Mean-Variance Analysis for the Supply Chain Sales Rebate Contract
Sales Rebate Contracts in Fashion Supply Chains1
Chun-Hung CHIUa, Tsan-Ming CHOIb,2, Ho-Ting YEUNGb, Yingxue ZHAOc
a b
Sun Yat-Sen Business School, Sun Yat-Sen University, China.
Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
c
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, P. R. China.
First version: July 26, 2012; revised: August 31, 2012.
A paper prepared for Mathematical Problems in Engineering: Special Issue on Mathematical Modeling Research in Fashion and Textiles Supply Chains and Operational Control Systems.
1 2
The authors sincerely thank the anonymous reviewers for their constructive comments on this paper. Corresponding author: email – jason.choi@polyu.edu.hk, phone – (852)27666450
Sales Rebate Contracts in Fashion Supply Chains
Abstract
We explore in this paper the performance of sales rebate contracts in fashion supply chains. We conduct both analytical and numerical analysis via a mean-variance framework with reference to real empirical data. To be specific, we evaluate the expected profits and variance of profits (risk) of the fashion supply chains, fashion retailers and manufacturers under 1) the currently implemented sales rebate practices, 2) the case without sales rebate, and 3) the theoretical coordination situation (if target sales rebate is adopted). In addition, we analyze how sales effort affects the performances of the supply chain and its agents. Our analysis indicates that the rebate contracts may hurt the retailer and the manufacturer of a fashion supply chain when it is inappropriately set. Moreover, a properly designed sales rebate contract not only can coordinate the supply chain (with retail sales effort) but can also improve expected profits and lower the levels of risk for both the manufacturer and the retailer. Keywords: Supply chain coordination, rebate contract, linear
Chun-Hung CHIUa, Tsan-Ming CHOIb,2, Ho-Ting YEUNGb, Yingxue ZHAOc
a b
Sun Yat-Sen Business School, Sun Yat-Sen University, China.
Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
c
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, P. R. China.
First version: July 26, 2012; revised: August 31, 2012.
A paper prepared for Mathematical Problems in Engineering: Special Issue on Mathematical Modeling Research in Fashion and Textiles Supply Chains and Operational Control Systems.
1 2
The authors sincerely thank the anonymous reviewers for their constructive comments on this paper. Corresponding author: email – jason.choi@polyu.edu.hk, phone – (852)27666450
Sales Rebate Contracts in Fashion Supply Chains
Abstract
We explore in this paper the performance of sales rebate contracts in fashion supply chains. We conduct both analytical and numerical analysis via a mean-variance framework with reference to real empirical data. To be specific, we evaluate the expected profits and variance of profits (risk) of the fashion supply chains, fashion retailers and manufacturers under 1) the currently implemented sales rebate practices, 2) the case without sales rebate, and 3) the theoretical coordination situation (if target sales rebate is adopted). In addition, we analyze how sales effort affects the performances of the supply chain and its agents. Our analysis indicates that the rebate contracts may hurt the retailer and the manufacturer of a fashion supply chain when it is inappropriately set. Moreover, a properly designed sales rebate contract not only can coordinate the supply chain (with retail sales effort) but can also improve expected profits and lower the levels of risk for both the manufacturer and the retailer. Keywords: Supply chain coordination, rebate contract, linear
References: [1] Anupindi, R. and Bassok Y. (1999), “Supply contracts with quantity commitments and stochastic demand”, in Tayur S., Ganeshan R. and. Magazine M. (Ed.), Quantitative Models for Supply Chain Management, Kluwer, Boston, pp.197-232. 10.1109/TSMCA.2012.2204739), forthcoming. [23] Spengler, J. (1950), “Vertical integration and antitrust policy”, Journal of Political Economy, pp.347-352. Appendix 1. Summary of Profits in No-Sales-Effort Model (with different demand) Demand sizes: Small (mean µ = 100, standard deviation σ = 30), medium (µ = 1000, σ = 300) and large (µ = 10000, σ = 3000) MRS Medium