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A multi-period profit maximizing model for retail supply chain management: An integration of demand and supply-side mechanisms. (English) Zbl 0961.90004

Summary: We present a multi-period inventory and pricing model for a single product, where the product has a fixed life perishability for a certain number of periods. This problem has significant importance for an efficient operation of the marketing/manufacturing interface at the retail end of the supply chain. The profit maximization problem is modeled as a dynamic program, and the Wagner-Whitin dynamic programming recursions are developed for both perishable and nonperishable products. The structural properties of the model are investigated, and it is shown that the maximum profit function is continuous piecewise concave. Two efficient search heuristics are presented, and the results are compared with benchmark optimum values. The heuristics have been extensively tested and the results indicate that the proposed approach is robust, efficient and practically viable. Directions for future research are presented.

MSC:

90B05 Inventory, storage, reservoirs
90C39 Dynamic programming

Software:

Mathematica
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References:

[1] Jeuland, A.P., Dolan, R.J., 1982. An aspect of new product planning: Dynamic pricing. In: Zoltners, A.A. (Ed.), Marketing Planning Models, TIMS Studies in the Management Sciences, vol. 18. North-Holland, New York
[2] Arrow, K.A.; Harris, T.E.; Marschak, J., Optimal inventory policy, Econometrica, 19, 250-272, (1951) · Zbl 0045.23205
[3] Arrow, K.A., Karlin, S., Scarf, H.E. (Ed.), 1958. Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford, CA · Zbl 0079.36003
[4] Bazaraa, M.S., Shetty, C.M., 1979. Nonlinear Programming: Theory and Algorithms. Wiley, New York · Zbl 0476.90035
[5] Bensoussan, A., Proth, J.M., 1982. Inventory planning in a deterministic environment concave cost setup in discrete and continuous time. In: Feichtinger, G. (Ed.), Optimal Control Theory and Economic Analysis. North-Holland, Amsterdam · Zbl 0513.90020
[6] Blattberg, R.C.; Eppen, G.C.; Lieberman, J., A theoretical and empirical evaluation of price deals for consumer nondurables, Journal of marketing, 45, 116-129, (1981)
[7] Chen, C.; Min, K.J., A multiproduct EOQ model with pricing consideration - T.C.E Cheng’s model revisited, Computers and industrial engineering, 26, 787-794, (1994)
[8] Cheng, T.C.E., An EOQ model with pricing consideration, Computers and industrial engineering, 18, 529-534, (1990)
[9] Dolan, R.J.; Jeuland, A.P., Experience curves and dynamic demand models: implications for optimal pricing strategies, Journal of marketing, 45, 52-62, (1981)
[10] Eppen, G.D.; Gould, F.J.; Pashigian, B.P., Extensions of the planning horizons theorem in the dynamic lot size model, Management science, 15, 268-277, (1969) · Zbl 0172.44102
[11] Gallego, G.; van Ryzin, G., Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Management science, 40, 999-1020, (1994) · Zbl 0816.90054
[12] Gold, F., 1981. Modern Supermarket Operations, 3rd ed. Fairchild Publications, New York
[13] Graves, et al., 1993. Handbooks in OR&MS, vol. 4. Elsevier, Amsterdam
[14] Hax, A.C., Candea, D., 1984. Production and Inventory Management. Prentice-Hall, Englewood Cliffs, NJ
[15] Kalish, S., Monopolistic pricing with dynamic demand and production cost, Marketing science, 2, 135-159, (1983)
[16] Kunreuther, H.; Schrage, L., Joint pricing and inventory decisions for constant priced items, Management science, 19, 732-738, (1973) · Zbl 0255.90010
[17] Ladany, S.; Sternlieb, A., The interaction of economic ordering quantities and marketing policies, AIIE transactions, 6, 35-40, (1974)
[18] Lazear, E.P., Retail pricing and clearance sales, American economic review, 76, 14-32, (1986)
[19] Lee, W.J., Determining order quantity and selling price by geometric programming: optimal solution, bounds and sensitivity, Decision sciences, 24, 76-87, (1993)
[20] Lundin, R.A.; Morton, T.E., Planning horizons for the dynamic lot size model: zabel vs protective procedures and computational results, Operations research, 23, 711-734, (1975) · Zbl 0317.90028
[21] Monroe, K.B.; Della Bitta, J., Models for pricing decisions, Journal of marketing research, 15, 413-428, (1978)
[22] Naddor, E., 1966. Inventory Systems. Wiley, New York · Zbl 0315.90019
[23] Nahmias, S., Perishable inventory theory: A review, Operations research, 30, 680-708, (1982) · Zbl 0486.90033
[24] Pashigian, B.P., Demand uncertainty and sales: A study of markdown pricing, American economic review, 78, 953-963, (1988)
[25] Polatoglu, L.H., Optimal order quantity and pricing decisions in single period inventory systems, International journal of production economics, 23, 175-185, (1991)
[26] Rajan, A.; Rakesh, A.; Steinberg, R., Dynamic pricing and ordering decisions by a monopolist, Management science, 38, 240-262, (1992) · Zbl 0763.90016
[27] Rao, V.R., Pricing research in marketing: the state of the art, Journal of business, 57, S39-S60, (1984)
[28] Robinson, B.; Lakhani, C., Dynamic price models for new-product planning, Management science, 21, 1113-1122, (1975) · Zbl 1231.90252
[29] Starr, K.M., Miller, W.D., 1962. Inventory control: Theory and practice. Prentice-Hall, Englewood Cliffs, NJ
[30] Varian, H.R., A model of sales, American economic review, 70, 651-659, (1980)
[31] Wagner, H.M.; Whitin, T.M., Dynamic version of the economic lot size model, Management science, 5, 89-96, (1958) · Zbl 0977.90500
[32] Wernerfelt, B., A special case of dynamic pricing policy, Management science, 32, 1562-1566, (1986)
[33] Wilson, R.H., 1934. A scientific routine for stock control. Harvard Business Review, 13
[34] Winston, W.L., 1996. Operations Research: Applications and Algorithms, 3rd ed. Duxbury Press, Pacific Grove, CA · Zbl 0723.90048
[35] Wolfram, S., 1991. Mathematica: A System for Doing Mathematics by Computer, 2nd ed. Addison-Wesley, Reading, MA · Zbl 0671.65002
[36] Zabel, E., Some generalizations of an inventory planning horizon theorem, Management science, 10, 465-471, (1964)
[37] Zangwill, W.I., The piecewise concave function, Management science, 13, 900-912, (1967) · Zbl 0171.18203
[38] Zangwill, W.I., A backlogging model and a multi-echelon model of a dynamic economic lot size production system – a network approach, Management science, 15, 506-527, (1969) · Zbl 0172.44603
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