Capacity Allocation with Multiple Suppliers and Multiple Demand Classes

We consider the capacity allocation problem for a retailer with multiple suppliers and multiple demand classes. The retailer offers one seasonal product and reserves capacity from multiple suppliers. Customers in different classes are charged with different selling prices for the same product. We analyze the optimal capacity allocation policies with the following three types of customers: (i) patient customers, (ii) impatient customers, and (iii) customers with limited patience. To empower our analysis, we propose a new preservation property of decomposition under a maximization operator. Based on the preservation property, we show that the value function in each period is decomposable for each type of customers. We then characterize the optimal capacity allocation policy for each type of customers and develop an efficient algorithm to obtain the respective optimal policy by exploiting decomposition. We also numerically investigate the optimal policy and show its value against a counterpart static heuristic policy. Finally, we extend our results to systems with multiple products, new capacity additions, etc.