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Coordinating inventory control and pricing strategies for perishable products. (English) Zbl 1302.91097
Summary: We analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon. In each period, demand depends on the price of the current period plus an additive random term. Inventories can be intentionally disposed of, and those that reach their lifetime have to be disposed of. The objective is to find a joint pricing, ordering, and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost, inventory holding and backlogging or lost-sales penalty cost, and disposal cost. Employing the concept of \(L^\natural\)-concavity, we show some monotonicity properties of the optimal policies. Our results shed new light on perishable inventory management, and our approach provides a significantly simpler proof of a classical structural result in the literature. Moreover, we identify bounds on the optimal order-up-to levels and develop an effective heuristic policy. Numerical results show that our heuristic policy performs well in both stationary and nonstationary settings. Finally, we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes.

91B24 Microeconomic theory (price theory and economic markets)
90B05 Inventory, storage, reservoirs
Full Text: DOI
[1] American Association of Blood Banks (AABB) (2009) The 2009 National Blood Collection and Utilization Survey Report. Bethesda, Maryland, MD. Accessed March 18, 2013, http://www.aabb.org/programs/biovigilance/nbcus/Documents/09-nbcus-report.pdf.
[2] Bertsekas DP (1995) Dynamic Programming and Optimal Control, Vol. I (Athena Scientific, Belmont, MA).
[3] Chan LMA, Max Shen ZJ, Simchi-Levi D, Swann J (2004) Coordination of pricing and inventory. Simchi-Levi D, Wu SD, Max Shen ZJ, eds. Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (Kluwer Academic Publishers, Boston).
[4] Chen X, Simchi-Levi D (2004a) Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case. Oper. Res. 52(6):887-896. [Abstract] · Zbl 1165.90308
[5] Chen X, Simchi-Levi D (2004b) Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case. Math. Oper. Res. 29(3):698-723. [Abstract] · Zbl 1082.90025
[6] Chen X, Simchi-Levi D (2006) Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The continuous review model. Oper. Res. Lett. 34:323-332. · Zbl 1098.90001
[7] Chen X, Simchi-Levi D (2012) Pricing and inventory management. Philips P, Özer Ö, eds. Oxford Hanbook of Pricing Management (Oxford University Press, UK), 784-822.
[8] Elmaghraby W, Keskinocak P (2003) Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions. Management Sci. 49(10):1287-1309. [Abstract] · Zbl 1232.90042
[9] Federgruen A, Heching A (1999) Combined pricing and inventory control under uncertainty. Oper. Res. 47(3):454-457. [Abstract] · Zbl 0979.90004
[10] Federgruen A, Heching A (2002) Multilocation combined pricing and inventory control. Manufacturing Service Oper. Management 4(4):275-295. [Abstract]
[11] Ferguson ME, Koenigsberg O (2007) How should a firm manage deteriorating inventory?Production Oper. Management 16(3):306-321.
[12] Food Market Institute (2012) Supermarket sales by department–Percent of total supermarket sales. Accessed January 20, 2012, http://www.fmi.org/docs/facts-figures/grocerydept.pdf.
[13] Fries B (1975) Optimal ordering policy for a perishable commodity with fixed lifetime. Oper. Res. 23(1):46-61. [Abstract] · Zbl 0324.90020
[14] Huh W, Janakiraman G (2008) (s, S) optimality in joint inventory-pricing control: An alternate approach. Oper. Res. 56(3):783-790. [Abstract] · Zbl 1167.90332
[15] Huh W, Janakiraman G (2010) On the optimal policy structure in serial inventory systems with lost sales. Oper. Res. 58(2):481-491. [Abstract] · Zbl 1226.90012
[16] Karaesmen IZ, Scheller-Wolf A, Deniz B (2011) Managing perishable and aging inventories: Review and future research directions. Kempf KG, Keskinocak P, Uzsoy P, eds. Planning Production and Inventories in the Extended Enterprise (Springer, Berlin), 393-436.
[17] Kocabiyikoglu A, Popescu I (2011) An elasticity perspective on the newsvendor with price sensitive demand. Oper. Res. 59(2):301-312. [Abstract]
[18] Li Y, Cheang B, Lim A (2012) Grocery perishables management. Prod. Oper. Management 21(3):504-517.
