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Pricing, Production, and Inventory Policies for Manufacturing with Stochastic Demand and Discretionary Sales

Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, 250 Durham Hall, Blacksburg, Virginia 24061-0118
Department of Civil and Environmental Engineering and the Engineering Systems Division, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive, Atlanta, Georgia 30332-0205
achan{at}vt.edu
dslevi{at}mit.edu
jswann{at}isye.gatech.edu

We study determining prices and production jointly in a multiple period horizon under a general, nonstationary stochastic demand function with a discrete menu of prices. We assume that the available production capacity is limited and that unmet demand is lost. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand is lost. We analyze and compare partial planning or delayed strategies. In delayed strategies, one decision may be planned in advance, whereas a second decision is delayed until the beginning of each time period, after observing the results of previous decisions. For example, in delayed production (delayed pricing), pricing (production) is determined at the beginning of the horizon, and the production (pricing) decision is made at the beginning of each period before new customer orders are received. A special case is where a single price is chosen over the horizon. We describe policies and heuristics for the strategies based on deterministic approximations and analyze their performances. Computational analysis yields additional insights about the strategies, such as that delayed production is usually better than delayed pricing except sometimes when capacity is tight. On average, the delayed production (pricing) heuristic achieved 99.3% (99.8%) of the corresponding optimal strategy.

Key Words: pricing; production; inventory control; discretionary sales; worst-case analysis
History: Received: January 15, 2004; accepted: August 16, 2005.