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Dynamic pricing of network goods in duopoly markets with boundedly rational consumers
Impact of reorder option in supply chain coordination
1. | School of Management and Economics, University of Electronic Science and Technology, Chengdu, China |
2. | Scheller College of Business, Georgia Institute of Technology, Atlanta, USA |
3. | Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong |
4. | Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia |
This paper studies the impacts of some reorder options on the performance as well as the coordination issues in a supply chain. A large category of products requires a long procurement lead time yet only has a relatively short selling season. Hence the purchase decisions usually have to be made well in advance of the opening of the sales. However, when uncertainty exists, the actual market demand may turn out to severely deviate from the initial order amount. To make up for the deficiency arising from this situation, a reorder option is introduced which renders a second manufacturing chance available shortly before he selling season. This reorder option facilitates an adjustment of the inventory level according to the realization of market demand. Since the market under investigation is facing a downward sloping demand curve, the effect of implementing this option is multi-fold. Moreover, the launch of the reorder option may also affect the decision makings at other levels of operations, such as altering the size of the initial order. Therefore, the overall impact of such option is not immediately clear. In this paper, it is shown that a properly designed reorder option is able to bring in profit growth and stabilize the fluctuations in the market retail price. Besides, quantity discount contracts are constructed to coordinate decisions on the initial inventory amount within the supply chain, so as to achieve higher economic efficiency. Finally, numerical examples are given to demonstrate the conclusions obtained in this paper.
References:
[1] |
P. L. Abad and V. Aggarwal, Incorporating transport cost in the lot size and pricing decisions with downward sloping demand, International Journal of Production Economics, 95 (2005), 297-305. Google Scholar |
[2] |
K. J. Arrow and G. Debreu,
Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
doi: 10.2307/1907353. |
[3] |
A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. Google Scholar |
[4] |
M. Baxter and A. Rennie, Financial Calculus An Introduction to Derivative Pricing, Cambridge University Press, 1996. Google Scholar |
[5] |
K. Donohue, Efficient supply contracts for fashion goods with forecast updating and two production modes, Management Science, 46 (2000), 1397-1411. Google Scholar |
[6] |
G. P. Cachon, Supply chain coordination with contracts, in Handbooks in Operations Research and Management Science: Supply Chain Management (eds. S. Graves and T. de Kok), NorthHolland, Amsterdam, The Netherlands, 2003, 227–339. Google Scholar |
[7] |
G. Cachon and M. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. Google Scholar |
[8] |
S. Dasu and L. Li, Optimal operating policies in the presence of exchange rate variability, Management Science, 43 (1997), 705-722. Google Scholar |
[9] |
R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Science, 6 (1987), 1-27. 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. Google Scholar |
[11] |
X. Huang, S. Choi, W. Ching, T. Siu and M. Huang, On supply chain coordination for false failure returns: A quantity discount contract approach, International Journal of Production Economics, 133 (2011), 634-644. Google Scholar |
[12] |
X. Huang, N. Song, W. Ching, T. Siu and K. Yiu,
A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379-389.
doi: 10.3934/jimo.2012.8.379. |
[13] |
X. Huang, J. Gu, W. Ching and T. Siu, Impact of secondary market on consumer return policies and supply chain coordination, Omega, 45 (2014), 57-70. Google Scholar |
[14] |
X. Huang, S. Choi and W. Ching, On improving incentive in a supply chain: Wholesale price contract vs quantity dependent contract, in Computers and Industrial Engineering (CIE), 2010 40th International Conference on, (2010), 1-6. Google Scholar |
[15] |
H. Hishamuddin, R. A. Sarker and D. Essam,
A disruption recovery model for a single stage production-inventory system, European Journal of Operational Research, 222 (2012), 464-473.