[19] Li Y, Lim A, Rodrigues B (2009) Pricing and inventory control for a perishable product. Manufacturing Service Oper. Management 11(3):538-542. [Abstract]
[20] Lu Y, Song JS (2005) Order-based cost optimization in assemble-to-order systems. Oper. Res. 53(1):151-169. [Abstract] · Zbl 1165.90330
[21] Murota K (2003) Discrete Convex Analysis. SIAM Monographs on Discrete Mathematics and Applications (Society for Industrial and Applied Mathematics, Philadelphia). · Zbl 1029.90055
[22] Murota K (2005) Note on multimodularity and L-convexity. Math. Oper. Res. 30(3):658-661. [Abstract] · Zbl 1082.90071
[23] Murota K (2009) Recent developments in discrete convexity. Cook W, Lovasz L, Vygen J, eds. Recent Developments in Combinatorial Optimization (Springer, Berlin). · Zbl 1359.05020
[24] Nahmias S (1975) Optimal ordering policies for perishable inventory-II. Oper. Res. 23(4):735-749. [Abstract] · Zbl 0316.90022
[25] Nahmias S (1976) Myopic approximations for the perishable inventory problem. Management Sci. 22(9):1002-1008. [Abstract] · Zbl 0348.90056
[26] Nahmias S (1982) Perishable inventory theory: A review. Oper. Res. 23(4):735-749. [Abstract] · Zbl 0316.90022
[27] Nahmias S (2011) Perishable Inventory Systems. International Series in Operations Research and Management Science, Vol. 160 (Springer, New York).
[28] Nahmias S, Pierskalla WP (1973) Optimal ordering policies for a product that perishes in two periods subject to stochastic demand. Naval Res. Logist. Quart. 20:207-229. · Zbl 0266.90020
[29] Nahmias S, Schmidt CP (1986) An application of the theory of weak convergence to the dynamic perishable inventory problem with discrete demand. Math. Oper. Res. 11(1):62-69. [Abstract] · Zbl 0601.90034
[30] National Supermarket Research Group (2006) 2005 Supermarket shrinking report. Assessed January 20, 2012, http://www.securestoreadvantage.com/pdfs/Supermarket_Survey_Executive_Summary.pdf.
[31] Pang Z (2011) Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Oper. Res. Lett. 39:375-379. · Zbl 1235.90014
[32] Pang Z, Chen F, Feng Y (2012) A note on the structure of joint inventory-pricing control with leadtimes. Oper. Res. 60(3):581-587. [Abstract] · Zbl 1260.90023
[33] Petruzzi NC, Dada M (1999) Pricing and the newsvendor model: A review with extensions. Oper. Res. 30(4):680-708.
[34] Pierskalla WP (2004) Supply chain management of blood banks. Brandeau M, Sainfort F, Pierskalla WP, eds. Operations Research and Health Care–A Handbook of Methods and Applications (Kluwer Academic Publishers, New York), 104-145.
[35] Simchi-Levi D, Chen X, Bramel J (2014) The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, 3rd ed. (Springer-Verlag, New York). · Zbl 1327.90020
[36] Song Y, Ray S, Boyaci T (2009) Optimal dynamic joint inventory-pricing control for multiplicative demand with fixed order costs and lost sales. Oper. Res. 57(6):245-250. [Abstract] · Zbl 1181.90024
[37] Webber B, Herrlein S, Hodge G (2011) Planet retail: The challenge of food waste. Accessed September 2012, http://www-03.ibm.com/press/uk/en/presskit/35447.wss.
[38] Xue Z, Ettl M, Yao DD (2012) Managing freshness inventory: Optimal policy, bounds and heuristics. Working paper, IBM T. J. Watson Research Center, Yorktown Heights, NY.
[39] Yano CA, Gilbert SM (2003) Coordinated pricing and production/procurement decisions: A review. Chakravarty A, Eliashberg J, eds. Managing Business Interfaces: Marketing, Engineering and Manufacturing Perspectives (Kluwer Academic Publishers, Boston).
[40] Zipkin P (2008) On the structure of lost-sales inventory models. Oper. Res. 56(4):937-944. [Abstract] · Zbl 1167.90369
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