American Institute of Mathematical Sciences

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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

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), 305-334. doi: 10.2307/2331098.  Google Scholar

[2]

W. Ching, Markov-modulated Poisson processes for multi-location inventory problems, International Journal of Production Economics, 53 (1997), 217-223. doi: 10.1016/S0925-5273(97)00114-X.  Google Scholar

[3]

W. Ching, An inventory model for manufacturing systems with delivery time guarantees, Computers and Operations Research, 25 (1998), 367-377. doi: 10.1016/S0305-0548(97)00077-4.  Google Scholar

[4]

W. Ching, T. Li and S. Choi, A tandem queueing system with applications to pricing strategy, J. Ind. Manag. Optim., 5 (2009), 103-114.  Google Scholar

[5]

T. Copeland, T. Koller and J. Murrin, "Valuation: Measuring and Managing the Value of Companies," 3rd edition, Wiley, New York, 2000. Google Scholar

[6]

M. Dai, H. Y. Wong and Y. K. Kwok, Quanto lookback options, Mathematical Finance, 14 (2004), 445-467. doi: 10.1111/j.0960-1627.2004.00199.x.  Google Scholar

[7]

A. Damodaran, "Damodaran on Valuation," Wiley, New York, 1994. Google Scholar

[8]

A. Dixit and R. Pindyck, "Investment Under Uncertainty," Princeton University Press, Princeton, NJ, 1994. Google Scholar

[9]

R. M. Feldman, A continuous review (s, S) inventory system in a random environment, Journal of Applied Probability, 15 (1978), 654-659. doi: 10.2307/3213131.  Google Scholar

[10]

S. M. Gilbert and R. H. Ballou, Supply chain benefits from advanced customer commitments, Journal of Operations Management, 18 (1999), 61-73. doi: 10.1016/S0272-6963(99)00012-1.  Google Scholar

[11]

V. Henderson, Valuing the option to invest in an incomplete market, Mathematics and Financial Economics, 1 (2007), 103-128. doi: 10.1007/s11579-007-0005-z.  Google Scholar

[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), 85-101. doi: 10.1287/mnsc.47.1.85.10661.  Google Scholar

[13]

D. Kellogg and J. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84. doi: 10.2469/faj.v56.n3.2362.  Google Scholar

[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), 626-643 doi: 10.1287/mnsc.46.5.626.12047.  Google Scholar

[15]

W. S. Lovejoy, Myopic policies for some inventory models with uncertain demand distributions, Management Science, 36 (1990), 724-738. doi: 10.1287/mnsc.36.6.724.  Google Scholar

[16]

E. Schwartz and M. Moon, Rational pricing of internet companies, Financial Analysts Journal, 56 (2000), 62-75. doi: 10.2469/faj.v56.n3.2361.  Google Scholar

[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), 404-420. doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[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), 177-197. doi: 10.3934/jimo.2006.2.177.  Google Scholar

[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), 97-123. doi: 10.1007/s00186-007-0190-9.  Google Scholar

[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), 843-859. doi: 10.3934/jimo.2008.4.843.  Google Scholar

[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), 81-94.  Google Scholar

show all references

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), 305-334. doi: 10.2307/2331098.  Google Scholar

[2]

W. Ching, Markov-modulated Poisson processes for multi-location inventory problems, International Journal of Production Economics, 53 (1997), 217-223. doi: 10.1016/S0925-5273(97)00114-X.  Google Scholar

[3]

W. Ching, An inventory model for manufacturing systems with delivery time guarantees, Computers and Operations Research, 25 (1998), 367-377. doi: 10.1016/S0305-0548(97)00077-4.  Google Scholar

[4]

W. Ching, T. Li and S. Choi, A tandem queueing system with applications to pricing strategy, J. Ind. Manag. Optim., 5 (2009), 103-114.  Google Scholar

[5]

T. Copeland, T. Koller and J. Murrin, "Valuation: Measuring and Managing the Value of Companies," 3rd edition, Wiley, New York, 2000. Google Scholar

[6]

M. Dai, H. Y. Wong and Y. K. Kwok, Quanto lookback options, Mathematical Finance, 14 (2004), 445-467. doi: 10.1111/j.0960-1627.2004.00199.x.  Google Scholar

[7]

A. Damodaran, "Damodaran on Valuation," Wiley, New York, 1994. Google Scholar

[8]

A. Dixit and R. Pindyck, "Investment Under Uncertainty," Princeton University Press, Princeton, NJ, 1994. Google Scholar

[9]

R. M. Feldman, A continuous review (s, S) inventory system in a random environment, Journal of Applied Probability, 15 (1978), 654-659. doi: 10.2307/3213131.  Google Scholar

[10]

S. M. Gilbert and R. H. Ballou, Supply chain benefits from advanced customer commitments, Journal of Operations Management, 18 (1999), 61-73. doi: 10.1016/S0272-6963(99)00012-1.  Google Scholar

[11]

V. Henderson, Valuing the option to invest in an incomplete market, Mathematics and Financial Economics, 1 (2007), 103-128. doi: 10.1007/s11579-007-0005-z.  Google Scholar

[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), 85-101. doi: 10.1287/mnsc.47.1.85.10661.  Google Scholar

[13]

D. Kellogg and J. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84. doi: 10.2469/faj.v56.n3.2362.  Google Scholar

[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), 626-643 doi: 10.1287/mnsc.46.5.626.12047.  Google Scholar

[15]

W. S. Lovejoy, Myopic policies for some inventory models with uncertain demand distributions, Management Science, 36 (1990), 724-738. doi: 10.1287/mnsc.36.6.724.  Google Scholar

[16]

E. Schwartz and M. Moon, Rational pricing of internet companies, Financial Analysts Journal, 56 (2000), 62-75. doi: 10.2469/faj.v56.n3.2361.  Google Scholar

[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), 404-420. doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[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), 177-197. doi: 10.3934/jimo.2006.2.177.  Google Scholar

[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), 97-123. doi: 10.1007/s00186-007-0190-9.  Google Scholar

[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), 843-859. doi: 10.3934/jimo.2008.4.843.  Google Scholar

[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), 81-94.  Google Scholar

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