Optimization of Supply Chain Systems with Price Elasticity of Demand

A centralized multi-echelon, multi-product supply chain network is presented in a multi-period setting with products that show varying demand against price. An important consideration in such complex supply chains is to maintain system performance at high levels for varying demands that may be sensitive to product price. In order to examine the price-centric behavior of the customers, the concept of price elasticity of demand is addressed. The proposed approach includes many realistic features of typical Supply Chain Systems such as production planning and scheduling, inventory management, transportation delay, transportation cost and transportation limits. In addition, the proposed system can be extended to meet unsatisfied demand in future periods by backordering. Effects of the elasticity in price demand in production and inventory decisions are also examined. The supply chain model is formulated as a convex mixed-integer nonlinear programming problem. Reformulations are presented to make the problem tractable. The differential equations are reformulated as difference equations and the unbounded derivative problem occured due to the non-linear objective function is dealed with an approximation. The approach is illustrated on a multi-echelon, multi-product supply chain network.