A mixed-integer linear programming model for multiechelon and multimodal supply chain system considering carbon emission

Considering carbon emissions when making supply chain decisions has been an essential contributor for keeping this world more sustainable. This paper presents a mixed-integer linear programming (MILP) model to optimize production and transportation decision where the transportation activities involve a multimodal combination. The proposed mathematical model was aimed at minimizing the total costs incurred from supply chain activities as well as the emissions generated. Carbon cap is used to ensure that the emissions produced in the whole activities do not exceed the allowable limit. In this research, we address a multi-product, multi-plant, multi-departure, and arrival stations where multiple customers are to be served for multiple periods. The numerical tests show that the demand, carbon tax, and distance significantly affected the total emissions and the total costs. Interestingly, we observed that the decisions are much more affected by the logistical costs rather than the emission costs. The model presented in this paper can assist the decision makers to make production, delivery, and inventory decisions when multi-modal transportation is involved.