A bi-objective batch processing problem with dual-resources on unrelated-parallel machines

In this paper, a bi-objective batch processing problem with dual-resources on unrelated-parallel machines is addressed. Typically, both machines and operators as dual-resources are required to process the setup and run of any batch on any machine. The pursuit of this research is motivated by the adoption of the just-in-time philosophy on unrelated-parallel machines, where both the production time and cost are considered. A mathematical programming model is proposed in four layers for simultaneously minimizing the production cost including total cost of tardy and early jobs along with total batch processing cost as well as the makespan with dual-resources. Four bi-objective particle swarm optimization based search algorithms are proposed to efficiently solve the optimization problem for medium- and large-size instances. To reflect the real industry requirements, dynamic machine and operator availability times, dynamic job release times, machine eligibility and capability for processing jobs, batch capacity limitations, machine-dependent setup time, and different skill levels of operators are considered. Several numerical examples are generated by a comprehensive data generation mechanism to compare the search algorithms with respect to four performance indicators. A comparison of small-size instances between performance indicators of the best search algorithm and optimization method shows the same performance to find non-dominated solutions in the final Pareto optimal solutions, while the best search algorithm spreads and extends more in the entire Pareto optimal region and shows that it is less capable in converging to the true Pareto optimal front. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for bi-objective batch processing problem with dual-resources. (C) 2017 Elsevier B.V. All rights reserved.