Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint

Abstract

Recent years have seen a great deal of attention in energy conservation for production and manufacturing activities, particularly for energy-intensive industries. One of the useful strategies in reducing unnecessary energy consumption is to schedule these activities by considering both energy-driven and time-oriented criteria. This scheduling model can make an interaction between the energy consumption and the production cost to realize an efficient and sustainable production process. In this regard, the customers' expectation for due date is another important factor for decision-makers to control the delay in delivery. Making these decisions is extremely difficult due to uncertain circumstances to extract the accurate information of facilities and jobs in advance. Aforementioned issues in the context of urgent need for energy-conservation as well as the advent of globalized and multi-factory manufacture motivate our attempts to address a stochastic multi-objective distributed permutation flow shop scheduling problem by considering total tardiness constraint via minimizing the makespan and the total energy consumption. Due to the uncertainty of the proposed problem, a chance-constrain approach is used to describe decision-makers’ awareness for the total tardiness, and accordingly, a chance-constrained programming model is utilized to formulate this problem. As a complicated optimization problem, a new multi-objective brain storm optimization algorithm incorporating stochastic simulation approach is specifically designed to better solve problem. A comparative study based on a set of benchmark test problems as well as two classical and popular algorithms is provided. The experimental results demonstrate that the proposed algorithm shows a very competitive performance in dealing with the investigated problem.