Scheduling jobs for three-stage hybrid flow-shop

Abstract

Although production systems with parallel duplicate machines have been well studied in the literature, relatively few works exist considering serial identical machines. Meanwhile this type of system is frequently utilized in practice and those scheduling algorithms are needed to utilize the existing system efficiently. This work deals with scheduling jobs for a flow-shop system that consists of three stages; one station in the first stage, and one station in the last stage. There are two identical stations in the middle stage. There is no buffer between machines and the objective is to minimize the maximum completion time (Cmax). Utilizing the identical stations is to smooth out production flow when the processing times for the second stage are longer than that in either stages Recently Branch and Bound, Genetic Algorithm (GA) and mathematical modeling (using Standard Solver) are proposed for systems with two stages. In this work, we extended the system to includ in third stage after the duplicate station, and formulate the problem using two different models: The first one employs existing dispatching policy and the next by using a newly created mathematical model. The newly created model avoids the overlooked deficiencies in the previously published works and guaranties finding optimal solutions in all cases. Integer programming solver (Lingo) has been used to produce benchmark solutions from the mathematical models. Additionally, a GA is developed to obtain effective solutions for practical size problems. A thorough experimental study is performed to analyze the performance of the solution approaches.