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Pricing, Variety, and Inventory Decisions for Product Lines of Substitutable Items

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Planning Production and Inventories in the Extended Enterprise

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 151))

Abstract

Integrating operations and marketing decisions greatly benefits a firm. Marketing actions drive consumer demand, which significantly influences operations management (OM) decisions in areas such as capacity planning and inventory control. On the other hand, the marketing department of a firm relies on OM cost estimates in making decisions concerning pricing, variety, promotions, etc. In this chapter, we review recent research on pricing, assortment (or variety), and inventory decisions in retail operations management, which contribute to the growing literature on joint marketing/OM models (e.g., Eliashberg and Steinberg 1993; Griffin and Hauser 1992; Karmarkar 1996; Pekgün et al. 2006, 2008; Porteus and Whang 1991). Other important contributions of the reviewed works account for inventory costs in pricing and variety models and utilize realistic demand models based on consumer choice theory. These contributions are discussed below.

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Notes

  1. 1.

    This model is a generalization of Hotelling (1929). It is based on perceiving a product as a “bundle of characteristics” rather than only utilizing location and transportation costs as in Hotelling (1929), (see Lancaster 1990 for details).

  2. 2.

    We write y ∗(p,k) and Π(p,k) as functions of both p and k because we will refer to this model later, in Sect. 14.6.2, to present the pricing analysis.

  3. 3.

    We are using the term “assortment size” loosely here to refer to variety level in terms of number of items in an assortment. Cachon et al. use a more precise measure.

  4. 4.

    In a “multiplicative” demand model, demand is of the form D(p)=f(p)ε, where ε is a random variable and f(p) is a function of the price, p. In an “additive” demand model, demand is of the form D(p)=f(p)+ε. In a “mixed multiplicative–additive” demand model, D(p)=g(p)+f(p)ε, where g(p) is also a function of the price.

  5. 5.

    Another practical setting where the mixed multiplicative-additive demand model is a good approximation for the actual demand is when the total number of customers visiting the store follows a Negative Binomial distribution (see Maddah and Bish 2007 for details).

  6. 6.

    F(.) is IFR if its failure rate, f(x)∕(1−F(x)), is increasing in x, where f(x) is the corresponding density function.

  7. 7.

    One issue that may wrongly appear as a mere technicality is how to incorporate price sensitivity in logit demand functions. We prefer natural adaptations based, for example, on assuming a Poisson or a negative binomial market size, which lead to mixed multiplicative-additive demand models, as in Bish and Maddah (2007, 2008) and Cattani et al. (2010). Simplified pure multiplicative or pure additive adaptations, as in Aydin and Porteus (2008), while popular in the academic literature, seem to be difficult to justify in practice.

  8. 8.

    The robustness of the MNL models seems to be due to the fact that the essential demand splitting and cross-price effects dominate other factors in most cases.

References

  • Agrawal N, Smith SA (2003) Optimal retail assortment for substitutable items purchased in sets. Naval Res Logist 50:793–822.

    Google Scholar 

  • Alptekinoglu A, Corbett CJ (2008) Mass customization versus mass production: variety and price competition. Manufact Serv Oper Manage 10:204–217.

    Google Scholar 

  • Anderson SP, de Palma A (1992) Multiproduct Firms: a nested logit approach. J Ind Econ 40: 264–276.

    Google Scholar 

  • Anderson SP, de Palma A, Thisse J (1992) Discrete choice theory of product differentiation. MIT Press, Cambridge, MA.

    Google Scholar 

  • Aydin G, Ryan J (2002) Product line selection and pricing under the multinomial logit choice model. Working paper, Purdue University.

    Google Scholar 

  • Aydin G, Porteus EL (2008) Joint inventory and pricing decisions for an assortment. Oper Res 56:1247–1255.

    Google Scholar 

  • Aydin G, Porteus EL (2009) Manufacturer-to-retailer versus manufacturer-to-consumer rebates in a supply chain. In: Agrawal N, Smith S (eds) Retail supply chain management, Springer, Boston, MA.

    Google Scholar 

  • Aydin G, Hausman WH (2009) The role of slotting fees in the coordination of assortment decisions. Prod Oper Manag 18:635–652.

    Google Scholar 

  • Ben-Akiva M (1973) Structure of passenger travel demand models. Ph.D. Dissertation, MIT.

    Google Scholar 

  • Ben-Akiva M, Lerman SR (1985) Discrete choice analysis. MIT Press, Cambridge, MA.

    Google Scholar 

  • Besanko D, Gupta S, Jain D (1998) Logit demand estimation under competitive pricing behavior: an equilibrium framework. Manage Sci 44:1533–1547.

    Google Scholar 

  • Bish EK, Maddah B (2008) On the interaction between retail pricing, assortment, and inventory decisions. Working paper, Virginia tech.

    Google Scholar 

  • Cachon PG, Terwiesh C, Xu Y (2005) Retail assortment planning in the presence of consumer search. Manufact Serv Oper Manage 7:330–346.

