Optimization of Supply Chain Systems with Price Elasticity of Demand

A centralized multiechelon, multiproduct supply chain network is presented in a multiperiod 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. 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 unbounded derivatives in the nonlinear objective function are handled with an approximation, with guaranteed bounds on the loss of optimality. The approach is illustrated on a multiechelon, multiproduct supply chain network.