Bi-criteria group scheduling in hybrid flowshops

We consider a group scheduling problem in a hybrid flowshop where the parallel machines in one or more stages of the flowshop are unrelated and have different run times for the same job. The objective of the problem is to simultaneously decrease the producer's cost by minimizing the Work-In-Process inventory (WIP) or equivalently the total weighted completion time, and increase the customers' satisfaction by minimizing the total weighted tardiness. All of the jobs and machines may not be ready at time zero, meaning that they can be released at different times during the scheduling period. The setup time required to switch between processing jobs from different families is considered to be sequence-dependent. A Mixed-Integer Linear Programming model is developed to mathematically represent this problem and obtain optimal solutions for small size problems. Since the problem is among the strongly NP-hard problems, four efficient algorithms based on tabu search are proposed to find optimal/near optimal solutions. The efficacy of these algorithms is compared to each other by means of a comprehensive statistical analysis, and the best algorithm is identified. Furthermore, the efficiency and effectiveness of the proposed search algorithms are verified by comparing the results of these algorithms with optimal solutions obtained from CPLEX for small size problems.