A conic quadratic model for supply chain network design under hub, capacity, delay and lost sale

In this paper, mathematical models are proposed for simultaneously modeling location and inventory control decisions in a four echelon supply chain network considering capacity. The echelons considered in this paper include suppliers, warehouses, hubs and retailers. The aim of the model is to minimize the location, transportation and inventory control costs. Hence, a non-linear mixed integer programming model is provided. The proposed model is then transformed to a conic mixed integer programming model in order to benefit from the higher solving speed of the commercial packages. To compare the different conditions of the inventory control, lost sale and delay strategies are also considered. The computational results show the reliability of the model in different inventory strategies and shorter required solution time for conic quadratic model. Therefore, the application of this formulating can be beneficial for large scale problems using commercial software.