Hybrid flow shop batching and scheduling with a bi-criteria objective

Abstract

This paper addresses the hybrid flow shop batching and scheduling problem where sequence-dependent family setup times are present and the objective is to simultaneously minimize the weighted sum of the total weighted completion time and total weighted tardiness. In particular, it disregards the group technology assumptions by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A benchmark of small size problems is considered to show the benefits of batching on group scheduling. Since the problem is strongly NP-hard, several algorithms based upon tabu search are developed at three levels, which move back and forth between batching and scheduling phases. Two algorithms incorporate tabu search into the framework of path-relinking to exploit the information on good solutions. These tabu search/path-relinking algorithms comprise several distinguishing features including two relinking procedures to effectively construct paths and the stage-based improvement procedure to consider the move interdependency. The best tabu search algorithm as a local search algorithm is compared to a population-based algorithm, and the superiority of the former over the latter is shown using a statistical experiment. The initial solution finding mechanism is implemented to trigger the search into the solution space. The efficiency and effectiveness of the best algorithm is verified with the help of the results found by CPLEX. The results show that the best algorithm, based on tabu search/path relinking and the stage-based improvement procedure, could find solutions at least as good as CPLEX, but in drastically shorter computational time. In order to reflect the real industry requirements, dynamic machine availability times, dynamic job release times, machine eligibility and machine capability for processing jobs, desired lower bounds on batch sizes, and job skipping are considered.