Selling Finite Capacity in Bulks*

We consider a firm that owns a limited capacity for the delivery of services or for the production of customized products. Potential buyers specify the amount of capacity they will require for the execution of their intended services, goods or projects. Based on the size of the requirement, the firm makes a bid while being challenged in various ways: (1) it only knows the underlying probability function from which its customers’ reservation prices are drawn, (2) arrival of additional future requests is stochastic, and, (3) the firm knows in advance neither the magnitude of these potential requests nor the buyer's reservation price. The firm aims to maximize its expected profit by choosing its pricing mechanism. The fact that capacity is demanded in varying amounts distinguishes this problem from most available literature in which standard sizes are sold or partial fulfillment and displacement are permitted. Lacking such allowances presents a new challenge to the firm as in conjunction with pricing it should also address the issue of various sizes requests’ compatibility to achieve optimal utilization of its capacity in order to maximize expected profit. In this article, we consider two approaches of handling this problem: myopic and foresighted. We formulate and analyze the problem to obtain the firm's optimal bidding decisions as well as managerial insight about the optimal bid level and its important role in coordinating buyers’ requests. Furthermore, due to this role, pricing patterns in this environment are different than those in standard unit sales.