American Institute of Mathematical Sciences

Advanced
doi: 10.3934/jimo.2019126

Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items

Musen Xue 1, and  Guowei Zhu 2,,

1. 

School of Management, Tianjin Normal University, Tianjin 300387, China
2. 

Business School, Hunan University, Changsha, Hunan 410082, China

* Corresponding author: Guowei Zhu

Received  November 2018 Revised  July 2019 Published  October 2019

Fund Project: The first author is supported by the Tianjin Philosophy and Social Sciences Planning Year Project grant TJGLQN17-010; The second author is supported by National Natural Science Foundation of China grant 71871089.

This paper studies a dynamic pricing and replenishment problem for perishable items considering the behavior of decision-maker (partially myopic or forward-looking) and the dynamic effects of cumulative sales. A dynamic optimization model is presented to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal pricing and replenishment strategies for partially myopic and forward-looking scenarios are obtained. By comparing the partially myopic and forward-looking strategies through numerical analysis, we find the main results: First, applying a skimming pricing strategy might be a good choice when the saturation effects are considered. Second, the decreasing rate of product sales, deterioration coefficient, and holding cost of perishable items per unit exhibit impact on the behavioral preference of decision-maker. Under certain conditions, partially myopic behavior can bring more profit than forward-looking behavior. These managerial implications provide useful guidelines for the decision-maker.

Keywords: Perishable items, dynamic pricing, inventory control, saturation effect, partial myopia.
Mathematics Subject Classification: Primary: 49J52, 49M30.
Citation: Musen Xue, Guowei Zhu. Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019126
References:
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G. W. Liu, S. P. Sethi and J. X. Zhang, Myopic vs. far-sighted behaviours in a revenue-sharing supply chain with reference quality effects, Internat. J. Prod. Res., 54 (2016), 1334-1357.  doi: 10.1080/00207543.2015.1068962.  Google Scholar

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F. X. Lu, G. W. Liu, J. X. Zhang and W. S. Tang, Benefits of partial myopia in a durable product supply chain considering pricing and advertising, J. Oper. Res. Society, 67 (2016), 1309-1324.  doi: 10.1057/jors.2016.27.  Google Scholar

[25]

P. Mahata, A. Gupta and G. C. Mahata, Optimal pricing and ordering policy for an EPQ inventory system with perishable items under partial tradecredit financing, Internat. J. Oper. Res., 21 (2015), 221-251.  doi: 10.1504/IJOR.2014.064607.  Google Scholar

[26]

R. Maihami and B. Karimi, Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts, Comput. Oper. Res., 51 (2014), 302-312.  doi: 10.1016/j.cor.2014.05.022.  Google Scholar

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M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numer. Algebra Control Optim., 8 (2018), 169-191.  doi: 10.3934/naco.2018010.  Google Scholar

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show all references

References:
[1]

N. Amrouche, G. Martín-Herrán and G. Zaccour, Feedback Stackelberg equilibrium strategies when the private label competes with the national brand, Appl. Math. Model., 164 (2008), 79-95.  doi: 10.1007/s10479-008-0320-7.  Google Scholar

[2]

M. Bakker, J. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001, European J. Oper. Res., 221 (2012), 275-284.  doi: 10.1016/j.ejor.2012.03.004.  Google Scholar

[3]

F. M. Bass and A. V. Bultez, A note on optimal strategic pricing of technological innovations, Marketing Science, 1 (1982), 371-378.  doi: 10.1287/mksc.1.4.371.  Google Scholar

[4]

H. Benchekroun, G. Martín-Herrán and S. Taboubi, Could myopic pricing be a strategic choice in marketing channels? A game theoretic analysis, J. Econom. Dynam. Control, 33 (2009), 1699-1718.  doi: 10.1016/j.jedc.2009.03.005.  Google Scholar

[5]

G. Bitran and R. Caldentey, An overview of pricing models for revenue management, Manufacturing & Service Oper. Manag., 5 (2003), 203-229.  doi: 10.1287/msom.5.3.203.16031.  Google Scholar

[6]

X. Q. Cai, Y. Feng, Y. J. Li and D. Shi, Optimal pricing policy for a deteriorating product by dynamic tracking control, Internat. J. Prod. Res., 51 (2013), 2491-2504.  doi: 10.1080/00207543.2012.743688.  Google Scholar

[7]

D. Chakravarti, A. Mitchell and R. Staelin, Judgment based marketing decision models: An experimental investigation of the decision calculus approach, Management Science, 25 (1979), 251-263.  doi: 10.1287/mnsc.25.3.251.  Google Scholar

[8]

