# American Institute of Mathematical Sciences

• Previous Article
Modeling and analyzing the chaotic behavior in supply chain networks: a control theoretic approach
• JIMO Home
• This Issue
• Next Article
A variational inequality approach for constrained multifacility Weber problem under gauge
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:

show all references

##### References:
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 $y$
 [1] Qiang Lin, Yang Xiao, Jingju Zheng. Selecting the supply chain financing mode under price-sensitive demand: Confirmed warehouse financing vs. trade credit. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2031-2049. doi: 10.3934/jimo.2020057 [2] Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021042 [3] Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169 [4] Xue Qiao, Zheng Wang, Haoxun Chen. Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021079 [5] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effects of disruption risk on a supply chain with a risk-averse retailer. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021024 [6] Peng Tong, Xiaogang Ma. Design of differentiated warranty coverage that considers usage rate and service option of consumers under 2D warranty policy. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1577-1591. doi: 10.3934/jimo.2020035 [7] Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021035 [8] Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023 [9] Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2217-2242. doi: 10.3934/jimo.2020066 [10] Jun Tu, Zijiao Sun, Min Huang. Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021062 [11] David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002 [12] Ziteng Wang, Shu-Cherng Fang, Wenxun Xing. On constraint qualifications: Motivation, design and inter-relations. Journal of Industrial & Management Optimization, 2013, 9 (4) : 983-1001. doi: 10.3934/jimo.2013.9.983 [13] Yu-Hsien Liao. Solutions and characterizations under multicriteria management systems. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021041 [14] Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 [15] Qing-Qing Yang, Wai-Ki Ching, Wan-Hua He, Na Song. Effect of institutional deleveraging on option valuation problems. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2097-2118. doi: 10.3934/jimo.2020060 [16] Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021077 [17] Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 [18] Claudia Lederman, Noemi Wolanski. An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2907-2946. doi: 10.3934/dcds.2020391 [19] Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou. Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021049 [20] Peng Zhang, Yongquan Zeng, Guotai Chi. Time-consistent multiperiod mean semivariance portfolio selection with the real constraints. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1663-1680. doi: 10.3934/jimo.2020039

2019 Impact Factor: 1.366