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Published online ahead of print August 27, 2007

OPERATIONS RESEARCH
Articles in Advance, pp. 1–19 issn 0030-364X eissn 1526-5463

informs

®

doi 10.1287/opre.1070.0411 © 2007 INFORMS

Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109, hsahn@umich.edu Desautels Faculty of Management, McGill University, Montréal, Quebec, Canada H3A 1G5, mehmet.gumus@mcgill.ca Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720, kaminsky@ieor.berkeley.edu

Hyun-soo Ahn

Mehmet Gümüs ¸

Philip Kaminsky

In most deterministic manufacturing decision models, demand is either known or induced by pricing decisions in the period that the demand is experienced. However, in more realistic market scenarios consumers make purchase decisions with respect to price, not only in the current period, but also in past and future periods. We model a joint manufacturing/pricing decision problem, accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods. We formulate a mathematical programming model and develop solution techniques. We identify structural properties of our models and develop closed-form solutions and effective heuristics for various special cases of our models. Finally, we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights. Subject classifications: inventory/production: uncertainty, deterministic; planning horizons; operating characteristics; marketing: pricing. Area of review: Manufacturing, Service, and Supply Chain Operations. History: Received February 2004; revisions received July 2005, October 2006; accepted November 2006. Published online in Articles in Advance.

1. Introduction
In recent years, as manufacturing and supply chains have become more and more efficient, the conflict between production planning and marketing has become more apparent. For example, in recent discussions with the manager of a bread production plant associated with a major supermarket chain, the manager indicated to us that the most significant factor leading to increased inventory levels and decreased efficiency in his plant is the unpredictability of demand due to promotional and pricing decisions made by the marketing group. As a result, there is a growing research literature focusing on joint marketing decision making and production planning. Its objective is to develop approaches that avoid conflicting marketing and operations planning decisions by integrating marketing/pricing decisions and manufacturing decisions to jointly achieve a common objective. A variety of aspects of joint pricing and manufacturing models have been analyzed in the operations management and marketing literature. The models vary from constant demand, EOQlike frameworks, to nonstationary discrete and continuoustime frameworks. Some models allow no replenishment during a price planning horizon (appropriate for perishable or fashion goods), while others consider models which allow production or inventory replenishment over time. The 1

models also differ in assumptions on demand and consumer behavior. A considerable body of work has been developed that considers joint pricing and production models of perishable or seasonal goods—typically referred to as revenue management—traditionally applied to the airline, hotel, and car rental industries, and similar techniques (such as mark-down pricing) have been adopted for perishable or seasonal products. Lazear (1986), Gallego and van Ryzin (1994, 1997), Bitran and Mondschein (1997), Subrahmanyan and Shoemaker (1996), Aviv and Pazgal (2005), and Elmaghraby et al. (2006) consider revenue management problems related to our models, and the area is surveyed in...
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