An effective zero-inventory-ordering policy for a single-warehouse multiple retailer problem with a modified all-unit discount

- This study considers a single product coordination model.
- In the model, the supplier replenishes all the buyers to minimize total system costs.
- It can obtain the optimal number of deliveries, shipping points and shipping quantities.

A warehouse is an important value-added service hub between a supplier, a retailer and a customer in a supply chain system. In order to encourage the retailer to purchase a large volume of goods and save in transportation costs, a modified all-unit discount cost structure is often used by warehouses. However, Chan, Muriel, Shen, and Simchi-Levi (2002) noted that the modified all-unit discount cost structure is an NP-hard problem. It is difficult to obtain the optimal solution for this problem. Therefore, Chan et al. developed a novel heuristic algorithm to solve a single-warehouse multiple retailer problem with a modified all-unit discount cost structure that was close to the optimal solution. This paper proposes an exact strategy to deal with the same problem that gives the optimal solution in polynomial time, without the need for binary variables, and regardless of the number of breakpoints. The proposed solution is also successfully demonstrated and can be extended to solve arbitrary piecewise linear functions.