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July 2018, 14(3): 1105-1122. doi: 10.3934/jimo.2018001

## Portfolio procurement policies for budget-constrained supply chains with option contracts and external financing

 1 School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China 2 Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong 3 Department of Marketing and International Business, Valdosta State University, Valdosta, USA

* Corresponding author: Xu Chen, E-mail: xchenxchen@263.net, Tel: +86-28-83206622

Received  October 2015 Revised  September 2017 Published  January 2018

This study investigates a budget-constrained retailer's optimal financing and portfolio order policies in a supply chain with option contracts. To this end, we develop two analytical models: a basic model with wholesale price contracts as the benchmark and a model with option contracts. Each model considers both the financing scenario and the no-financing scenario. Our analyses show that the retailer uses wholesale price contracts for procurement, instead of option contracts, when its budget is extremely tight. The retailer starts to use a combination of these two types of contracts when the budget constraint is relieved. As the budget increases, the retailer adjusts the procurement ratio through both types until it can implement the optimal ordering policy with an adequate budget. In addition, the condition for seeking external financing is determined by the retailer's initial budget, financing cost, and profit margin.

Citation: Benyong Hu, Xu Chen, Felix T. S. Chan, Chao Meng. Portfolio procurement policies for budget-constrained supply chains with option contracts and external financing. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1105-1122. doi: 10.3934/jimo.2018001
##### References:
 [1] D. Barnes-Schuster, Y. Bassok and R. Anupindi, Coordination and flexibility in supply contracts with options, Manufacturing & Service Operations Management, 4 (2002), 171-207. doi: 10.1287/msom.4.3.171.7754. [2] A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. doi: 10.1287/mnsc.1040.0342. [3] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. doi: 10.1287/mnsc.1040.0278. [4] G. P. Cachon and M. A. Lariviere, Capacity choice and allocation: Strategic behavior and supply chain performance, Management Science, 45 (1999), 1091-1108. doi: 10.1287/mnsc.45.8.1091. [5] R. Caldentey and X. F. Chen, Handbook of Integrated Risk Management in Global Supply Chains: The Role of Financing Service in Procurement Contracts (eds. P. Kouvelis, O. Boyabatli, L. Dong and R. Li), John Wiley & Sons, Inc., New York, 2011. [6] R. Caldentey and M. B. Haugh, Supply contracts with financial hedging, Operations Research, 57 (2009), 47-65. doi: 10.1287/opre.1080.0521. [7] Y. K. Che and I. Gale, The optimal mechanism for selling to a budget-constrained buyer, Journal of Economic Theory, 92 (2000), 198-233. doi: 10.1006/jeth.1999.2639. [8] X. Chen and Z. J. Shen, An analysis of a supply chain with options contracts and service requirements, IIE Transactions, 44 (2012), 805-819. doi: 10.1080/0740817X.2011.649383. [9] X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004. [10] X. Chen and X. Wang, Free or bundled: Channel selection decisions under different power structures, OMEGA-International Journal of Management Science, 53 (2015), 11-20. doi: 10.1016/j.omega.2014.11.008. [11] X. Chen, X. Wang and X. Jiang, The impact of power structure on retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. doi: 10.1057/jors.2015.6. [12] X. Chen, X. Wang and H. Chan, Manufacturer and retailer coordination for environmental and economic competitiveness: A power perspective, Transportation Research Part E: Logistics and Transportation Review, 97 (2017), 268-281. doi: 10.1016/j.tre.2016.11.007. [13] X. Chen, N. Wan and X. Wang, Flexibility and coordination in a supply chain with bidirectional option contracts and service requirement, International Journal of Production Economics, 