applied Mathematics  
Research on scheduling and sequencing in reentrant flow shops has received much attention in recent years. In a reentrant flow shop, jobs have to enter a certain machine or a set of machines for processing more than once. Thus a reentrant flow shop is an extension of the classical flow shop, but a special case of the job shop due to the fact that all jobs pass through the machines over the same route. Many real-life applications in semiconductor manufacturing and flexible machining systems can
more » ... e modeled as reentrant flow shops, e.g., the assembly of printed circuit boards and wafer fabrication. Moreover, the reentrant flow shop has been examined in a client-server computer application by Błażewicz et al. [1]. There are various types of reentrant processing depending on the job-processing route. Here we consider a twomachine reentrant flow shop, where there are n jobs to be processed on two machines, M 1 and M 2 . Each job j ∈ {1, 2, . . . , n} has a sequence of three operations in the order O 1j → O 2j → O 3j . We assume that two consecutive operations of a job are processed on different machines. Therefore, for each job j, O 1j , O 2j and O 3j have to be processed without preemption on M 1 , M 2 , and again on M 1 , respectively. Each machine can only process one operation at a time, and there is unlimited input and output buffer space available for each machine. We focus on the makespan minimization problem, i.e., scheduling and sequencing the jobs so as to minimize the completion time of the last job. Following the standard three-field notation for machine scheduling problems, we denote the problem as RF2| = 3|C max , where RF2 indicates a two-machine reentrant flow shop, = 3 describes that each job has three operations, and C max denotes the makespan objective. This problem has been considered in various settings. Lev and Adiri [3] study the problem in a V-shop where the jobs follow the route M 1 → M 2 → · · · → M m−1 → M m → M m−1 → · · · → M 2 → M 1 . They show that the problem is NP-hard for m = 2. Wang et al. [6] analyze the problem in a chain-reentrant shop where the jobs follow the route M 1 → M 2 → · · · → M m → M 1 . They present a branch-and-bound algorithm and an approximation algorithm with worst-case performance guarantee of 3 2 for the m = 2 case. Hall et al. [2] investigate the cycle time minimization 0166-218X/$ -see front matter
doi:10.1016/j.dam.2005.09.001 fatcat:c3n5otty6vagde7ejc3rtlnczi