A real option approach to optimal inventory management of retail products

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April 2012, 8(2): 379-389. doi: 10.3934/jimo.2012.8.379

A real option approach to optimal inventory management of retail products

Ximin Huang ^1, , Na Song ^2, , Wai-Ki Ching ^2, , Tak-Kuen Siu ^3, and Ka-Fai Cedric Yiu ^4,

1.	College of Management, Georgia Institute of Technology, 800 West Peachtree Street NW Atlanta, Georgia 30308-0520
2.	Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
3.	Department of Applied Finance and Actuarial Studies and the Centre for Financial Risk, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
4.	Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received March 2011 Revised October 2011 Published April 2012

Abstract
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This paper introduces a novel approach to discuss an optimal inventory level of a retail product using a real option framework. We consider stochastic models for the evolution of the demand and unit price of the product over time. The profit structure of the retailer is represented by the payoff of the real option. An actuarial approach is then used to price the option. The retailer determines an optimal inventory level of the product with a view to maximizing the net expected profit. Numerical examples will be given to illustrate the practical implementation of the proposed approach and to investigate the impacts of changes in parameters on the optimal inventory level of the product.

Keywords: pricing, Supply chain management, inventory level., actuarial valuation, real option, retail product, stochastic demand.

Mathematics Subject Classification: Primary: 90B22; Secondary: 91A0.

Citation: Ximin Huang, Na Song, Wai-Ki Ching, Tak-Kuen Siu, Ka-Fai Cedric Yiu. A real option approach to optimal inventory management of retail products. Journal of Industrial & Management Optimization, 2012, 8 (2) : 379-389. doi: 10.3934/jimo.2012.8.379

References:

[1]	P. D. Childsa, S. H. Ott and A. J. Triantis, Capital budgeting for interrelated projects: A real options approach,, Journal of Financial and Quantitative Analysis, 33 (1998), 305. doi: 10.2307/2331098.
[2]	W. Ching, Markov-modulated Poisson processes for multi-location inventory problems,, International Journal of Production Economics, 53 (1997), 217. doi: 10.1016/S0925-5273(97)00114-X.
[3]	W. Ching, An inventory model for manufacturing systems with delivery time guarantees,, Computers and Operations Research, 25 (1998), 367. doi: 10.1016/S0305-0548(97)00077-4.
[4]	W. Ching, T. Li and S. Choi, A tandem queueing system with applications to pricing strategy,, J. Ind. Manag. Optim., 5 (2009), 103.
[5]	T. Copeland, T. Koller and J. Murrin, "Valuation: Measuring and Managing the Value of Companies,", 3^rd edition, (2000).
[6]	M. Dai, H. Y. Wong and Y. K. Kwok, Quanto lookback options,, Mathematical Finance, 14 (2004), 445. doi: 10.1111/j.0960-1627.2004.00199.x.
[7]	A. Damodaran, "Damodaran on Valuation,", Wiley, (1994).
[8]	A. Dixit and R. Pindyck, "Investment Under Uncertainty,", Princeton University Press, (1994).
[9]	R. M. Feldman, A continuous review (s, S) inventory system in a random environment,, Journal of Applied Probability, 15 (1978), 654. doi: 10.2307/3213131.
[10]	S. M. Gilbert and R. H. Ballou, Supply chain benefits from advanced customer commitments,, Journal of Operations Management, 18 (1999), 61. doi: 10.1016/S0272-6963(99)00012-1.
[11]	V. Henderson, Valuing the option to invest in an incomplete market,, Mathematics and Financial Economics, 1 (2007), 103. doi: 10.1007/s11579-007-0005-z.
[12]	A. Huchzermeier and C. H. Loch, Project management under risk: Using the real options approach to evaluate flexibility in R&D,, Management Science, 47 (2001), 85. doi: 10.1287/mnsc.47.1.85.10661.
[13]	D. Kellogg and J. Charnes, Real-options valuation for a biotechnology company,, Financial Analysts Journal, 56 (2000), 76. doi: 10.2469/faj.v56.n3.2362.
[14]	H. L. Lee, K. C. So and C. S. Tang, The value of information sharing in a two-level supply chain,, Management Science, 46 (2000), 626. doi: 10.1287/mnsc.46.5.626.12047.
[15]	W. S. Lovejoy, Myopic policies for some inventory models with uncertain demand distributions,, Management Science, 36 (1990), 724. doi: 10.1287/mnsc.36.6.724.
[16]	E. Schwartz and M. Moon, Rational pricing of internet companies,, Financial Analysts Journal, 56 (2000), 62. doi: 10.2469/faj.v56.n3.2361.
[17]	M. E. Schweitzer and G. P. Cachon, Decision bias in The newsvendor problems with a known demand distribution: Experimental evidence,, Management Science, 46 (2000), 404. doi: 10.1287/mnsc.46.3.404.12070.
[18]	Tak Kuen Siu, Howell Tong and Hailiang Yang, Option pricing under threshold autoregressive models by threshold Esscher transform,, J. Ind. Manag. Optim., 2 (2006), 177. doi: 10.3934/jimo.2006.2.177.
[19]	C.-O. Ewald and Z. Yang, Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk,, Mathematical Methods of Operations Research, 68 (2008), 97. doi: 10.1007/s00186-007-0190-9.
[20]	X. Xu and X. Cai, Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium,, J. Ind. Manag. Optim., 4 (2008), 843. doi: 10.3934/jimo.2008.4.843.
[21]	K. F. C. Yiu, S. Y. Wang and K. L. Mak, Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains,, J. Ind. Manag. Optim., 4 (2008), 81.