193 (2017), 183-192. doi: 10.1016/j.ijpe.2017.07.013. [14] X. Chen, X. Wang and K. Gong, The effect of bidimensional power structure on supply chain decisions and performance, IEEE Transactions on Systems Man and Cybernetics: Systems, PP (2017), 1-16. doi: 10.1109/TSMC.2017.2704445. [15] X. Chen and G. Wan, The effect of financing on a budget-constrained supply chain under wholesale price contract, Asia-Pacific Journal of Operational Research, 28 (2011), 457-485. doi: 10.1142/S0217595911003193. [16] K. Chen and T. Xiao, Reordering policy and coordination of a supply chain with a loss-averse retailer, Journal of Industrial and Management Optimization, 9 (2013), 827-853. doi: 10.3934/jimo.2013.9.827. [17] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573. doi: 10.1016/j.orl.2008.06.004. [18] K. L. Donohue, Efficient supply contracts for fashion goods with forecast updating and two production modes, Management Science, 46 (2000), 1397-1411. doi: 10.1287/mnsc.46.11.1397.12088. [19] G. Eppen and A. Iyer, Backup agreements in fashion buying-the value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469. [20] M. Erkoc and S. D. Wu, Managing high-tech capacity expansion via reservation contracts, Production and Operations Management, 14 (2005), 232-251. doi: 10.1111/j.1937-5956.2005.tb00021.x. [21] D. Farlow, G. Schmidt and A. Tsay, Supplier management at Sun Microsystems (A), Palo Alto, CA: Stanford University Graduate School of Business, OIT-16-A and OIT-16-B, (1996). [22] S. Graves and T. de Kok, Handbooks in Operations Research and Management Science, North-Holland/Elsevier, 2003. [23] H. L. Lee, V. Padmanabhan and S. Whang, The bullwhip effect in supply chains, IEEE Engineering Management Review, 43 (2015), 108-117. doi: 10.1109/EMR.2015.7123235. [24] R. Levaggi, Optimal procurement contracts under a binding budget constraint, Public Choice, 101 (1999), 23-37. doi: 10.1023/A:1018311920072. [25] Z. Liu, L. Chen and L. Li, Risk hedging in a supply chain: Option vs. price discount, International Journal of Production Economics, 151 (2014), 112-120. doi: 10.1016/j.ijpe.2014.01.019. [26] Z. Luo, X. Chen and J. Chen, Optimal pricing policies for differentiated brands under different supply chain power structures, European Journal of Operational Research, 259 (2017), 437-451. doi: 10.1016/j.ejor.2016.10.046. [27] Z. Luo, X. Chen and M. Kai, The effect of customer value and power structure on product choice and pricing decisions, OMEGA-International Journal of Management Science, Forthcoming, (2017). doi: 10.1016/j.omega.2017.06.003. [28] J. Nasiry and I. Popescu, Dynamic pricing with loss-averse consumers and peak-end anchoring, Operations Research, 59 (2011), 1361-1368. doi: 10.1287/opre.1110.0952. [29] S. Ng, Supply Chain Management at Solectron, Presentation[C] // Industrial Symposium on Supply Chain Management, Stanford University, Stanford, CA, (1997). [30] Ö. Özer and W. Wei, Strategic commitments for an optimal capacity decision under asymmetric forecast information, Management Science, 52 (2006), 1238-1257. doi: 10.1287/mnsc.1060.0521. [31] S. I. Park and J. S. Kim, A mathematical model for a capacity reservation contract, Applied Mathematical Modelling, 38 (2014), 1866-1880. doi: 10.1016/j.apm.2013.10.005. [32] P. H. Ritchken and C. S. Tapiero, Contingent claims contracting for purchasing decisions in inventory management, Operations Research, 34 (1986), 864-870. doi: 10.1287/opre.34.6.864. [33] S. Saghafian and M. P. Van Oyen, The value of flexible backup suppliers and disruption risk information: newsvendor analysis with recourse, IIE Transactions, 44 (2012), 834-867. doi: 10.1080/0740817X.2012.654846. [34] N. Song, X. Huang and Y. Xie, Impact of reorder option in supply chain coordination, Journal of Industrial and Management Optimization, 13 (2017), 447-473. doi: 10.3934/jimo.2016026. [35] A. Tsay, The quantity flexibility contract and supplier-customer incentives, Management Science, 45 (1999), 1339-1358. doi: 