A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Sustainable production scheduling considers economic, environmental, and social criteria while generating the schedule of jobs in a factory. This paper formulates a Sustainable Distributed Permutation Flow-shop Scheduling Problem (SDPFSP) by considering that each machine used to process the jobs can be operated under different operating modes ranging from manual to automatic. In addition, the energy consumption as well as the number of operators required and the number of working days lost to train them have been taken into account in the proposed SDPFSP. Most importantly, this study considers multiple uncertainties including machine breakdowns, variable processing times, and random arrivals of new jobs. These uncertainties are formulated by a scenario-based robust optimization model as the main significant contribution of this research where the goal is to minimize the expected makespan and its deviations from probabilistic scenarios. To deal with this complex optimization problem, another innovation of this research is to propose a new metaheuristic algorithm named Adaptive Large Neighborhood Search (ALNS). The proposed algorithm uses four constructive heuristics to identify an initial solution. Then, the current solution is destroyed and repaired efficiently by the use of removal and construction heuristics to explore the search space. Thus, a local search algorithm is developed to exploit new solutions in this search space. After implementing the proposed ALNS, an extensive computational study is provided to analyze the calibration of parameters and components of the proposed algorithm. Then, a comparison of the results with those obtained using the exact solver and state-of-the-art metaheuristics found in the literature is provided. The SDPFSP is validated through a numerical example of a flow-shop production system. Based on the results derived from our numerical example, we can conclude that our solution holds the potential to improve energy consumption by 24%, bolster job opportunities by 67%, and decrease lost workdays by 18%. Moreover, the impact of robust optimization parameters and uncertainties on optimality is investigated by performing sensitivity analysis. Finally, an in-depth discussion is provided to identify the main findings and recommendations of this research for flow-shop production systems to highlight the performance of our scenario-based robust model and the ALNS algorithm.