doi: 10.1016/j.ejor.2012.05.033. |
[16] |
A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272. Google Scholar |
[17] |
A. Kaul, V. Mehrotra and R. Morck, Demand curves for stocks do slope down: New evidence from an index weights adjustment, The Journal of Finance, 55 (2000), 893-912. Google Scholar |
[18] |
H. Krishman, R. Kapuscinski and D. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63. Google Scholar |
[19] |
B. Kogut and N. Kulatilaka, Operating flexibility, global manufacturing, and the option value of a multinational network, Management Science, 40 (1994), 123-139. Google Scholar |
[20] |
S. Kolay, G. Shaffer and J. A. Ordover, All-unit discounts in retail contracts, Journal of Economics and Management Strategy, 13 (2004), 429-459. Google Scholar |
[21] |
C. Li and P. Kouvelis, Flexible and risk-sharing supply contracts under price uncertainty, Management Science, 45 (1999), 1378-1398. Google Scholar |
[22] |
L. Liang, X. Wang and J. Gao, An option contract pricing model of relief material supply chain, Omega, 40 (2012), 594-600. Google Scholar |
[23] |
B. Pasternack, Optimal pricing and returns policies for perishable commodities, Marketing Science, 4 (1985), 166-176. Google Scholar |
[24] |
O. D. Palsule-Desai, Supply chain coordination using revenue-dependent revenue sharing contracts, Omega, 41 (2013), 780-796. Google Scholar |
[25] |
S. K. Paul, A. Azeem, R. Sarker and D. Essam,
Development of a production inventory model with uncertainty and reliability considerations, Optimization and Engineering, 15 (2014), 697-720.
doi: 10.1007/s11081-013-9218-6. |
[26] |
S. K. Paul, R. Sarker and D. Essam,
Managing risk and disruption in production-inventory and supply chain systems: A review, Journal of Industrial and Management Optimization, 12 (2016), 1009-1029.
doi: 10.3934/jimo.2016.12.1009. |
[27] |
S. K. Paul, R. Sarker and D. Essam, Managing disruption in an imperfect production-inventory system, Computers & Industrial Engineering, 84 (2015), 101-112. Google Scholar |
[28] |
S. K. Paul, R. Sarker and D. Essam,
A disruption recovery plan in a three-stage production-inventory system, Computers and Operations Research, 57 (2015), 60-72.
doi: 10.1016/j.cor.2014.12.003. |
[29] |
S. K. Paul, R. Sarker and D. Essam,
Real time disruption management for a two-stage batch production inventory system with reliability considerations, European Journal of Operational Research, 237 (2014), 113-128.
doi: 10.1016/j.ejor.2014.02.005. |
[30] |
S. K. Paul, R. Sarker and D. Essam, A disruption recovery model in a production-inventory system with demand uncertainty and process reliability, Computer Information Systems and Industrial Management, (2013), 511-522. Google Scholar |
[31] |
J. Spengler, Vertical integration and anti-trust policy, Journal of Political Economy, 58 (1950), 347-352. Google Scholar |
[32] |
T. A. Taylor, Supply chain coordination under channel rebates with dales effort effects, Management Science, 48 (2002), 992-1007. Google Scholar |
[33] |
A. Tsay, S. Nahmias and N. Agrawal, Modeling supply chain contracts: A review in Quantitative Models for Supply Chain Management (eds. S. Tayur, R. Ganeshan and M. Magazine), Kluwer Academic Publishers, Dordrecht (Chapter 10), (1999), 1339-1358. Google Scholar |
[34] |
R. Wilson,
Nonlinear Pricing, Oxford University Press, Oxford, 1993. |
[35] |
S. M. Wagner, S. S. Padhi and I. Zanger, A real option-based supply chain project evaluation and scheduling method, International Journal of Production Research, 52 (2014), 3725-3743. Google Scholar |
show all references
References:
[1] |
P. L. Abad and V. Aggarwal, Incorporating transport cost in the lot size and pricing decisions with downward sloping demand, International Journal of Production Economics, 95 (2005), 297-305. Google Scholar |
[2] |
K. J. Arrow and G. Debreu,
Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
doi: 10.2307/1907353. |
[3] |
A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. Google Scholar |
[4] |
M. Baxter and A. Rennie, Financial Calculus An Introduction to Derivative Pricing, Cambridge University Press, 1996. Google Scholar |
[5] |
K. Donohue, Efficient supply contracts for fashion goods with forecast updating and two production modes, Management Science, 46 (2000), 1397-1411. Google Scholar |
[6] |
G. P. Cachon, Supply chain coordination with contracts, in Handbooks in Operations Research and Management Science: Supply Chain Management (eds. S. Graves and T. de Kok), NorthHolland, Amsterdam, The Netherlands, 2003, 227–339. Google Scholar |
[7] |
G. Cachon and M. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. Google Scholar |
[8] |
S. Dasu and L. Li, Optimal operating policies in the presence of exchange rate variability, Management Science, 43 (1997), 705-722. Google Scholar |
[9] |
R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Science, 6 (1987), 1-27. 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. Google Scholar |
[11] |
X. Huang, S. Choi, W. Ching, T. Siu and M. Huang, On supply chain coordination for false failure returns: A quantity discount contract approach, International Journal of Production Economics, 133 (2011), 634-644. Google Scholar |
[12] |
X. Huang, N. Song, W. Ching, T. Siu and K. Yiu,
A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379-389.