10.1287/mnsc.45.10.1339. [36] C. Wang and X. Chen, Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty, International Journal of Production Research, 53 (2015), 6279-6293. doi: 10.1080/00207543.2015.1053577. [37] C. Wang and X. Chen, Option pricing and coordination in the fresh produce supply chain with portfolio contracts, Annals of Operations Research, 248 (2017), 471-491. doi: 10.1007/s10479-016-2167-7. [38] C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, Forthcoming, (2017), 1-11. doi: 10.1057/s41274-017-0228-1. [39] X. Wang and L. Liu, Coordination in a retailer-led supply chain through option contract, International Journal of Production Economics, 110 (2007), 115-127. doi: 10.1016/j.ijpe.2007.02.022. [40] 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. [41] D. J. Wu, P. R. Kleindorfer and Y. Sun, Optimal capacity expansion in the presence of capacity options, Decision Support Systems, 40 (2005), 553-561. doi: 10.1016/j.dss.2004.09.005. [42] J. H. Wu, Quantity flexibility contracts under Bayesian updating, Computer & Operations Research, 32 (2005), 1267-1288. doi: 10.1016/j.cor.2003.11.004. [43] X. Xu and J. R. Birge, Operational decisions, capital structure, and managerial compensation: A news vendor perspective, The Engineering Economist, 53 (2008), 173-196. doi: 10.1080/00137910802262887. [44] Y. Zhao, L. Ma and G. Xie, Coordination of supply chains with bidirectional option contracts, Contract Analysis and Design for Supply Chains with Stochastic Demand, 234 (2016), 115-129. doi: 10.1007/978-1-4899-7633-8_5.

show all references

##### References:
 [1] D. Barnes-Schuster, Y. Bassok and R. Anupindi, Coordination and flexibility in supply contracts with options, Manufacturing & Service Operations Management, 4 (2002), 171-207. doi: 10.1287/msom.4.3.171.7754. [2] A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. doi: 10.1287/mnsc.1040.0342. [3] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. doi: 10.1287/mnsc.1040.0278. [4] G. P. Cachon and M. A. Lariviere, Capacity choice and allocation: Strategic behavior and supply chain performance, Management Science, 45 (1999), 1091-1108. doi: 10.1287/mnsc.45.8.1091. [5] R. Caldentey and X. F. Chen, Handbook of Integrated Risk Management in Global Supply Chains: The Role of Financing Service in Procurement Contracts (eds. P. Kouvelis, O. Boyabatli, L. Dong and R. Li), John Wiley & Sons, Inc., New York, 2011. [6] R. Caldentey and M. B. Haugh, Supply contracts with financial hedging, Operations Research, 57 (2009), 47-65. doi: 10.1287/opre.1080.0521. [7] Y. K. Che and I. Gale, The optimal mechanism for selling to a budget-constrained buyer, Journal of Economic Theory, 92 (2000), 198-233. doi: 10.1006/jeth.1999.2639. [8] X. Chen and Z. J. Shen, An analysis of a supply chain with options contracts and service requirements, IIE Transactions, 44 (2012), 805-819. doi: 10.1080/0740817X.2011.649383. [9] X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004. [10] X. Chen and X. Wang, Free or bundled: Channel selection decisions under different power structures, OMEGA-International Journal of Management Science, 53 (2015), 11-20. doi: 10.1016/j.omega.2014.11.008. [11] X. Chen, X. Wang and X. Jiang, The impact of power structure on retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. doi: 10.1057/jors.2015.6. [12] X. Chen, X. Wang and H. Chan, Manufacturer and retailer coordination for environmental and economic competitiveness: A power perspective, Transportation Research Part E: Logistics and Transportation Review, 97 (2017), 268-281. doi: 10.1016/j.tre.2016.11.007. [13] X. Chen, N. Wan and X. Wang, Flexibility and coordination in a supply chain with bidirectional option contracts and service requirement, International Journal of Production Economics, 193 (2017), 183-192. doi: 10.1016/j.ijpe.2017.07.013. [14] X. Chen, X. Wang and K. Gong, The effect of bidimensional power structure on supply chain decisions and performance, IEEE Transactions on Systems Man and Cybernetics: Systems, PP (2017), 1-16. doi: 10.1109/TSMC.2017.2704445. [15] X. Chen and G. Wan, The effect of financing on a budget-constrained supply chain under wholesale price contract, Asia-Pacific Journal of Operational Research, 28 (2011), 457-485. doi: 10.1142/S0217595911003193. [16] K. Chen and T. Xiao, Reordering policy and coordination of a supply chain with a loss-averse retailer, Journal of Industrial and Management Optimization, 9 (2013), 827-853. doi: 10.3934/jimo.2013.9.827. [17] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573. doi: 10.1016/j.orl.2008.06.004. [18] K. L. Donohue, Efficient supply contracts for fashion goods with forecast updating and two production modes, Management Science, 46 (2000), 1397-1411. doi: 10.1287/mnsc.46.11.1397.12088. [19] G. Eppen and A. Iyer, Backup agreements in fashion buying-the value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469. [20] M. Erkoc and S. D. Wu, Managing high-tech capacity expansion via reservation contracts, Production and Operations Management, 14 (2005), 232-251. doi: 10.1111/j.1937-5956.2005.tb00021.x. [21] D. Farlow, G. Schmidt and A. Tsay, Supplier management at Sun Microsystems (A), Palo Alto, CA: Stanford University Graduate School of Business, OIT-16-A and OIT-16-B, (1996). [22] S. Graves and T. de Kok, Handbooks in Operations Research and Management Science, North-Holland/Elsevier, 2003. [23] H. L. Lee, V. Padmanabhan and S. Whang, The bullwhip effect in supply chains, IEEE Engineering Management Review, 43 (2015), 108-117. doi: 10.1109/EMR.2015.7123235. [24] R. Levaggi, Optimal procurement contracts under a binding budget constraint, Public Choice, 101 (1999), 23-37. doi: 10.1023/A:1018311920072. [25] Z. Liu, L. Chen and L. Li, Risk hedging in a supply chain: Option vs. price discount, International Journal of Production Economics, 151 (2014), 112-120. doi: 10.1016/j.ijpe.2014.01.019. [26] Z. Luo, X. Chen and J. Chen, Optimal pricing policies for differentiated brands under different supply chain power structures, European Journal of Operational Research, 259 (2017), 437-451. doi: 10.1016/j.ejor.2016.10.046. [27] Z. Luo, X. Chen and M. Kai, The effect of customer value and power structure on product choice and pricing decisions, OMEGA-International Journal of Management Science, Forthcoming, (2017). doi: 10.1016/j.omega.2017.06.003. [28] J. Nasiry and I. Popescu, Dynamic pricing with loss-averse consumers and peak-end anchoring, Operations Research, 59 (2011), 1361-1368. doi: 10.1287/opre.1110.0952. [29] S. Ng, Supply Chain Management at Solectron, Presentation[C] // Industrial Symposium on Supply Chain Management, Stanford University, Stanford, CA, (1997). [30] Ö. Özer and W. Wei, Strategic commitments for an optimal capacity decision under asymmetric forecast information, Management Science, 52 (2006), 1238-1257. doi: 10.1287/mnsc.1060.0521. [31] S. I. Park and J. S. Kim, A mathematical model for a capacity reservation contract, Applied Mathematical Modelling, 38 (2014), 1866-1880. doi: 10.1016/j.apm.2013.10.005. [32] P. H. Ritchken and C. S. Tapiero, Contingent claims contracting for purchasing decisions in inventory management, Operations Research, 34 (1986), 864-870. doi: 10.1287/opre.34.6.864. [33] S. Saghafian and M. P. Van Oyen, The value of flexible backup suppliers and disruption risk information: newsvendor analysis with recourse, IIE Transactions, 44 (2012), 834-867. doi: 10.1080/0740817X.2012.654846. [34] N. Song, X. Huang and Y. Xie, Impact of reorder option in supply chain coordination, Journal of Industrial and Management Optimization, 13 (2017), 447-473. doi: 10.3934/jimo.2016026. [35] A. Tsay, The quantity flexibility contract and supplier-customer incentives, Management Science, 45 (1999), 1339-1358. doi: 10.1287/mnsc.45.10.1339. [36] C. Wang and X. Chen, Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty, International Journal of Production Research, 53 (2015), 6279-6293. doi: 10.1080/00207543.2015.1053577. [37] C. Wang and X. Chen, Option