Joint economic lot-sizing problem for a two-stage supply chain with price-sensitive demand

This paper studies joint economic lot-sizing problem (JELS) for a single vendor-single buyer system while demand is dependent on selling price. This problem is modeled for geometric shipment policy and a solution procedure is developed to find a well approximation of the global optimal solution of the problem. Since the equal size shipment policy or geometric shipment policy may yield more joint profit compared to each other, the most important factor that affects the break-even-point of geometric and equal-size policies is determined. The JELS problem for dependent demand is also modeled for geometric-then-equal size and optimal shipment policies. Solution procedures to find a well approximation of the global optimum of each problem are also developed for these models. The models and solution procedures for geometric, geometric-then-equal size and shipment policies are novel in the literature. Numerical results of the models show considerable improvement in the joint profit of the chain compared to lot-for-lot and equal-size shipment policies for chains with price-sensitive demand and could be very interesting for supply chain coordinators and practitioners.