A Biased-Randomized Discrete-Event Algorithm for the Hybrid Flow Shop Problem with Time Dependencies and Priority Constraints

Abstract

Based on a real-world application in the semiconductor industry, this article models and discusses a hybrid flow shop problem with time dependencies and priority constraints. The analyzed problem considers a production where a large number of heterogeneous jobs are processed by a number of machines. The route that each job has to follow depends upon its type, and, in addition, some machines require that a number of jobs are combined in batches before starting their processing. The hybrid flow model is also subject to a global priority rule and a “same setup” rule. The primary goal of this study was to find a solution set (permutation of jobs) that minimizes the production makespan. While simulation models are frequently employed to model these time-dependent flow shop systems, an optimization component is needed in order to generate high-quality solution sets. In this study, a novel algorithm is proposed to deal with the complexity of the underlying system. Our algorithm combines biased-randomization techniques with a discrete-event heuristic, which allows us to model dependencies caused by batching and different paths of jobs efficiently in a near-natural way. As shown in a series of numerical experiments, the proposed simulation-optimization algorithm can find solutions that significantly outperform those provided by employing state-of-the-art simulation software.

Investigation of Flexible Job Shop with Machine Availability Constraints

“…One of the work centres utilizes only one machine (W6), whereas others make use of three to four machines. Each grey shade in Table II represents a set of parallel, identical machines stationed at work centres named CM (1,3,6), GS (15,21,26), CM (2,6) and M (5,19). From Table II, there are three rows that designate three jobs with processing times pij in parentheses (fifth parameter values: processing times (in minutes) to complete each operation for each job on each machine).…”

“…In real-world manufacturing environments, the operations of a job being scheduled would have different processing times and different processing orders on machines. The jobs would also have agreed delivery dates, and the solution procedure differs as the goal of the scheduling varies [2]. From the practical standpoint, the decision-makers have many concerns about what and how certain measures can improve: (1) throughput rate, (2) customer satisfaction, particularly, on-time deliveries, and (3) cost reduction, for instance, inventory holding cost.…”

A Biased-Randomized Simheuristic for a Hybrid Flow Shop with Stochastic Processing Times in the Semiconductor Industry

“…In the studied problem, the values of processing times follow a stochastic distribution (Section 5) and are not deterministic. Laroque et al (2022) propose an approach to solve a deterministic version of a similar problem. Their approach utilizes a multi-start biased-randomized version of the popular NEH heuristic.…”

“…In Laroque et al (2022), the makespan of each proposed solution is computed using a deterministic discrete-event simulation. Our work extends the previous one by considering stochastic processing times, which obviously represent an additional challenge for any optimization solver.…”

“…Figure 2 illustrates the logic behind our algorithm. A biased-randomized heuristic component takes care of generating new solutions (permutations of jobs) as explained in Laroque et al (2022). Then, a stochastic discrete-event simulation component is responsible for executing the proposed solution in an environment with random processing times, which allows us to get a random observation of the makespan associated with the solution proposed by the heuristic component.…”