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References:

[1]	P. D. Childsa, S. H. Ott and A. J. Triantis, Capital budgeting for interrelated projects: A real options approach,, Journal of Financial and Quantitative Analysis, 33 (1998), 305. doi: 10.2307/2331098.
[2]	W. Ching, Markov-modulated Poisson processes for multi-location inventory problems,, International Journal of Production Economics, 53 (1997), 217. doi: 10.1016/S0925-5273(97)00114-X.
[3]	W. Ching, An inventory model for manufacturing systems with delivery time guarantees,, Computers and Operations Research, 25 (1998), 367. doi: 10.1016/S0305-0548(97)00077-4.
[4]	W. Ching, T. Li and S. Choi, A tandem queueing system with applications to pricing strategy,, J. Ind. Manag. Optim., 5 (2009), 103.
[5]	T. Copeland, T. Koller and J. Murrin, "Valuation: Measuring and Managing the Value of Companies,", 3^rd edition, (2000).
[6]	M. Dai, H. Y. Wong and Y. K. Kwok, Quanto lookback options,, Mathematical Finance, 14 (2004), 445. doi: 10.1111/j.0960-1627.2004.00199.x.
[7]	A. Damodaran, "Damodaran on Valuation,", Wiley, (1994).
[8]	A. Dixit and R. Pindyck, "Investment Under Uncertainty,", Princeton University Press, (1994).
[9]	R. M. Feldman, A continuous review (s, S) inventory system in a random environment,, Journal of Applied Probability, 15 (1978), 654. doi: 10.2307/3213131.
[10]	S. M. Gilbert and R. H. Ballou, Supply chain benefits from advanced customer commitments,, Journal of Operations Management, 18 (1999), 61. doi: 10.1016/S0272-6963(99)00012-1.
[11]	V. Henderson, Valuing the option to invest in an incomplete market,, Mathematics and Financial Economics, 1 (2007), 103. doi: 10.1007/s11579-007-0005-z.
[12]	A. Huchzermeier and C. H. Loch, Project management under risk: Using the real options approach to evaluate flexibility in R&D,, Management Science, 47 (2001), 85. doi: 10.1287/mnsc.47.1.85.10661.
[13]	D. Kellogg and J. Charnes, Real-options valuation for a biotechnology company,, Financial Analysts Journal, 56 (2000), 76. doi: 10.2469/faj.v56.n3.2362.
[14]	H. L. Lee, K. C. So and C. S. Tang, The value of information sharing in a two-level supply chain,, Management Science, 46 (2000), 626. doi: 10.1287/mnsc.46.5.626.12047.
[15]	W. S. Lovejoy, Myopic policies for some inventory models with uncertain demand distributions,, Management Science, 36 (1990), 724. doi: 10.1287/mnsc.36.6.724.
[16]	E. Schwartz and M. Moon, Rational pricing of internet companies,, Financial Analysts Journal, 56 (2000), 62. doi: 10.2469/faj.v56.n3.2361.
[17]	M. E. Schweitzer and G. P. Cachon, Decision bias in The newsvendor problems with a known demand distribution: Experimental evidence,, Management Science, 46 (2000), 404. doi: 10.1287/mnsc.46.3.404.12070.
[18]	Tak Kuen Siu, Howell Tong and Hailiang Yang, Option pricing under threshold autoregressive models by threshold Esscher transform,, J. Ind. Manag. Optim., 2 (2006), 177. doi: 10.3934/jimo.2006.2.177.
[19]	C.-O. Ewald and Z. Yang, Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk,, Mathematical Methods of Operations Research, 68 (2008), 97. doi: 10.1007/s00186-007-0190-9.
[20]	X. Xu and X. Cai, Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium,, J. Ind. Manag. Optim., 4 (2008), 843. doi: 10.3934/jimo.2008.4.843.
[21]	K. F. C. Yiu, S. Y. Wang and K. L. Mak, Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains,, J. Ind. Manag. Optim., 4 (2008), 81.

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