Capacity rationing decision procedures with order profit as a continuous random variable

When expected demand is more than available capacity, a make-to-order manufacturer should take the more profitable orders and reject the less profitable orders in order to better allocate its limited capacity and maximize its profit. However, various orders will arrive at different times in the future, so the manufacturer cannot look at all the order inquiries at the same time and choose the most profitable ones. When an order inquiry arrives, the manufacturer must promptly determine, without knowing exactly what the future orders might be, whether to accept the order or to reject the order, thus reserving the capacity for future more profitable orders. This study focuses on such an order selection decision problem under the following assumptions: (1) the arrival of future customer orders is a Poisson process; (2) the capacity requirement of a future customer order is a continuous random variable; and (3) the profit per unit capacity used by an order is also a continuous random variable. Under the stochastic problem assumptions, this study investigates two decision procedures that determine whether to accept or to reject an order inquiry based on the available information, including (1) current available manufacturing capacity, (2) capacity requirement by the order, and (3) the profit per unit capacity of the order. One procedure is called static probability capacity rationing decision procedure (SPCR); the other one is called dynamic stochastic capacity rationing decision procedure (DSCR). Simulation experiments are conducted to validate the proposed procedures. An optimal solution method, that uses 0-1 knapsack problem formulation to obtain the decisions with perfect information, is used to measure the effectiveness of the proposed procedures. The results show that the approach utilizing DSCR outperforms other approaches by providing the highest profit and is also very robust under various problem conditions.