A bi-objective inventory routing problem by considering customer satisfaction level in context of perishable product

In this paper, we study a joint inventory and routing problem (IRP) for the food supply chain and we investigate the impact of customer satisfaction level under the optimization of the total expected cost. We propose a new bi-objective mathematical model by taking into account multi capacitated vehicles for perishable products from one supplier to many customers by considering total traveling time. The first objective in our optimization minimizes the different inventory and distribution costs (holding cost, shortage cost, ordering cost, fixed, variable transportation cost and recycling cost) while the second objective considers the customer satisfaction level, which is measured based on delays of vehicles. We consider perishable items and we also manage in this framework their shelf life (expiration date). The proposed framework is modelled as a mixed-integer linear program and is solved by using the software GAMS.