doi: 10.3934/jimo.2012.8.379. |
[13] |
X. Huang, J. Gu, W. Ching and T. Siu, Impact of secondary market on consumer return policies and supply chain coordination, Omega, 45 (2014), 57-70. Google Scholar |
[14] |
X. Huang, S. Choi and W. Ching, On improving incentive in a supply chain: Wholesale price contract vs quantity dependent contract, in Computers and Industrial Engineering (CIE), 2010 40th International Conference on, (2010), 1-6. Google Scholar |
[15] |
H. Hishamuddin, R. A. Sarker and D. Essam,
A disruption recovery model for a single stage production-inventory system, European Journal of Operational Research, 222 (2012), 464-473.
doi: 10.1016/j.ejor.2012.05.033. |
[16] |
A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272. Google Scholar |
[17] |
A. Kaul, V. Mehrotra and R. Morck, Demand curves for stocks do slope down: New evidence from an index weights adjustment, The Journal of Finance, 55 (2000), 893-912. Google Scholar |
[18] |
H. Krishman, R. Kapuscinski and D. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63. Google Scholar |
[19] |
B. Kogut and N. Kulatilaka, Operating flexibility, global manufacturing, and the option value of a multinational network, Management Science, 40 (1994), 123-139. Google Scholar |
[20] |
S. Kolay, G. Shaffer and J. A. Ordover, All-unit discounts in retail contracts, Journal of Economics and Management Strategy, 13 (2004), 429-459. Google Scholar |
[21] |
C. Li and P. Kouvelis, Flexible and risk-sharing supply contracts under price uncertainty, Management Science, 45 (1999), 1378-1398. Google Scholar |
[22] |
L. Liang, X. Wang and J. Gao, An option contract pricing model of relief material supply chain, Omega, 40 (2012), 594-600. Google Scholar |
[23] |
B. Pasternack, Optimal pricing and returns policies for perishable commodities, Marketing Science, 4 (1985), 166-176. Google Scholar |
[24] |
O. D. Palsule-Desai, Supply chain coordination using revenue-dependent revenue sharing contracts, Omega, 41 (2013), 780-796. Google Scholar |
[25] |
S. K. Paul, A. Azeem, R. Sarker and D. Essam,
Development of a production inventory model with uncertainty and reliability considerations, Optimization and Engineering, 15 (2014), 697-720.
doi: 10.1007/s11081-013-9218-6. |
[26] |
S. K. Paul, R. Sarker and D. Essam,
Managing risk and disruption in production-inventory and supply chain systems: A review, Journal of Industrial and Management Optimization, 12 (2016), 1009-1029.
doi: 10.3934/jimo.2016.12.1009. |
[27] |
S. K. Paul, R. Sarker and D. Essam, Managing disruption in an imperfect production-inventory system, Computers & Industrial Engineering, 84 (2015), 101-112. Google Scholar |
[28] |
S. K. Paul, R. Sarker and D. Essam,
A disruption recovery plan in a three-stage production-inventory system, Computers and Operations Research, 57 (2015), 60-72.
