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July  2012, 8(3): 577-590. doi: 10.3934/jimo.2012.8.577

Single-period inventory model with discrete stochastic demand based on prospect theory

Wei Liu 1, , Shiji Song 1, and  Cheng Wu 1,

1. 

Department of Automation, Tsinghua University, Beijing 100084, China, China, China

Received  March 2011 Revised  November 2011 Published  June 2012

This paper studies a single-period inventory (newsvendor) problem with discrete stochastic demand. In general, most of the previous works are based on the expected profit/cost criterion or expected utility criterion. We consider the effect of irrational factor under uncertainty and therefore incorporate prospect theory into inventory model. Our objective is to maximize the overall value of the prospect, which can be calculated by using the value function and the weighting function. For any given initial inventory level, it can be shown that a state-dependent order-up-to policy is optimal. Further, the optimal policy has a simple structure, and the retailer can easily decide whether to place an order or not. Moreover, the impacts of parameters on the optimal policy are illustrated through numerical experiments.
Keywords: Prospect theory, inventory, the overall value of the prospect, order-up-to policy..
Mathematics Subject Classification: Primary: 90B05; Secondary: 91B4.
Citation: Wei Liu, Shiji Song, Cheng Wu. Single-period inventory model with discrete stochastic demand based on prospect theory. Journal of Industrial & Management Optimization, 2012, 8 (3) : 577-590. doi: 10.3934/jimo.2012.8.577
References:
[1]

V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 2 (2000), 410-423. Google Scholar

[2]

M. Allais, Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'ecole americaine, Econometrica, 21 (1953), 503-546. doi: 10.2307/1907921.  Google Scholar

[3]

N. Barberis and M. Huang, Mental accounting, loss aversion, and individual stock returns, Journal of Finance, 56 (2001), 1247-1292. doi: 10.1111/0022-1082.00367.  Google Scholar

[4]

A. O. Brown and C. S. Tang, The impact of alternative performance measures on single-period inventory policy, Journal of Industrial and Management Optimization, 2 (2006), 297-318.  Google Scholar

[5]

L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794. doi: 10.1287/mnsc.41.5.786.  Google Scholar

[6]

M. Fisher and A. Raman, Reducing the cost of demand uncertainty through accurate response to early sales, Operations Research, 44 (1996), 87-99. doi: 10.1287/opre.44.1.87.  Google Scholar

[7]

W. Geng, X. Zhao and D. Gao, A single-period inventory system with a general s-shaped utility and exponential demand, Journal of Systems Science and Systems Engineering, 19 (2010), 227-236. doi: 10.1007/s11518-010-5128-8.  Google Scholar

[8]

J. A. Kahn, Why is production more volatile than sales? Theory and evidence on the stockout-avoidance motive for inventory holding, Quarterly Journal of Economics, 107 (1992), 481-510. doi: 10.2307/2118479.  Google Scholar

[9]

D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291. doi: 10.2307/1914185.  Google Scholar

[10]

B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem, European Journal of Operational Research, 174 (2006), 1643-1650. doi: 10.1016/j.ejor.2005.03.047.  Google Scholar

[11]

M. Khouja, The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega-International Journal of Management Science, 27 (1999), 537-553. doi: 10.1016/S0305-0483(99)00017-1.  Google Scholar

[12]

H. Lau and A. H. Lau, The newsstand problem: A capacitated multiple-product single-period inventory problem, European Journal of Operational Research, 94 (1996), 29-42. doi: 10.1016/0377-2217(95)00192-1.  Google Scholar

[13]

S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.  Google Scholar

[14]

Y. Liu, M. Peng and L. Li, A prospect theory-based order model under stochastic demand, Chinese Control and Decision Conference, (2009), 2539-2544. Google Scholar

[15]

N. C. Petruzzi and M. Dada, Pricing and the newsvendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. doi: 10.1287/opre.47.2.183.  Google Scholar

[16]

M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[17]

E. Stavrulaki, Inventory decisions for substitutable products with stock-dependent demand, International Journal of Production Economics, 129 (2011), 65-78. doi: 10.1016/j.ijpe.2010.09.002.  Google Scholar

[18]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323. Google Scholar

[19]

