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Management of Multi-Item Retail Inventory Systems with Demand Substitution

Author

Listed:
  • Stephen A. Smith

    (Operations and Management Information Systems, Leavey School of Business, Santa Clara University, Santa Clara, CA 95053)

  • Narendra Agrawal

    (Operations and Management Information Systems, Leavey School of Business, Santa Clara University, Santa Clara, CA 95053)

Abstract

Customers for retail merchandise can often be satisfied with one of several items. Accounting for demand substitution in defining customer service influences the choice of items to stock and the optimal inventory level for each item stocked. Further, when certain items are not stocked, the resulting substitutions increase the demand for other items, which also affects the optimal stock levels. In this paper, we develop a probabilistic demand model for items in an assortment that captures the effects of substitution and a methodology for selecting item inventory levels so as to maximize total expected profit, subject to given resource constraints. Illustrative examples are solved to provide insights concerning the behavior of the optimal inventory policies, using the negative binomial demand distribution, which has performed well in fitting retail sales data.

Suggested Citation

  • Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:1:p:50-64
    DOI: 10.1287/opre.48.1.50.12443
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    References listed on IDEAS

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    1. John W. Mamer & Stephen A. Smith, 1982. "Optimizing Field Repair Kits Based on Job Completion Rate," Management Science, INFORMS, vol. 28(11), pages 1328-1333, November.
    2. Lawrence J. Watters, 1967. "Letter to the Editor—Reduction of Integer Polynomial Programming Problems to Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 15(6), pages 1171-1174, December.
    3. Morris A. Cohen & Narendra Agrawal & Vipul Agrawal & Ananth Raman, 1995. "Analysis of Distribution Strategies in the Industrial Paper and Plastics Industry," Operations Research, INFORMS, vol. 43(1), pages 6-18, February.
    4. Jain, Dipak C & Vilcassim, Naufel J & Chintagunta, Pradeep K, 1994. "A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 317-328, July.
    5. David W. Pentico, 1974. "The Assortment Problem with Probabilistic Demands," Management Science, INFORMS, vol. 21(3), pages 286-290, November.
    6. Edward J. McGavin & James E. Ward & Leroy B. Schwarz, 1997. "Balancing Retailer Inventories," Operations Research, INFORMS, vol. 45(6), pages 820-830, December.
    7. Narendra Agrawal & Stephen A. Smith, 1996. "Estimating negative binomial demand for retail inventory management with unobservable lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 839-861, September.
    8. Rachelle S. Klein & Hanan Luss & Uriel G. Rothblum, 1993. "Minimax Resource Allocation Problems with Resource-Substitutions Represented by Graphs," Operations Research, INFORMS, vol. 41(5), pages 959-971, October.
    9. Morris A. Cohen & Paul R. Kleindorfer & Hau L. Lee, 1989. "Near-Optimal Service Constrained Stocking Policies for Spare Parts," Operations Research, INFORMS, vol. 37(1), pages 104-117, February.
    10. Chand, Suresh & Ward, James E. & Kevin Weng, Z., 1994. "A parts selection model with one-way substitution," European Journal of Operational Research, Elsevier, vol. 73(1), pages 65-69, February.
    11. David W. Pentico, 1976. "The Assortment Problem with Nonlinear Cost Functions," Operations Research, INFORMS, vol. 24(6), pages 1129-1142, December.
    12. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
    13. Peter Tryfos, 1985. "Technical Note—On the Optimal Choice of Sizes," Operations Research, INFORMS, vol. 33(3), pages 678-684, June.
    14. Shelby Brumelle & Daniel Granot, 1993. "The Repair Kit Problem Revisited," Operations Research, INFORMS, vol. 41(5), pages 994-1006, October.
    15. Ricardo Ernst & David F. Pyke, 1992. "Component part stocking policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 509-529, June.
    16. Steven Nahmias & Stephen A. Smith, 1994. "Optimizing Inventory Levels in a Two-Echelon Retailer System with Partial Lost Sales," Management Science, INFORMS, vol. 40(5), pages 582-596, May.
    17. Kamran Moinzadeh & Charles Ingene, 1993. "An Inventory Model of Immediate and Delayed Delivery," Management Science, INFORMS, vol. 39(5), pages 536-548, May.
    18. David W. Pentico, 1988. "The Discrete Two-Dimensional Assortment Problem," Operations Research, INFORMS, vol. 36(2), pages 324-332, April.
    19. Jonsson, Henrik & Silver, Edward A., 1989. "Common component inventory problems with a budget constraint: Heuristics and upper bounds," Engineering Costs and Production Economics, Elsevier, vol. 18(1), pages 71-81, October.
    20. Kenneth R. Baker & Michael J. Magazine & Henry L. W. Nuttle, 1986. "The Effect of Commonality on Safety Stock in a Simple Inventory Model," Management Science, INFORMS, vol. 32(8), pages 982-988, August.
    21. Steven M. Shugan, 1989. "Product Assortment in a Triopoly," Management Science, INFORMS, vol. 35(3), pages 304-320, March.
    22. Yigal Gerchak & Michael J. Magazine & A. Bruce Gamble, 1988. "Component Commonality with Service Level Requirements," Management Science, INFORMS, vol. 34(6), pages 753-760, June.
    23. Lawrence W. Robinson, 1995. "Optimal and Approximate Control Policies for Airline Booking with Sequential Nonmonotonic Fare Classes," Operations Research, INFORMS, vol. 43(2), pages 252-263, April.
    24. Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
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