Supply chain coordination using wholesale prices with multiple products, multiple periods, and multiple retailers: Bi-level optimization approach

We study a two-level decentralized supply chain that consists of a single manufacturer and multiple retailers. The manufacturer produces and distributes multiple products to multiple retailers. The retailers face time varying demands. A multi-product multi-period wholesale price coordination technique is proposed to restore the efficiency of the decentralized supply chain. A nonlinear bi-level programming model is developed to coordinate the supply chain. The manufacturer uses the optimal multi-period wholesale prices solved from the proposed coordination model as the incentive to change retailers' decisions, thereby improving the supply chain performance. Due to the complexity, the nonlinear bi-level model is transformed into an equivalent mixed integer linear programming model and solved for the optimal solution. The numerical experiments show that the wholesale prices determined by the model can induce coordinated decisions in all cases. When the manufacturer's profit is maximized with a minimum profit increase for the retailers of at least 2%, centralized decisions are achieved. The multi-period wholesale price mechanism can adjust the profit sharing among members. A discount on wholesale prices is given to avoid the overtime cost at the manufacturer. The benefits of using our model over the decentralized model are greater when the production setup or holding costs at the manufacturer is high and the marginal cost of adding a product to an order or the cost of placing an order at retailers is low. We found that as the total demand increases, the manufacturer should increase the number of discount periods and the summation of discounts to spread out the production time.