Theory and Methodology Production, inventory, and pricing under cost and demand learning eects Steen Jùrgensen a, * , Peter M. Kort b , Georges Zaccour c a Department of Management, Odense University, Campusvej 55, DK-5230 Odense M, Denmark b Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands c GERAD and Department of Marketing,  Ecole des Hautes  Etudes Commerciales, 3000 Chemin de la C^ ote-Sainte-Catherine, Montr eal, Canada H3T 1V6 Received 1 November 1997; accepted 1 June 1998 Abstract The paper considers a monopolist ®rm that plans its production, inventory, and pricing policy over a ®xed and ®nite horizon. The problem is represented by an optimal control model which combines elements from three streams of literature. The ®rst of these is a classical OR area and deals with optimal production and inventory under exogenously given demand conditions. The second is an area of marketing science which studies dynamic pricing under demand learning eects. Demand learning refers to the situation where current demand for a product is in¯uenced by past demand. The third area belongs to microeconomics and industrial organization and is concerned with the eects of learning-by-doing in a ®rm's production process. Learning is re¯ected in a unit production cost that decreases with cumulative production. Using a path-synthezising procedure we obtain closed-form characterizations of optimal production, pricing, and inventory policies. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Production; Inventory; Pricing; Optimal control theory 1. Introduction This paper studies an optimal control problem positioned in the intersection between three streams of research. The ®rst of these streams originates in the inventory and production model of Holt et al. (1960) where the problem was to determine an optimal production and inventory policy facing a time-varying but exogenously given demand. Examples of this type of modeling are found in Thompson et al. (1984) and Teng et al. (1984). Pekelman (1974) introduced product price as an explicit decision variable in the pro- duction-inventory problem but con®ned his interest to a simple speci®cation of the demand function in which the demand rate at time t depends linearly on the price at that speci®c instant. Even if the coecients European Journal of Operational Research 117 (1999) 382±395 www.elsevier.com/locate/orms * Corresponding author. Tel.: 45 66 158 600; fax: 45 65 930 726; e-mail: stj@busieco.ou.dk 0377-2217/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 9 8 ) 0 0 2 7 3 - 2