Minimizing Maximum Tardiness in a Distributed Flow Shop Manufacturing Problem under No-Waiting and Sequence Dependent Setup Time Constraints

The distributed no-wait flow-shop manufacturing problem with sequence dependent setup time (DNWFSMP-SDST) is a challenging optimization problem that arises in various industries, including manufacturing and logistics. This problem involves scheduling a set of jobs on multiple machines in a distributed environment, where each job has a specific processing time and requires setup time between different machine transitions. The objective is to minimize the maximum tardiness of all jobs, which represents the maximum delay in completing any job beyond its desired due date. This study addresses the DNWFSMP-SDST optimization problem by employing two algorithms: Nawaz-Enscore-Ham (NEH) and Greedy Randomized Adaptive Search Procedure (GRASP). The NEH is a constructive heuristic that constructs an initial solution by iteratively inserting jobs into a partially ordered sequence. In contrast, GRASP combines a greedy randomized construction phase with a local search procedure to iteratively enhance the initial solution. The simulation study compares NEH and GRASP algorithms for solving DNWFSMP-SDST using bench-marking instance. The results show the pros and cons of each algorithm, helping practitioners make better decisions. Where the NEH algorithm outperform for GRASP technique solving the kind of problem. Overall, this research has enabled us to improve our methods for solving scheduling problems in distributed environments.