    Google Scholar 

  • Cachon PG, Kök AG (2007) Category management and coordination in retail assortment planning in the presence of basket shopping consumers. Manage Sci, 53:934–951.

    Google Scholar 

  • Cattani K, Dahan E, Schmidt G (2010) Lowest cost may not lower total cost: Using “spackling” to smooth mass-customized production.

    Google Scholar 

  • Choi SC (1991) Price Competition in a Channel Structure with a Common Retailer. Market Sci 10:271–296.

    Google Scholar 

  • Corstjens M, Doyle P (1981) A model for optimizing retail space allocation. Manage Sci 27: 822–833.

    Google Scholar 

  • Dobson G, Kalish S (1988) Positioning and pricing of a product-line: formulation and heuristics. Market Sci 7: 107–125.

    Google Scholar 

  • Dobson G, Kalish S (1993) Heuristics for pricing and positioning a product-line using conjoint and cost data. Manage Sci 39:160–175.

    Google Scholar 

  • Drake MJ, Swann JL (2006) Mechanisms to improve decentralized category management with vendor-specific product portfolios. Working paper, Georgia Institute of Technology,

    Google Scholar 

  • Eliashberg J, Steinberg J (1993) Marketing production joint decision making. In: Eliashberg J, Lilien GL (eds) Handbooks in operations research and management science, vol. 5. Elsevier, NY.

    Google Scholar 

  • Elmaghraby W, Keskinocak P (2003) Dynamic pricing in the presence of inventory considerations: research overview, current practices and future directions. Manage Sci 49:1287–1309.

    Google Scholar 

  • Frantz M RIS news recognizes JCPenney in 1st annual fusion awards. RIS News, October, 2004.

    Google Scholar 

  • Food Marketing Institute. Food retailing in the 21st century: riding a consumer revolution.

    Google Scholar 

  • Gaur V, Honhon D (2006) Assortment planning and inventory decisions under a locational choice model. Manage Sci 52:1528–1543.

    Google Scholar 

  • Green PE, Krieger AM (1985) Models and heuristics for product-line selection. Market Sci 4:1–19.

    Google Scholar 

  • Green PE, Krieger AM (1989) Recent contributions to optimal product positioning and buyer segmentation. Eur J Oper Res 41:127–141.

    Google Scholar 

  • Griffin A, Hauser JR (1992) Patterns of communication among marketing, engineering and manufacturing - a comparison between two new product teams. Manage Sci 38:360–373.

    Google Scholar 

  • Guadagni PM, Little JDC (1983) A logit model of brand choice calibrated on scanner data. Market Sci 2:203–238.

    Google Scholar 

  • Irion J, Al-Khayyal F, Liu JC (2006) A piecewise linearization framework for retail shelf space management models. Working paper, Georgia Institute of Technology

    Google Scholar 

  • Jain D, Vilcassim N, Chintagunta PA (1994) A random-coefficients logit brand-choice model applied to panel data. J Bus Econ Statistics, 12:317–328.

    Google Scholar 

  • Hall JM, Kopalle PK, Krishna A (2010) Retailer dynamic pricing and ordering decisions: category management versus brand-by-brand approaches. J Retailing 86:172–183.

    Google Scholar 

  • Hauser JR (1978) Testing the accuracy, usefulness, and significance of probabilistic choice models: an information theoretic approach. Oper Res, 26:406–421.

    Google Scholar 

  • Hopp WJ, Xu, X (2003) A competitive marketing/operations model of differentiated product decisions. Working paper, Northwestern University.

    Google Scholar 

  • Hopp WJ, Xu X (2005) Product line selection and pricing with modularity in design. Manufact Serv Oper Manage, 7:172–187.

    Google Scholar 

  • Hotelling H (1929) Stability in competition. Econ J, 39:41–57.

    Google Scholar 

  • Kalakesh SR (2006) Pricing, variety and inventory decisions under nested logit consumer choice. Master Thesis, American University of Beirut.

    Google Scholar 

  • Karlin S, Carr CR (1962) Prices and optimal inventory policy. In: Arrow KJ, Karlin S, Scarf H (eds) Studies in Applied Probability and Management Science. Stanford University Press, Stanford, CA.

    Google Scholar 

  • Karmarkar US (1996) Integrative research in marketing and operations management. J Market Res 33:125–133.

    Google Scholar 

  • Kaul A, Rao VR (1995) Research for product positioning and design decisions: an integrative review. Int J Res Market 12:293–320.

    Google Scholar 

  • Kurtuluş M, Toktay LB (2005) Category captain: outsourcing retail category management. Working paper, Georgia Institute of Technology.

    Google Scholar 

  • Kurtuluş M, Toktay LB (2006) Retail assortment planning under category captainship. Working paper, Georgia Institute of Technology.

    Google Scholar 

  • Kurtuluş M, Toktay LB (2009) Category captainship practices in the retail industry. In: Agrawal N, Smith S (eds) retail supply chain management, Springer, Boston, MA.

    Google Scholar 

  • Lancaster K (1966) A new approach to consumer theory. J Pol Econ, 74:132–157.