pricing and coordination in the fresh produce supply chain with portfolio contracts, Annals of Operations Research, 248 (2017), 471-491. doi: 10.1007/s10479-016-2167-7. [38] C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, Forthcoming, (2017), 1-11. doi: 10.1057/s41274-017-0228-1. [39] X. Wang and L. Liu, Coordination in a retailer-led supply chain through option contract, International Journal of Production Economics, 110 (2007), 115-127. doi: 10.1016/j.ijpe.2007.02.022. [40] 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. [41] D. J. Wu, P. R. Kleindorfer and Y. Sun, Optimal capacity expansion in the presence of capacity options, Decision Support Systems, 40 (2005), 553-561. doi: 10.1016/j.dss.2004.09.005. [42] J. H. Wu, Quantity flexibility contracts under Bayesian updating, Computer & Operations Research, 32 (2005), 1267-1288. doi: 10.1016/j.cor.2003.11.004. [43] X. Xu and J. R. Birge, Operational decisions, capital structure, and managerial compensation: A news vendor perspective, The Engineering Economist, 53 (2008), 173-196. doi: 10.1080/00137910802262887. [44] Y. Zhao, L. Ma and G. Xie, Coordination of supply chains with bidirectional option contracts, Contract Analysis and Design for Supply Chains with Stochastic Demand, 234 (2016), 115-129. doi: 10.1007/978-1-4899-7633-8_5.
The structure of the optimal order policies
The effects of option contracts without financing
The effects of option contracts with financing
Suppliers possible production quantity function
Nomenclature
 Notation Description $D$ Random variable for market demand with $D\geq0$ $f(x)$ Probability density function for market demand $F(x)$ Cumulative distribution function for market demand, which is a continuous, strictly increasing and invertible function of $x$ with $F(x)=0$ $F^{-1}(x)$ Inverse function of $F(x)$ $p$ Product retail price (＄/unit) $c$ Product manufacturing cost (＄/unit) $s$ Product salvage value (＄/unit) $g$ Retailer's shortage penalty (＄/unit) $w$ Product wholesale price under wholesale price contracts (＄/unit) $w_1$ Product wholesale price under option contracts (＄/unit) $b$ Product option price (＄/unit) $w_2$ Option exercise price (＄/unit) $q$ Retailer's order quantity in the basic model $q^1$ Retailer's firm order quantity in the model with option contracts $q^2$ Retailer's option order quantity in the model with option contracts $q^1+q^2$ Retailer's portfolio order quantity in the model with option contracts, denoted as $q^1+q^2=q$ $Y$ Retailer's initial budget $H$ Retailer's financing amount $\lambda_i$ Generalized Lagrange multiplier, $i=1, 2, 3$ $x^+$ $x^+=max(0, x)$ $u$ Mean of market demand, $u=E(D)$ $E(x)$ Expected value of variable $x$ $min(x, y)$ Minimum between $x$ and $y$
 Notation Description $D$ Random variable for market demand with $D\geq0$ $f(x)$ Probability density function for market demand $F(x)$ Cumulative distribution function for market demand, which is a continuous, strictly increasing and invertible function of $x$ with $F(x)=0$ $F^{-1}(x)$ Inverse function of $F(x)$ $p$ Product retail price (＄/unit) $c$ Product manufacturing cost (＄/unit) $s$ Product salvage value (＄/unit) $g$ Retailer's shortage penalty (＄/unit) $w$ Product wholesale price under wholesale price contracts (＄/unit) $w_1$ Product wholesale price under option contracts (＄/unit) $b$ Product option price (＄/unit) $w_2$ Option exercise price (＄/unit) $q$ Retailer's order quantity in the basic model $q^1$ Retailer's firm order quantity in the model with option contracts $q^2$ Retailer's option order quantity in the model with option contracts $q^1+q^2$ Retailer's portfolio order quantity in the model with option contracts, denoted as $q^1+q^2=q$ $Y$ Retailer's initial budget $H$ Retailer's financing amount $\lambda_i$ Generalized Lagrange multiplier, $i=1, 2, 3$ $x^+$ $x^+=max(0, x)$ $u$ Mean of market demand, $u=E(D)$ $E(x)$ Expected value of variable $x$ $min(x, y)$ Minimum between $x$ and $y$
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