H. Che, K. Sudhir and P. B. Seetharaman, Bounded rationality in pricing under state-dependent demand: Do firms look ahead, and if so, how far?, J. of Marketing Research, 44 (2007), 434-449.  doi: 10.1509/jmkr.44.3.434.  Google Scholar

[9]

W. Y. K. Chiang, Supply chain dynamics and channel efficiency in durable product pricing and distribution, Manufacturing & Service Oper. Manag., 14 (2012), 327-343.  doi: 10.1287/msom.1110.0370.  Google Scholar

[10]

C. Y. Dye, Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega - Internat. J. Manag. Science, 35 (2007), 184-189.  doi: 10.1016/j.omega.2005.05.002.  Google Scholar

[11]

L. Feng, Dynamic pricing, quality investment, and replenishment model for perishable items, Int. Trans. Oper. Res., 26 (2019), 1558-1575.  doi: 10.1111/itor.12505.  Google Scholar

[12]

M. Ferguson and M. E. Ketzenberg, Information sharing to improve retail product freshness of perishables, Prod. and Oper. Manag., 15 (2006), 57-73.   Google Scholar

[13]

G. Fibich, A. Gavious and O. Lowengart, Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects, Oper. Res., 51 (2003), 721-734.  doi: 10.1287/opre.51.5.721.16758.  Google Scholar

[14]

S. K. Goyal and B. C. Giri, Recent trends in modeling of deteriorating inventory, European J. Oper. Res., 134 (2001), 1-16.  doi: 10.1016/S0377-2217(00)00248-4.  Google Scholar

[15]

G. J. Gutierrez and X. L. He, Life-cycle channel coordination issues in launching an innovative durable product, Prod. and Oper. Manag., 20 (2011), 268-279.  doi: 10.1111/j.1937-5956.2010.01197.x.  Google Scholar

[16]

J. R. Hauser, D. I. Simester and B. Wernerfelt, Customer satisfaction incentives, Marketing Science, 13 (1994), 327-350.  doi: 10.1287/mksc.13.4.327.  Google Scholar

[17]

S. Jørgensen, S. Taboubi and G. Zaccour, Retail promotions with negative brand image effects: Is cooperation possible?, European J. Oper. Res., 150 (2003), 395-405.  doi: 10.1016/S0377-2217(02)00641-0.  Google Scholar

[18]

S. Jørgensen and G. Zaccour, Differential Games in Marketing, International Series in Quantitative Marketing, Kluwer Academic Publishers, Boston, 2004. Google Scholar

[19]

M. I. Kamien and N. L. Schwartz, Dynamic Optimization: The calculus of variations and optimal control in economics and management, Advanced Textbooks in Economics, North-Holland Publishing Co, Amsterdam, 1991.  Google Scholar

[20]

S. Kumar and S. P. Sethi, Dynamic pricing and advertising for web content providers, European J. Oper. Res., 197 (2009), 924-944.  doi: 10.1016/j.ejor.2007.12.038.  Google Scholar

[21]

S. T. Law and H. M. Wee, An integrated production-inventory model for ameliorating and deteriorating items taking account of time discounting, Math. and Comput. Modelling, 43 (2006), 673-685.  doi: 10.1016/j.mcm.2005.12.012.  Google Scholar

[22]

Y. Levin, J. Mcgill and M. Nediak, Optimal dynamic pricing of perishable items by a monopolist facing strategic consumers, Prod. and Oper. Manag., 19 (2010), 40-60.  doi: 10.1111/j.1937-5956.2009.01046.x.  Google Scholar

[23]

G. W. Liu, S. P. Sethi and J. X. Zhang, Myopic vs. far-sighted behaviours in a revenue-sharing supply chain with reference quality effects, Internat. J. Prod. Res., 54 (2016), 1334-1357.  doi: 10.1080/00207543.2015.1068962.  Google Scholar

[24]

F. X. Lu, G. W. Liu, J. X. Zhang and W. S. Tang, Benefits of partial myopia in a durable product supply chain considering pricing and advertising, J. Oper. Res. Society, 67 (2016), 1309-1324.  doi: 10.1057/jors.2016.27.  Google Scholar

[25]

P. Mahata, A. Gupta and G. C. Mahata, Optimal pricing and ordering policy for an EPQ inventory system with perishable items under partial tradecredit financing, Internat. J. Oper. Res., 21 (2015), 221-251.  doi: 10.1504/IJOR.2014.064607.  Google Scholar

[26]

R. Maihami and B. Karimi, Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts, Comput. Oper. Res., 51 (2014), 302-312.  doi: 10.1016/j.cor.2014.05.022.  Google Scholar

[27]

