A Comparative Study to Find the Optimal Ordering Quantity of the Risk-Neutral and Risk-Averse Newsvendor
DOI:
https://doi.org/10.2298/YJOR210815015MKeywords:
Optimal ordering quantity, risk-neutral, risk-averse, expected utility, initial wealth, salvage valueAbstract
In the classical newsvendor problem, it is considered that the newsvendor is risk-neutral and the Optimal Ordering Quantity (OOQ) was found which maximizes the newsvendor expected profit. In the real world, different investors have different attitudes towards risk. Accordingly, this paper considers the utility function which is commonly being used to model the attitude of the investor who makes the investment decision to maximize his expected utility instead of expected profit. This study considers the quadratic utility function and demonstrates that it can be used to describe the riskaverse as well as a risk-neutral investor with some conditions. Finally, by considering the risk profile of the investor at different levels of investor initial wealth, we have developed a method to determine the OOQ which maximizes the expected utility. From the numerical examples, it is clear that the OOQ and hence the expected utility varies depending on an investor’s attitude toward the risk and investment decision. At different levels of initial wealth, the attitudes toward the risk of the investors are different and the sensitivity analysis demonstrates how an investor can choose the initial wealth and OOQ to maximize his expected utility.References
Y. Fathi, and H.L.W. Nuttle, “AIDS: maximin vs. expected profit and the faithful newsboy problem”, IIE Transactions, vol. 19, no. 2, pp. 238-240, 1987.
H. S. Lau, “The newsboy problem under alternative optimization objectives”, Journal of the Operational Research Society, vol. 31, no. 1, pp. 525-535, 1980.
M-G. Huang, “Economic ordering model for deteriorating items with random demand and deterioration”, Int. J. of Production Research, vol. 51, no.18, pp. 5612-5624, 2013.
M. Anvari, “Optimality Criteria and Risk in Inventory Models: The Case of the newsvendor Problem”, Journal of the Operational Research Society, vol. 38, no.7, pp. 625-632, 1987.
K. Chung, “Risk in inventory models: the case of the newsboy problem optimality conditions”, Journal of Operations Research Society, vol. 41, no. 2, pp. 173-176, 1990.
G. C. Mahata, “A single period inventory model for incorporating two-ordering opportunities under imprecise demand information”, International Journal of Industrial Engineering Computations, vol. 2, no. 1, pp, 385-394, 2011.
V. Mohan,(in press) “An Inventory Model for Decaying Items with Pareto Distribution, Time- Dependent Demand and Shortages”, International Journal of Mathematics in Operational Research.
S. Sindhuja, (in press) “A Quadratic Demand EOQ Model for Deteriorating Items with Time-Dependent Shortage”, International Journal of Mathematics in Operational Research.
K. Kumar, N. Kumar, and M. Meenu, “An inventory system for varying decaying medicinal products in healthcare trade”, Yugoslav Journal of Operations Research, vol. 31, no. 2, pp. 273-283. 2021. https://doi.org/10.2298/yjor200125011k
I. Sangal, B. K. Shaw, B. Sarkar, and R. Guchhait, “A joint inventory model with reliability, carbon emission, and inspection errors in a defective production system”, Yugoslav Journal of Operations Research, vol. 30, no. 2, pp. 379-396, 2020. https://doi.org/10.2298/YJOR190415020S
W. A. Jauhari, R. Sulistyanto, and P. W. Laksono, “Coordinating a two-level supply chain with defective items, inspection errors and price-sensitive demand”, Songklanakarin Journal of Science and Technology, vol. 40, no. 1, pp. 135-145, 2018. https://doi.org/10.14456/sjstpsu.2018.2
W. A. Jauhari, and R. S. Saga, “A stochastic periodic review inventory model for vendor-buyer system with setup cost reduction and service-level constraint”, Production and Manufacturing Research, vol. 5, no. 1, pp. 371-389, 2017. https://doi.org/10.1080/21693277.2017.1401965
W. A. Jauhari, “Integrated vendor-buyer model with defective items, inspection error and stochastic demand”, International Journal of Mathematics in Operational Research, vol. 8, no. 3, pp. 342-359, 2016. https://doi.org/10.1504/IJMOR.2016.075520
A. Khanna, P. Gautam, A. Hasan, and C. K. Jaggi, “Inventory and pricing decisions for an imperfect production system with quality inspection, rework, and carbonemissions”, Yugoslav Journal of Operations Research, vol. 30, no. 2, pp. 337-358, 2020. https://doi.org/10.2298/YJOR190410012K
R.H. Su, and W.L. Pearn, “Profitability evaluation for newsboy-type product with normally distributed demand”, European J. Industrial Engineering, vol. 7, no. 1, pp. 2-15, 2013.
J. Li, H-S. Lau, and A.H-L. Lau, “A two-product newsboy problem with satisfying objective and independent exponential demands”, IIE Transactions, vol. 23, no. 1, pp 29-39, 1991.
L. H. Chen, and Y. C. Chen, “A newsboy problem with a simple reservation arrangement”, Computers and Industrial Engineering, vol.56, no. 1, pp 157-160, 2009.
L-H. Chen, and Y-C. Chen, “A newsboy problem considering reservation policy with fuzzy demand”, International Journal of Innovative Computing, Information and Control, vol. 6, no. 1, pp. 4937-4956, 2010.
L-H. Chen, and Y-C. Chen, “A multiple-item budget-constraint newsboy problem with a reservation policy”, Omega, vol.38, no. 1, pp. 431-439, 2010.
M. Khouja, and A. Mehrez, “A multi product constrained newsboy problem with progressive multiple discounts”, Computers and Industrial Engineering, vol. 30, no. 1, pp. 95-101, 1996.
C.S. Chung, and J. Flynn, “A newsboy problem with reactive production”, Computers and Operations Research, vol. 28, no. 1, pp. 751-765, 2001.
Z. T. Balkhi, and L. Benkherouf, “On an Inventory Model for Deteriorating Items with Stock Dependent and Time-Varying Demand Rate”, Computers and Operations Research, vol. 31, no.2, pp. 223-240, 2004.
M. Khouja, “The Single-Period (News-Vendor) Problem: Literature Review and Suggestions for Future Research”, Omega, vol. 27, no. 5, pp. 537-553, 1999.
B. C. Giria, and A. Chakraborty, “A Supply chain coordination for a deteriorating product under stock-dependent consumption rate and unreliable production process”, International Journal of Industrial Engineering Computations, vol. 2, no. 1, pp. 263-272, 2011.
J. Ibarra-Salazar, “The risk averse and prudent newsboy: changes in risk and costs”, International Journal of Operational Research, vol. 31, no. 3, pp. 357-367, 2018.
M. Bouakiz, and M. J. Sobel, “Inventory Control with an Exponential Utility Criterion”, Operations Research, vol. 40, no. 3, pp. 603-608, 1992.
G. Zhang, Y. Xu, Y. Dong, and H. Li, “Managing reward and risk of the newsboy problem with range information”, European Journal of Industrial Engineering, vol. 6, no. 6, pp.733-750, 2012.
M. Ota, S. Srinivasan, and C. D. Nandakumar, “Optimal order quantity by maximising expected utility for the newsboy model”, International Journal of Procurement Management, vol. 12, no. 4, pp. 410-424, 2019.
M. Ota, S. Srinivasan, C.D. Nandakumar, and K. Waheed, “Manufacturer optimal stock requirement and production rate to maximise the expected profit during peak time”, International Journal of Procurement Management, vol. 13, no. 2, pp. 257-277, 2020.
Downloads
Published
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
