Stochastic capacity allocation, revenue management approach: the existence of modularity property

In the literature, although a few studies can be found regarding the application of revenue management to special cases of Make-to-Order manufacturing systems with stochastic capacity, there is not any study when capacity or demand (or both) are random variables with general distribution function. Therefore, in this paper, an approach is developed to study a more general case of Make-to-Order manufacturing systems based on the concept of revenue management. Due to the random nature of capacity and demand, the exact size of capacity to satisfy the orders is not known at the time of arriving orders. Consequently, the vital decision is either to accept or reject an order at the time of arrival. If an order is accepted but later rejected due to the lack of capacity, a penalty has to be paid to the customer. On the other hand, an order can be rejected by anticipating the capacity shortage at the time its arrival, while there will be some unused capacity at the processing stage. Then, this also results in the loss of revenue. We assume there are two classes of customers. The price paid by the customers of each class or the penalty paid to them is different from those of the other class customers. Although the objective function which represents the expected total revenue is not necessarily concave, this study demonstrates that it has unimodal property and as a result the existence of an optimal solution is guaranteed. This property has been proved previously for special cases where demand or capacity is continuous random variable. This study confirms this property also holds in more general cases. The proposed approach for a variety of scenarios, discrete and mixed random variables, is investigated by simulation techniques.