G. Martín-Herrán and S. Taboubi, Shelf-space allocation and advertising decisions in the marketing channel: A differential game approach, Int. Game Theory Rev., 7 (2005), 313-330.  doi: 10.1142/S0219198905000545.  Google Scholar

[28]

G. Martín-Herrán, S. Taboubi and G. Zaccour, Dual role of price and myopia in a marketing channel, European J. Oper. Res., 219 (2012), 284-295.  doi: 10.1016/j.ejor.2011.12.015.  Google Scholar

[29]

R. J. Meyer and J. W. Hutchinson, Bumbling geniuses: The power of everyday reasoning in multistage decision making, Wharton on Making Decisions, 2001, 37–61. Google Scholar

[30]

F. Ngendakuriyo and S. Taboubi, Pricing strategies of complementary products in distribution channels: A dynamic approach, Dyn. Games Appl., 7 (2017), 48-66.  doi: 10.1007/s13235-016-0181-7.  Google Scholar

[31]

L. Y. Ouyang, K. S. Wu, C. T. Yang and H. F. Yen, Optimal order policy in response to announced price increase for deteriorating items with limited special order quantity, Internat. J. Systems Sci., 47 (2016), 718-729.  doi: 10.1080/00207721.2014.902157.  Google Scholar

[32]

Z. Pang, Optimal dynamic pricing and inventory control with stock deterioration and partial backordering, Oper. Res. Lett., 39 (2011), 375-379.  doi: 10.1016/j.orl.2011.06.009.  Google Scholar

[33]

M. Pervin, G. C. Mahata and S. K. Roy, An inventory model with demand declining market for deteriorating items under trade credit policy, Internat. J. Manag. Sci. and Engineering Manag., 11 (2016), 243-251.  doi: 10.1080/17509653.2015.1081082.  Google Scholar

[34]

M. Pervin, S. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann. Oper. Res., 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[35]

M. Pervin, S. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price- and stock-sensitive demand, J. Ind. Manag. Optim., (2019). doi: 10.3934/jimo.2019019.  Google Scholar

[36]

M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numer. Algebra Control Optim., 8 (2018), 169-191.  doi: 10.3934/naco.2018010.  Google Scholar

[37]

M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.  Google Scholar

[38]

M. Pervin, S. K. Roy and G. W. Weber, A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numer. Algebra Control Optim., 7 (2017), 21-50.  doi: 10.3934/naco.2017002.  Google Scholar

[39]

I. Popescu and Y. Wu, Dynamic pricing strategies with reference effects, Oper. Res., 55 (2007), 413-429.  doi: 10.1287/opre.1070.0393.  Google Scholar

[40]

Y. Qin, J. Wang and C. Wei, Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Internat. J. Produc. Econ., 152 (2014), 42-48.  doi: 10.1016/j.ijpe.2014.01.005.  Google Scholar

[41]

M. Rabbani, N. P. Zia and H. Rafiei, Joint optimal dynamic pricing and replenishment policies for items with simultaneous quality and physical quantity deterioration, Appl. Math. Comput., 287 (2016), 149-160.  doi: 10.1016/j.amc.2016.04.016.  Google Scholar

[42]

R. C. Rao and F. M. Bass, Competition, strategy, and price dynamics: A theoretical and empirical investigation, J. Marketing Res., 22 (1985), 283-297.  doi: 10.1177/002224378502200304.  Google Scholar

[43]

S. Saha, I. Nielsenb and I. Moon, Optimal retailer investments in green operations and preservation technology for deteriorating items, J. Cleaner Produc., 140 (2017), 1514-1527.  doi: 10.1016/j.jclepro.2016.09.229.  Google Scholar

[44]

N. H. Shah, H. N. Soni and K. Patel, Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates, Omega - Int. J. Manag. Science, 41 (2013), 421-430.  doi: 10.1016/j.omega.2012.03.002.  Google Scholar

[45]

Y. C. Tsao and G. J. Sheen, Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Comput. Oper. Res., 35 (2008), 3562-3580.  doi: 10.1016/j.cor.2007.01.024.  Google Scholar

[46]

H. M. Wee, Joint pricing and replenishment policy for deteriorating inventory with declining market, Internat. J. Produc. Econ., 40 (1995), 163-171.  doi: 10.1016/0925-5273(95)00053-3.  Google Scholar

[47]

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Figure 1.  The unit time total profits $ J_m(T) $ and $ J_f(T) $ versus $ T $
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Figure 2.  The optimal pricing strategies $ p^*_m $ and $ p^*_f $ versus $ t $
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Figure 3.  The effect of $ \delta $ on the unit time total profits $ J_m $ and $ J_f $
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Figure 4.  The effect of $ \theta $ on the unit time total profits $ J_m $ and $ J_f $
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