doi: 10.1016/j.cor.2014.12.003. |
[29] |
S. K. Paul, R. Sarker and D. Essam,
Real time disruption management for a two-stage batch production inventory system with reliability considerations, European Journal of Operational Research, 237 (2014), 113-128.
doi: 10.1016/j.ejor.2014.02.005. |
[30] |
S. K. Paul, R. Sarker and D. Essam, A disruption recovery model in a production-inventory system with demand uncertainty and process reliability, Computer Information Systems and Industrial Management, (2013), 511-522. Google Scholar |
[31] |
J. Spengler, Vertical integration and anti-trust policy, Journal of Political Economy, 58 (1950), 347-352. Google Scholar |
[32] |
T. A. Taylor, Supply chain coordination under channel rebates with dales effort effects, Management Science, 48 (2002), 992-1007. Google Scholar |
[33] |
A. Tsay, S. Nahmias and N. Agrawal, Modeling supply chain contracts: A review in Quantitative Models for Supply Chain Management (eds. S. Tayur, R. Ganeshan and M. Magazine), Kluwer Academic Publishers, Dordrecht (Chapter 10), (1999), 1339-1358. Google Scholar |
[34] |
R. Wilson,
Nonlinear Pricing, Oxford University Press, Oxford, 1993. |
[35] |
S. M. Wagner, S. S. Padhi and I. Zanger, A real option-based supply chain project evaluation and scheduling method, International Journal of Production Research, 52 (2014), 3725-3743. Google Scholar |









market clearing price of the product | |
amount of products at time |
|
optimal amount of products at time |
|
amount of products at time |
|
optimal amount of products at time |
|
the slope of the demand curve | |
the indicator of the market condition in the high (low) state | |
Arrow-Debreu state price for the high (low) state | |
present value of the risk-free coupon that pays 1 dollar regardless of the state | |
present value of the security that pays |
|
risk-neutral probability of the occurrence of the high (low) state | |
the mean of the uncertain factor |
|
the variance of the uncertain factor |
|
the unit production cost of a product at time |
|
the unit production cost of a product at time |
|
a pre-determined amount of products in the reorder option |
market clearing price of the product | |
amount of products at time |
|
optimal amount of products at time |
|
amount of products at time |
|
optimal amount of products at time |
|
the slope of the demand curve | |
the indicator of the market condition in the high (low) state | |
Arrow-Debreu state price for the high (low) state | |
present value of the risk-free coupon that pays 1 dollar regardless of the state | |
present value of the security that pays |
|
risk-neutral probability of the occurrence of the high (low) state | |
the mean of the uncertain factor |
|
the variance of the uncertain factor |
|
the unit production cost of a product at time |
|
the unit production cost of a product at time |
|
a pre-determined amount of products in the reorder option |
a fixed wholesale price which is higher than |
|
strike price which is pre-determined by the supplier | |
amount of products ordered by the retailer at time |
|
optimal amount of products ordered by the retailer at time |
|
maximum size of products ordered by the retailer at time |
|
parameters in the function of wholesale price |
|
the portion of the maximized supply chain total profit earned by the retailer (supplier) |
a fixed wholesale price which is higher than |
|
strike price which is pre-determined by the supplier | |
amount of products ordered by the retailer at time |
|
optimal amount of products ordered by the retailer at time |
|
maximum size of products ordered by the retailer at time |
|
parameters in the function of wholesale price |
|
the portion of the maximized supply chain total profit earned by the retailer (supplier) |
A | B | c | |||
16 dollars | 0.8 dollar | 4 dollars | 7 dollars | 4 | 1 |
| |||||
0.64 dollar | 0.16 dollar | 20 dollars |
A | B | c | |||
16 dollars | 0.8 dollar | 4 dollars | 7 dollars | 4 | 1 |
| |||||
0.64 dollar | 0.16 dollar | 20 dollars |
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