C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.009.  Google Scholar

[20]

C. X. Wang and S. Webster, The loss-averse newsvendor problem, Omega-International Journal of Management Science, 37 (2009), 93-105. doi: 10.1016/j.omega.2006.10.003.  Google Scholar

[21]

C. X. Wang, S. Webster and N. C. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European Journal of Operational Research, 196 (2009), 544-553. doi: 10.1016/j.ejor.2008.04.002.  Google Scholar

[22]

X. Zhao, W. Gen and X. Chao and D. Gao, A periodic review inventory system with s-shaped utility function, Working paper, 2009. Available from: http://ioe.engin.umich.edu/techrprt/pdf/TR09-04.pdf. Google Scholar

show all references

References:
[1]

V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 2 (2000), 410-423. Google Scholar

[2]

M. Allais, Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'ecole americaine, Econometrica, 21 (1953), 503-546. doi: 10.2307/1907921.  Google Scholar

[3]

N. Barberis and M. Huang, Mental accounting, loss aversion, and individual stock returns, Journal of Finance, 56 (2001), 1247-1292. doi: 10.1111/0022-1082.00367.  Google Scholar

[4]

A. O. Brown and C. S. Tang, The impact of alternative performance measures on single-period inventory policy, Journal of Industrial and Management Optimization, 2 (2006), 297-318.  Google Scholar

[5]

L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794. doi: 10.1287/mnsc.41.5.786.  Google Scholar

[6]

M. Fisher and A. Raman, Reducing the cost of demand uncertainty through accurate response to early sales, Operations Research, 44 (1996), 87-99. doi: 10.1287/opre.44.1.87.  Google Scholar

[7]

W. Geng, X. Zhao and D. Gao, A single-period inventory system with a general s-shaped utility and exponential demand, Journal of Systems Science and Systems Engineering, 19 (2010), 227-236. doi: 10.1007/s11518-010-5128-8.  Google Scholar

[8]

J. A. Kahn, Why is production more volatile than sales? Theory and evidence on the stockout-avoidance motive for inventory holding, Quarterly Journal of Economics, 107 (1992), 481-510. doi: 10.2307/2118479.  Google Scholar

[9]

D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291. doi: 10.2307/1914185.  Google Scholar

[10]

B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem, European Journal of Operational Research, 174 (2006), 1643-1650. doi: 10.1016/j.ejor.2005.03.047.  Google Scholar

[11]

M. Khouja, The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega-International Journal of Management Science, 27 (1999), 537-553. doi: 10.1016/S0305-0483(99)00017-1.  Google Scholar

[12]

H. Lau and A. H. Lau, The newsstand problem: A capacitated multiple-product single-period inventory problem, European Journal of Operational Research, 94 (1996), 29-42. doi: 10.1016/0377-2217(95)00192-1.  Google Scholar

[13]

S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.  Google Scholar

[14]

Y. Liu, M. Peng and L. Li, A prospect theory-based order model under stochastic demand, Chinese Control and Decision Conference, (2009), 2539-2544. Google Scholar

[15]

N. C. Petruzzi and M. Dada, Pricing and the newsvendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. doi: 10.1287/opre.47.2.183.  Google Scholar

[16]

M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[17]

E. Stavrulaki, Inventory decisions for substitutable products with stock-dependent demand, International Journal of Production Economics, 129 (2011), 65-78. doi: 10.1016/j.ijpe.2010.09.002.  Google Scholar

[18]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323. Google Scholar

[19]

C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.009.  Google Scholar

[20]

C. X. Wang and S. Webster, The loss-averse newsvendor problem, Omega-International Journal of Management Science, 37 (2009), 93-105. doi: 10.1016/j.omega.2006.10.003.  Google Scholar

[21]

C. X. Wang, S. Webster and N. C. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European Journal of Operational Research, 196 (2009), 544-553. doi: 10.1016/j.ejor.2008.04.002.  Google Scholar

[22]

X. Zhao, W. Gen and X. Chao and D. Gao, A periodic review inventory system with s-shaped utility function, Working paper, 2009. Available from: http://ioe.engin.umich.edu/techrprt/pdf/TR09-04.pdf. Google Scholar

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