Joint pricing and inventory control for additive demand models with reference effects.

*(English)*Zbl 1309.90003Summary: We study a periodic review joint inventory and pricing problem of a single item with stochastic demand subject to reference effects. The random demand is contingent on the current price and the reference price that acts a benchmark against which customers compare the price of a product. Randomness is introduced with an additive random term. The customers perceive the difference between the price and the reference price as a loss or a gain. Hence, they have different attitudes towards them, such as loss aversion, loss neutrality or loss seeking. We model the problem using safety stock as the decision variable and show that the problem can be decomposed into two subproblems for all demand models under mild conditions. Using the decomposition, we show that a steady state solution exists for the infinite horizon problem and we characterize the steady state solution. Defining the modified revenue as revenue less the production cost, we show that a state-dependent order-up-to policy is optimal for concave demand models with concave modified revenue functions and provide example demand models with absolute difference reference effects and loss-averse customers. We also show that the optimal inventory level increases with the reference price. All of our results hold for finite and infinite horizon problems.

##### MSC:

90B05 | Inventory, storage, reservoirs |

91B24 | Microeconomic theory (price theory and economic markets) |

90C39 | Dynamic programming |

PDF
BibTeX
XML
Cite

\textit{M. G. Güler} et al., Ann. Oper. Res. 226, 255--276 (2015; Zbl 1309.90003)

Full Text:
DOI

##### References:

[1] | Anderson, CK; Rasmussen, H; MacDonald, L, Competitive pricing with dynamic asymmetric price effects, International Transactions in Operational Research, 12, 509-525, (2005) · Zbl 1152.91437 |

[2] | Arslan, H., & Kachani, S. (2010). Dynamic pricing under consumer reference-price effects. In Wiley encyclopedia of operations research and management science, pp. 1-17. · Zbl 0143.21703 |

[3] | Bertsekas, D. P., & Shreve, S. E. (1996). Stochastic optimal control: The discrete-time case. Belmont: Athena Scientific. · Zbl 0471.93002 |

[4] | Chen, X., Hu, P., Shum, S., & Zhang, Y. (2014). Dynamic stochastic inventory management with reference price effects. Submitted for publication, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign. · Zbl 1354.90010 |

[5] | Chen, X; Simchi-Levi, D, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the finite horizon case, Operations Research, 52, 887-896, (2004) · Zbl 1165.90308 |

[6] | Chen, X; Simchi-Levi, D, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the infinite horizon case, Mathematics of Operations Research, 29, 698-723, (2004) · Zbl 1082.90025 |

[7] | Chen, YF; Ray, S; Song, Y, Optimal pricing and inventory control policy in periodic review systems with fixed ordering cost and lost sales, Naval Research Logistics, 53, 117-136, (2006) · Zbl 1106.90008 |

[8] | Chen, X; Simchi-Levi, D, Coordinating inventory control and pricing strategies: the continuous review model, Operations Research Letters, 34, 323-332, (2006) · Zbl 1098.90001 |

[9] | Chen, X; Simchi-Levi, D; Özer, Ö (ed.); Phillips, R (ed.), Pricing and inventory management, (2012), Oxford |

[10] | Elmaghraby, W; Keskinocak, P, Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions, Management Science, 49, 1287-1309, (2003) · Zbl 1232.90042 |

[11] | Federgruen, A; Heching, A, Combined pricing and inventory control under uncertainty, Operations Research, 47, 454-475, (1999) · Zbl 0979.90004 |

[12] | Feng, Y., & Chen, F. Y. (2003). Joint pricing and inventory control with setup costs and demand uncertainty. In Working paper. The Chinese University of Hong-Kong. · Zbl 1241.91069 |

[13] | Fibich, G; Gavious, A; Lowengart, O, Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects, Operations Research, 51, 721-734, (2003) · Zbl 1165.91325 |

[14] | Gimpl-Heersink, L. (2008). Joint pricing and inventory control under reference price effects, PhD thesis, Vienna University of Economics and Business Administration. |

[15] | Greenleaf, EA, The impact of reference price effect on the profitability of price promotions, Marketing Science, 14, 82-104, (1995) |

[16] | Güler, M. G., & Akan, M. (2013). Optimal pricing-inventory decisions under reference effects. Working paper. · Zbl 1274.90029 |

