{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T03:28:17Z","timestamp":1787887697518,"version":"build-2784847793"},"reference-count":17,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research"],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:p>We analyze a finite horizon, single product, periodic review model in which pricing and production\/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s, S, p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s, S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s, S, p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions, and apply it to provide a characterization of the optimal policy.<\/jats:p>","DOI":"10.1287\/opre.1040.0127","type":"journal-article","created":{"date-parts":[[2004,12,2]],"date-time":"2004-12-02T05:31:46Z","timestamp":1101965506000},"page":"887-896","source":"Crossref","is-referenced-by-count":352,"title":["Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case"],"prefix":"10.1287","volume":"52","author":[{"given":"Xin","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Simchi-Levi","sequence":"additional","affiliation":[{"name":"Operations Research Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"109","reference":[{"key":"B1","volume-title":"Dynamic Programming and Optimal Control","volume":"1","author":"Bertsekas D.","year":"1995"},{"key":"B2","unstructured":"Chan L. M. A., Simchi-Levi D., Swann J. Effective dynamic pricing strategies with stochastic demand.  (2001) (Massachusetts Institute of Technology, Cambridge, MA)"},{"key":"B3","unstructured":"Chen X. Coordinating inventory control and pricing strategies.  (2003) . Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA"},{"key":"B4","unstructured":"Chen X., Simchi-Levi D. A new approach for the stochastic cash balance problem with fixed costs.  (2003) (Massachusetts Institute of Technology, Cambridge, MA)"},{"key":"B5","author":"Chen X.","year":"2004","journal-title":"Math. Oper. 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