Optimising the design of a supply chain network with economies of scale using mixed integer programming

In this paper, we formulate and analyse the design of a supply chain network where the concept of economies of scale in transportations are considered. Having the demand of different products from various retailers, the model determines the numbers and locations of the consolidation and distribution centres. It also determines the routes and lot sizes of the shipments to fulfil the demand by the retailers. Piecewise linearisation technique is utilised to transform the non‐linear concave‐cost function of the transportation into a linear form. Using this linearisation technique, a mixed integer linear programming model is developed that can be efficiently solved using a branch‐and‐bound‐based optimisation package. Numerical examples are presented to demonstrate the features of the proposed model and the impacts of certain input parameters on the design of the supply chain network.