A bi-objective MILP model for lot sizing and scheduling problem: possibilistic fuzzy goal programming approach

This paper proposes a bi-objective mixed-integer linear programming model for formulating a lot- sizing and scheduling problem for the perishable yogurt industry under demand uncertainty. The objectives of the proposed model are to simultaneously minimize the overall cost and the total production completion time.  The proposed MILP formulation integrates many distinctive features of yogurt processing, including shelf-life constraints, setups, packaging rates, minimum and maximum lot size limits, future time for holding products, and fuzzy demand. Additionally, the proposed model, including inventory control, is a multi-product and multi-period model hence, it is categorized as an operational-strategic model. We introduce a hybrid approach focused on fuzzy possibility programming and a fuzzy goal programming approach for solving the suggested bi-objective model, where possibility, necessity and credibility measures are adopted according to the decision makers’ preference.  Compared to the traditional model of lot sizing and scheduling, better decision-making and sensitivity analysis for DMs can be made based on the three obtained efficiency values. Data from the yogurt plant were used to assess the feasibility of the proposed model and solution approach. The results obtained from applying the method and sensitivity analysis showed the effectiveness of the mathematical formulation as well as the proposed solution method.