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July  2017, 13(3): 1417-1429. doi: 10.3934/jimo.2016080

## The loss-averse newsvendor problem with random supply capacity

 1 Department of Basic Science, Military Economics Academy, Wuhan 430035, China 2 Department of Automation, Tsinghua University, Beijing 100084, China 3 School of Business Administration, Hubei University of Economics, Wuhan 430205, China

* Corresponding author: Wei Liu

Received  April 2015 Published  October 2016

Fund Project: The paper is supported by Research Fund for the Doctoral Program of Higher Education (No.20120002110035,20130002130010) and Natural Science Foundation of China (No. 61273233)

This paper studies a newsvendor problem with random supply capacity, where the retailer (newsvendor) is loss-averse and the shortage cost is considered. When the retailer orders, the quantity actually received is the minimum between the order quantity and supply capacity, and his objective is to choose an order quantity to maximize the expected utility. It is shown that under different conditions, the loss-averse retailer may order larger than, equal to or less than the risk-neutral one, which is different from the existing result in the case without considering shortage cost. Further, if the shortage cost is less than a critical value, then the loss-averse retailer's optimal order quantity is always less than the risk-neutral retailer's. The numerical experiments are conducted to demonstrate our theoretical results.

Citation: Wei Liu, Shiji Song, Ying Qiao, Han Zhao. The loss-averse newsvendor problem with random supply capacity. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1417-1429. doi: 10.3934/jimo.2016080
##### References:
 [1] S. Benartzi and R. H. Thaler, Myopic loss aversion and the equity premium puzzle, Quarterly Journal of Economics, 110 (1995), 73-92. doi: 10.3386/w4369. Google Scholar [2] X. Chao, H. Chen and S. Zheng, Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity, European Journal of Operational Research, 191 (2008), 142-155. doi: 10.1016/j.ejor.2007.08.012. Google Scholar [3] F. W. Ciarallo, R. Akella and T. E. Morton, A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies, Management Science, 40 (1994), 320-332. doi: 10.1287/mnsc.40.3.320. Google Scholar [4] M. Dada, N. C. Petruzzi and L. B. Schwarz, A newsvendor's procurement problem when suppliers are unreliable, Manufacturing & Service Operations Management, 9 (2007), 9-32. doi: 10.1287/msom.1060.0128. Google Scholar [5] X. Deng, J. Xie and H. Xiong, Manufacturer-retailer contracting with asymmetric information on retailer's degree of loss aversion, International Journal of Production Economics, 142 (2013), 372-380. doi: 10.1016/j.ijpe.2012.12.013. Google Scholar [6] M. A. 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] D. Genesove and C. Mayer, Loss aversion and seller behavior: Evidence from the housing market, Quarterly Journal of Economics, 116 (2001), 1233-1260. doi: 10.3386/w8143. Google Scholar [8] R. Gullu, E. Onol and N. Erkip, Analysis of an inventory system under supply uncertainty, International Journal of Production Economics, 59 (1999), 377-385. doi: 10.1016/S0925-5273(98)00024-3. Google Scholar [9] T. Iida, A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand, European Journal of Operational Research, 140 (2002), 670-683. doi: 10.1016/S0377-2217(01)00218-1. Google Scholar [10] U. Juttner, Supply chain risk management: Understanding the business requirements from a practitioner perspective, International Journal of Logistics Management, 16 (2005), 120-141. doi: 10.1108/09574090510617385. Google Scholar [11] 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 [12] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-292. doi: 10.2307/1914185. Google Scholar [13] W. Liu, S. Song, B. Li and C. Wu, A periodic review inventory model with loss-averse retailer, random supply capacity and demand, International Journal of Production Research, 53 (2015), 3623-3634. doi: 10.1080/00207543.2014.985391. Google Scholar [14] W. Liu, S. Song and C. Wu, Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359. doi: 10.1016/j.ijpe.2012.08.017. Google Scholar [15] W. Liu, S. Song and C. Wu, The loss-averse newsvendor problem with random yield, Transactions of the Institute of Measurement and Control, 36 (2014), 312-320. doi: 10.1177/0142331213497622. Google Scholar [16] B. Masih-Tehrani, S. H. Xu, S. Kumara and H. Li, A single-period analysis of a two-echelon inventory system with dependent supply uncertainty, Transportation Research Part B, 45 (2011), 1128-1151. doi: 10.1016/j.trb.2011.04.003. Google Scholar [17] A. Norrman and U. Jansson, Ericsson's proactive supply chain risk management approach after a serious sub-supplier accident, International Journal of Physical Distribution & Logistics Management, 34 (2004), 434-456. doi: 10.1108/09600030410545463. Google Scholar [18] 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 [19] D. A. Serel, Inventory and pricing decisions in a single-period problem involving risky supply, International Journal of Production Economics, 116 (2008), 115-128. doi: 10.1016/j.ijpe.2008.07.012. Google Scholar [20] H. C. Shen, Z. Pang and T. C. E. Cheng, The component procurement problem for the loss-averse manufacturer with spot purchase, Journal of Production Economics, 132 (2011), 146-153. doi: 10.1016/j.ijpe.2011.03.025. Google Scholar [21] C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.007. Google Scholar [22] C. X. Wang and S. Webster, Channel coordination for a supply chain with a risk-neutral manufacturer and a loss-averse retailer, Decision Sciences, 38 (2007), 361-389. doi: 10.1111/j.1540-5915.2007.00163.x. Google Scholar [23] 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.2006.08.003. Google Scholar

