A New Mathematical Model for Flexible Flow Lines with Blocking Processor and Sequence-Dependent Setup Time

This chapter presents a novel, mixed-integer programming model of the flexible flow line problem that minimizes the makespan of a product. The proposed model considers two main constraints, namely blocking processors and sequence-dependent setup time between jobs. We extend two previous studies conducted by Kurz and Askin (2004) and Sawik (2001), which considered only one of the foregoing constraints. However, this chapter considers both constraints jointly for flexible flow lines. A flexible flow line consists of several parallel processing stages in series, separated by finite intermediate buffers, in which each stage has one or more identical parallel processors. The line produces several different jobs, and each job must be processed by at most one processor at each stage. The completed job may remain on a machine and block the processor until a downstream processor becomes available for processing in the next stage; this is known as the blocking processor constraint. In the sequence-dependent setup time constraint , the processing of each job requires a setup time for preparing the processor that is immediately dependent on the preceding job. The objective, therefore, is to determine a production schedule for all jobs in such a way that they are completed in a minimum period of time (i.e., makespan). A number of numerical examples are solved and some computational results are reported to verify the performance of the proposed model. Finally, areas for future research are identified. A flexible flow line consists of several processing stages in series, separated by finite interstage buffers, where each stage includes one or more identical parallel machines. The line produces several different job types. Each job must be processed by at most one machine in each stage. A processed job on a machine in some stage is transferred either directly to an available machine in the next stage (or another downstream stage depending on the jobprocessing route), or, when no intermediate buffer storage is available, to a buffer ahead of that stage. The job may remain on the machine and block it until a downstream machine becomes available (i.e., a blocking processor) (McCormick, 1989; Hall and Sriskandarajah, 1996; Sawik, 2000; Sawik, 2002). However, this blockage prevents another job from being processed on the blocked machine. Actually, a flexible flow line represents a special type of traditional flow shop, in which there is only one machine in each stage and unlimited intermediate storage between successive machines. The flexible flow line with unlimited O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m