    Google Scholar 

  • Lancaster K (1990) The economics of product variety: a survey. Market Sci, 9:189–206.

    Google Scholar 

  • Luce R (1959) Individual choice behavior: a theoretical analysis. Wiley, New York.

    Google Scholar 

  • Luce R, Suppes P (1965) Preference, utility, and subjective probability. In: Luce R, Bush R, Galanter E (eds) Handbook of mathematical psychology, Wiley, New York.

    Google Scholar 

  • Maddah B (2005) Pricing, variety, and inventory decisions in retail operations management. Ph.D. Dissertation, Virginia Tech.

    Google Scholar 

  • Maddah B, Bish EK (2007) Joint pricing, variety, and inventory decisions for a retailer’s product line. Naval Res Logist 54:315–330.

    Google Scholar 

  • Mahajan S, van Ryzin G (1999) Retail inventories and consumer choice. In: Tayur S, Ganeshan R, Magazine MJ (eds) Quantitative Models for Supply Chain Management, Kluwer Academic Publishing, Boston.

    Google Scholar 

  • Mahajan S, van Ryzin G (2001) Inventory competition under dynamic consumer choice. Oper Res 49:646–657.

    Google Scholar 

  • Manski CF, McFadden D (eds). (1981) Structural analysis of discrete data and econometric applications MIT Press, Cambridge, MA.

    Google Scholar 

  • Martín-Herrán G, Taboubib S, Zaccour G (2006) The impact of manufacturers wholesale prices on retailers shelf-space and pricing decisions. Decis Sci, 37:71–90.

    Google Scholar 

  • McFadden D (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (eds). Frontiers in econometrics, Academic Press, New York. pp. 105–142.

    Google Scholar 

  • McFadden D, Train K, Tye WB (1978) An Application of diagnostic tests for the independence from irrelevant alternatives property of the multinomial logit model Transportation Research Record: forecasting passenger and fright travel. Transport Res Board 637:39–46.

    Google Scholar 

  • Mills ES (1959) Uncertainty and price theory. Quart. J. Econom., 73:116–130.

    Google Scholar 

  • Okun A (2004) Assortment agility. RIS News, October.

    Google Scholar 

  • Petruzzi NC, Dada M (1999) Pricing and the newsvendor problem: a review with extensions. Oper Res, 47:183–194.

    Google Scholar 

  • Pekgün, P, Griffin P, Keskinocak P (2006) Centralized vs. decentralized competition for price and lead-time sensitive demand. Working paper, Georgia Tech.

    Google Scholar 

  • Pekgün P, Griffin P, Keskinocak P (2008) Coordination of marketing and production for price and leadtime decisions. IIE Trans, 40:12–30

    Google Scholar 

  • Porteus EL, Whang SJ (1991) On manufacturing/marketing incentives. Manage Sci, 37: 1166–1181.

    Google Scholar 

  • Van Ryzin G, Mahajan S (1999) On the relationship between inventory costs and variety benefits in retail assortments. Manage Sci, 45:1496–1509.

    Google Scholar 

  • Smith SA, Agrawal N (2000) Management of multi-item retail inventory system with demand substitution. Oper Res, 48:50–64.

    Google Scholar 

  • US Census Bureau. Annual benchmark report for retail trade and food services: January 1992 through

    Google Scholar 

  • Wang Y, Raju JS, Dhar SK (2003) The choice and consequences of using a category captain for category management. Working paper, University of Pennsylvania.

    Google Scholar 

  • Yücel E, Karaesmen F, Salman FS, Türkay M (2009) Optimizing product assortment under customer-driven demand substitution. Eur J Oper Res 199:759–768.

    Google Scholar 

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Acknowledgements

We thank Dr. Walid Nasr from the American University of Beirut for his prompt help in proofreading and editing the final version of this chapter.

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Authors and Affiliations

  1. Engineering Management Program, American University of Beirut, Beirut, 1107 2020, Lebanon

    Bacel Maddah

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  1. Bacel Maddah
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  2. Ebru K. Bish
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  3. Brenda Munroe
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Correspondence to Bacel Maddah .

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Editors and Affiliations

  1. Decision Technologies, Intel Corporation, W. Chandler Blvd. 5000, Chandler, 85226, Arizona, USA

    Karl G. Kempf

  2. School of Industrial &, Systems Engineering, Georgia Institute of Technology, Ferst Drive NW., 765, Atlanta, 30332-0205, Georgia, USA

    Pınar Keskinocak

  3. , Edward P. Fitts Department of Industrial, North Carolina State University, Daniels Hall 300, Raleigh, 27695, North Carolina, USA

    Reha Uzsoy

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Maddah, B., Bish, E.K., Munroe, B. (2011). Pricing, Variety, and Inventory Decisions for Product Lines of Substitutable Items. In: Kempf, K., Keskinocak, P., Uzsoy, R. (eds) Planning Production and Inventories in the Extended Enterprise. International Series in Operations Research & Management Science, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6485-4_14

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