show all references

##### References:
 [1] S. Benartzi and R. H. Thaler, Myopic loss aversion and the equity premium puzzle, Quarterly Journal of Economics, 110 (1995), 73-92. doi: 10.3386/w4369. Google Scholar [2] X. Chao, H. Chen and S. Zheng, Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity, European Journal of Operational Research, 191 (2008), 142-155. doi: 10.1016/j.ejor.2007.08.012. Google Scholar [3] F. W. Ciarallo, R. Akella and T. E. Morton, A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies, Management Science, 40 (1994), 320-332. doi: 10.1287/mnsc.40.3.320. Google Scholar [4] M. Dada, N. C. Petruzzi and L. B. Schwarz, A newsvendor's procurement problem when suppliers are unreliable, Manufacturing & Service Operations Management, 9 (2007), 9-32. doi: 10.1287/msom.1060.0128. Google Scholar [5] X. Deng, J. Xie and H. Xiong, Manufacturer-retailer contracting with asymmetric information on retailer's degree of loss aversion, International Journal of Production Economics, 142 (2013), 372-380. doi: 10.1016/j.ijpe.2012.12.013. Google Scholar [6] M. A. 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] D. Genesove and C. Mayer, Loss aversion and seller behavior: Evidence from the housing market, Quarterly Journal of Economics, 116 (2001), 1233-1260. doi: 10.3386/w8143. Google Scholar [8] R. Gullu, E. Onol and N. Erkip, Analysis of an inventory system under supply uncertainty, International Journal of Production Economics, 59 (1999), 377-385. doi: 10.1016/S0925-5273(98)00024-3. Google Scholar [9] T. Iida, A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand, European Journal of Operational Research, 140 (2002), 670-683. doi: 10.1016/S0377-2217(01)00218-1. Google Scholar [10] U. Juttner, Supply chain risk management: Understanding the business requirements from a practitioner perspective, International Journal of Logistics Management, 16 (2005), 120-141. doi: 10.1108/09574090510617385. Google Scholar [11] 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 [12] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-292. doi: 10.2307/1914185. Google Scholar [13] W. Liu, S. Song, B. Li and C. Wu, A periodic review inventory model with loss-averse retailer, random supply capacity and demand, International Journal of Production Research, 53 (2015), 3623-3634. doi: 10.1080/00207543.2014.985391. Google Scholar [14] W. Liu, S. Song and C. Wu, Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359. doi: 10.1016/j.ijpe.2012.08.017. Google Scholar [15] W. Liu, S. Song and C. Wu, The loss-averse newsvendor problem with random yield, Transactions of the Institute of Measurement and Control, 36 (2014), 312-320. doi: 10.1177/0142331213497622. Google Scholar [16] B. Masih-Tehrani, S. H. Xu, S. Kumara and H. Li, A single-period analysis of a two-echelon inventory system with dependent supply uncertainty, Transportation Research Part B, 45 (2011), 1128-1151. doi: 10.1016/j.trb.2011.04.003. Google Scholar [17] A. Norrman and U. Jansson, Ericsson's proactive supply chain risk management approach after a serious sub-supplier accident, International Journal of Physical Distribution & Logistics Management, 34 (2004), 434-456. doi: 10.1108/09600030410545463. Google Scholar [18] 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 [19] D. A. Serel, Inventory and pricing decisions in a single-period problem involving risky supply, International Journal of Production Economics, 116 (2008), 115-128. doi: 10.1016/j.ijpe.2008.07.012. Google Scholar [20] H. C. Shen, Z. Pang and T. C. E. Cheng, The component procurement problem for the loss-averse manufacturer with spot purchase, Journal of Production Economics, 132 (2011), 146-153. doi: 10.1016/j.ijpe.2011.03.025. Google Scholar [21] C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.007. Google Scholar [22] C. X. Wang and S. Webster, Channel coordination for a supply chain with a risk-neutral manufacturer and a loss-averse retailer, Decision Sciences, 38 (2007), 361-389. doi: 10.1111/j.1540-5915.2007.00163.x. Google Scholar [23] 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.2006.08.003. Google Scholar
A graphical presentation of demand and capacity outcomes
Optimal order quantity vs loss aversion level for different levels of demand variation
Value of $M(h, Q_0)$ vs shortage cost for different levels of demand variation
Optimal order quantity vs selling price
Optimal order quantity vs purchasing cost
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