Active demand management for substitute products through price optimisation

This paper presents a systematic mathematical programming approach for active demand management in process industries. The proposed methodology aims to determine optimal pricing policies as well as output levels for substitute products, while taking into consideration manufacturing costs, resource availability, customer demand elasticity, outsourcing and market competition. First, profit maximisation analytical formulae are derived for determining Nash equilibrium in prices for a duopolistic market environment where each company produces only one product. An iterative algorithm is then proposed so as to determine the decision-making process by solving a series of non-linear mathematical programming (NLP) models before determining the Nash equilibrium in prices for the competing companies. The proposed algorithm is extended in order to accommodate the case of multi-product companies, each one selling a set of substitute products at different prices. The applicability of the proposed methodology is demonstrated by a number of illustrative examples.

[1]  H. Hotelling.  Stability in Competition , 1929 .

[2]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[3]  A. Smithies.  Optimum Location in Spatial Competition , 1941, Journal of Political Economy.

[4]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[5]  Spyros Makridakis,et al.  The Handbook of forecasting: A manager's guide , 1983 .

[6]  Hanif D. Sherali,et al.  Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations , 1983, Oper. Res..

[7]  David M. Kreps,et al.  Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes , 1983 .

[8]  P. Kotler,et al.  Principles of Marketing , 1983 .

[9]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[10]  J. Eliashberg,et al.  Marketing-production decisions in an industrial channel of distribution , 1987 .

[11]  Thomas T. Nagle.  The Strategy and Tactics of Pricing: A Guide to Profitable Decision-Making , 1987 .

[12]  G. Tellis.  The Price Elasticity of Selective Demand: A Meta-Analysis of Econometric Models of Sales , 1988 .

[13]  Hanif D. Sherali,et al.  A Mathematical Programming Approach to a Nash-Cournot Equilibrium Analysis for a Two-Stage Network of Oligopolies , 1988, Oper. Res..

[14]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[15]  R. V. Zugbach.  The handbook of forecasting — A manager's guide , 1988 .

[16]  C. Shapiro.  Theories of oligopoly behavior , 1989 .

[17]  W. DeSarbo,et al.  Product Positioning Under Price Competition , 1990 .

[18]  Philip D. Straffin,et al.  Game theory and strategy , 1993 .

[19]  B. Pashigian,et al.  Price Theory and Applications , 1994 .

[20]  J. Stavins.  Estimating demand elasticities in a differentiated product industry : the personal computer market , 1997 .

[21]  M. Acutt,et al.  Cross-elasticities of demand for travel , 1995 .

[22]  L. Krishnamurthi,et al.  Relating price sensitivity to retailer promotional variables and pricing policy: An empirical analysis , 1996 .

[23]  David Besanko,et al.  Logit Demand Estimation Under Competitive Pricing Behavior: An Equilibrium Framework , 1998 .

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

[25]  Qiong Wang,et al.  Optimal planning for optical transport networks , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[26]  T. Kaihara.  Supply chain management with market economics , 2001 .

[27]  Hokey Min,et al.  Supply chain modeling: past, present and future , 2002 .

[28]  Wenjiao Zhao,et al.  Coordination of joint pricing-production decisions in a supply chain , 2002 .

[29]  Rodrigo Bueno,et al.  Short-run, long-run and cross elasticities of gasoline demand in Brazil , 2003 .

[30]  Mahmut Parlar,et al.  Coordinating pricing and production decisions in the presence of price competition , 2006, Eur. J. Oper. Res..

[31]  Augustin M. Cournot.  Cournot, Antoine Augustin: Recherches sur les principes mathématiques de la théorie des richesses , 2019, Die 100 wichtigsten Werke der Ökonomie.