[17] | Güler, M. G., Bilgiç, T., & Güllü, R. (2011). Joint pricing and inventory control for additive demand models with reference effects, Technical Report FBE-IE-07/2011-08, Bogazici University, Dept. of Industrial Engineering. · Zbl 1165.91325 |

[18] | Güler, MG; Bilgiç, T; Güllü, R, Joint inventory and pricing decisions with reference effects, IIE Transactions, 46, 330-343, (2014) |

[19] | Helson, M. (1964). Adaptation level theory. New York: Harper and Row. |

[20] | Heyman, D. P., & Sobel, M. J. (2004). Stochastic models in operations research, vol. II. NY: Dover. · Zbl 1076.90001 |

[21] | Huh, WT; Janakiraman, G, (s, S) optimality in joint inventory-pricing control: an alternate approach, Operations Research, 56, 783-790, (2008) · Zbl 1167.90332 |

[22] | Kahneman, D; Tversky, A, Prospect theory: an analysis of decision under risk, Econometrica, 29, 263-291, (1979) · Zbl 0411.90012 |

[23] | Kalyanaram, G; Winer, RS, Empirical generalizations from reference price research, Marketing Science, 14, 161-169, (1995) |

[24] | Köbberling, V; Wakker, PP, An index of loss aversion, Journal of Economic Theory, 122, 199-131, (2005) · Zbl 1118.91057 |

[25] | Kopalle, PK; Rao, AG; Assunção, JL, Assymmetric reference price effects and dynamic pricing policies, Marketing Science, 15, 60-85, (1996) |

[26] | Mazumdar, T; Raj, SP; Sinha, I, Reference price research: review and propositions, Journal of Marketing, 69, 84-102, (2005) |

[27] | Monroe, KB, Buyers’ subjective perceptions of price, Journal of Marketing Research, 10, 70-80, (1973) |

[28] | Nasiry, J; Popescu, I, Dynamic pricing with loss-averse consumers and peak-end anchoring, Operations Research, 59, 1361-1368, (2011) · Zbl 1241.91069 |

[29] | Nerlove, M, Adaptive expectations and cobweb phenomena, Quarterly Journal of Economics, 72, 227-240, (1958) |

[30] | Polatoğlu, H; Şahin, I, Optimal procurement policies under price-dependent demand, International Journal of Production Economics, 65, 141-171, (2000) |

[31] | Popescu, I; Wu, Y, Dynamic pricing strategies with reference effects, Operations Research, 55, 413-429, (2007) · Zbl 1167.91348 |

[32] | Porteus, E. L. (2002). Foundations of stochastic inventory theory. California: Stanford University Press. |

[33] | Rossi, R; Tarim, SA; Hnich, B; Prestwich, S, Constraint programming for stochastic inventory systems under shortage cost, Annals of Operations Research, 195, 49-71, (2012) · Zbl 1251.90036 |

[34] | Rudin, W. (1976). Principles of mathematical analysis. New York: McGraw-Hill. · Zbl 0346.26002 |

[35] | Shi, J; Katehakis, MN; Melamed, B, Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands, Annals of Operations Research, 208, 593-612, (2013) · Zbl 1274.90029 |

[36] | Song, Y; Ray, S; Boyaci, T, Optimal dynamic joint inventory pricing control for multiplicative demand with fixed order costs and lost sales, Operations Research, 57, 245-250, (2009) · Zbl 1181.90024 |

[37] | Taudes, A; Rudloff, C, Integrating inventory control and a price change in the presence of reference price effects: A two-period model, Mathematical Methods of Operations Research, 75, 1-37, (2012) · Zbl 1259.90006 |

[38] | Veinott, AF, Optimal policy for a multi-product, dynamic nonstatinary inventory problem, Management Science, 12, 206-222, (1965) · Zbl 0143.21703 |

[39] | Winer, RS, A reference price model of demand for frequently purchased products, Journal of Consumer Research, 13, 250-256, (1986) |

[40] | Zhang, Y. (2010). Essays on robust optimization, integrated inventory and pricing, and reference price effect, PhD thesis, University of Illinois at Urbana-Champaign. · Zbl 1259.90006 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.