A Hybrid Biobjective Markov Chain Based Optimization Model for Sustainable Aggregate Production Planning

This research addresses the sustainable aggregate production planning problem by considering the outsourcing option and workforce skill levels as well as taking a Markov process approach for the inventory level. For this purpose, a hybrid biobjective mixed-integer nonlinear programming model featuring a continuous-time Markov chain to accommodate the inventory decision process is developed. The proposed Markov chain approach efficiently describes system dynamics modeling of the production system through a stochastic process. The objective functions are to minimize total cost and total environmental pollution at the same time. To validate the applicability of the methodology and to evaluate the model complexity, three numerical examples are generated based on one of the previous studies in the literature. It is demonstrated that the suggested methodology is able to come up with the final feasible solution based on optimal inventory decisions in less than 65 s. Finally, a number of sensitivity analyses are presented to study the behavior of the objectives under real-world instability and discuss the practical implications and managerial insights. As one of the main findings, it is revealed that the objective functions have no sensitivity to some change intervals of the parameters, which can be analyzed more earnestly by the management in case of the resource allocation process.