Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem

This paper studies the analytical and managerial implications of product substitutability on the joint pricing and procurement decisions. We consider a single-period model with two products: an existing product and an improved new product that can substitute the demand for the existing product in case of a shortage. Demand for each product follows a general distribution with an expected value that is a linear function of the price of the new product. While the price of the existing product is determined by the market, it is necessary to determine the new product's price and the procurement quantities of both products so as to maximize the profits. We analytically show that the expected profit function is unimodal and in the existence of substitution: the expected total profit is higher; the optimal price and the safety stock of the new product are higher; and the optimal safety stock of the existing product is less. Using these properties an efficient algorithm is developed. We also provide a numerical analysis to demonstrate that considering substitution in advance could increase the profitability by 58% and the new product price by 5% while decreasing the total procurement quantity by 15%.

[1]  M. Dada,et al.  Estimation of Consumer Demand with Stock-Out Based Substitution: An Application to Vending Machine Products , 1998 .

[2]  Nils Rudi,et al.  Centralized and Competitive Inventory Models with Demand Substitution , 2002, Oper. Res..

[3]  Kumar Rajaram,et al.  The impact of product substitution on retail merchandising , 2001, Eur. J. Oper. Res..

[4]  Serguei Netessine,et al.  Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation , 2002, Oper. Res..

[5]  F. Bass.  A new product growth model for consumer durables , 1976 .

[6]  Alain Bultez,et al.  Asymmetric cannibalism in retail assortments , 1989 .

[7]  Hayriye Ayhan,et al.  Relationships Among Three Assumptions in Revenue Management , 2004, Oper. Res..

[8]  V. Srinivasan,et al.  A Simultaneous Approach to Market Segmentation and Market Structuring , 1987 .

[9]  Z. Griliches.  HYBRID CORN: AN EXPLORATION IN THE ECONOMIC OF TECHNOLOGICAL CHANGE , 1957 .

[10]  Ram Akella,et al.  Single-Period Multiproduct Inventory Models with Substitution , 1999, Oper. Res..

[11]  John D. C. Little,et al.  A Logit Model of Brand Choice Calibrated on Scanner Data , 2011, Mark. Sci..

[12]  D. Simchi-Levi,et al.  Coordination of Pricing and Inventory Decisions: A Survey and Classification , 2004 .

[13]  M. An.  Log-Concave Probability Distributions: Theory and Statistical Testing , 1996 .

[14]  M. Bagnoli,et al.  Log-concave probability and its applications , 2004 .

[15]  Zvi Drezner,et al.  Optimal inventory policies for substitutable commodities with stochastic demand , 1991 .

[16]  Maqbool Dada,et al.  Pricing and the Newsvendor Problem: A Review with Extensions , 1999, Oper. Res..

[17]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[18]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[19]  Christopher S. Tang,et al.  A Modeling Framework for Category Assortment Planning , 2001, Manuf. Serv. Oper. Manag..

[20]  E. Silver,et al.  Some Concepts For Inventory Control Under Substitutable Demand , 1978 .

[21]  J. Birge,et al.  Setting Single-Period Optimal Capacity Levels and Prices for Substitutable Products , 1998 .

[22]  David Simchi-Levi,et al.  Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science) , 2004 .

[23]  M. Karakul.  Joint pricing and procurement of fashion products in the existence of clearance markets , 2008 .

[24]  E. Mansfield.  TECHNICAL CHANGE AND THE RATE OF IMITATION , 1961 .

[25]  Vipul Agrawal,et al.  Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem , 2000, Manuf. Serv. Oper. Manag..