Development of a multi-period model to minimise logistic costs and maximise service level in a three-echelon multi-product supply chain considering back orders

Abstract

In this paper, a multi-objective multi-period supply chain design and planning problem is introduced. The problem seeks to minimise logistic costs and maximise service level in a three-echelon multi-product supply chain considering back orders. The layers of chain include suppliers, manufacturers and distribution centres. The parts of logistic costs are discussed and modelled while service level is also interpreted as low level of backorder and shortening the delivery time of products to customers. This problem is modelled using a multi-objective mixed integer mathematical programming. Several constraints due to real-world conditions are also considered in the proposed model. As the objective functions, i.e., logistic costs and satisfaction levels are conflictive so a posteriori multi-objective mathematical approach, called efficient epsilon-constraint is proposed to generate several non-dominated solutions on Pareto front of the problem. Illustrated numerical example is solved using proposed approach in order to demonstrate the efficacy and applicability of proposed model and the solution procedure.