Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T11:06:59.455Z Has data issue: false hasContentIssue false
  • English
  • Français

BI-LEVEL PROGRAMMING APPROACH TO OPTIMAL STRATEGY FOR VENDOR-MANAGED INVENTORY PROBLEMS UNDER RANDOM DEMAND

Part of: Design of experiments Artificial intelligence (68Txx)

Published online by Cambridge University Press:  20 November 2017

YINXUE LI ,
ZHONG WAN Open the ORCID record for ZHONG WAN [Opens in a new window]  and
JINGJING LIU
YINXUE LI
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
ZHONG WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
JINGJING LIU
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
*
✉wanmath@csu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present an extension of vendor-managed inventory (VMI) problems by considering advertising and pricing policies. Unlike the results available in the literature, the demand is supposed to depend on the retail price and advertising investment policies of the manufacturer and retailers, and is a random variable. Thus, the constructed optimization model for VMI supply chain management is a stochastic bi-level programming problem, where the manufacturer is the upper level decision-maker and the retailers are the lower-level ones. By the expectation method, we first convert the stochastic model into a deterministic mathematical program with complementarity constraints (MPCC). Then, using the partially smoothing technique, the MPCC is transformed into a series of standard smooth optimization subproblems. An algorithm based on gradient information is developed to solve the original model. A sensitivity analysis has been employed to reveal the managerial implications of the constructed model and algorithm: (1) the market parameters of the model generate significant effects on the decision-making of the manufacturer and the retailers, (2) in the VMI mode, much attention should be paid to the holding and shortage costs in the decision-making.

Keywords

game theorystochastic modelssmoothing algorithmoptimizationvendor-managed inventory problems

MSC classification

Primary: 90C30: Nonlinear programming
Secondary: 62K05: Optimal designs 68T37: Reasoning under uncertainty
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 247 - 270
Copyright
© 2017 Australian Mathematical Society 

References

Birge, J. R., Qi, L. and Wei, Z., “A variant of the Topkis–Veinott method for solving inequality constrained optimization problems”, Appl. Math. Optim. 41 (2000) 309–330 ; doi:10.1007/s002459911015.Google Scholar
Burgin, T. A., “Inventory control with normal demand and gamma lead times”, J. Oper. Res. Soc. 23 (1972) 73–80; doi:10.1057/jors.1972.7.Google Scholar
Chen, X., Hao, G., Li, X. and Yiu, K. F. C., “The impact of demand variability and transshipment on vendor’s distribution policies under vendor managed inventory strategy”, Int. J. Prod. Econ. 139 (2012) 42–48; doi:10.1016/j.ijpe.2011.05.005.Google Scholar
Chen, X. R., Liu, Y. M. and Wan, Z., “Optimal decision-making for the online and offline retailers under BOPS model”, ANZIAM J. 58 (2016) 187–208; doi:10.1017/S1446181116000201.Google Scholar
Chen, Y. and Wan, Z., “A locally smoothing method for mathematical programs with complementarity constraints”, ANZIAM J. 56 (2015) 299–315; doi:10.1017/S1446181115000048.CrossRefGoogle Scholar
Chu, Y. and You, F., “Integrated scheduling and dynamic optimization by Stackelberg game: bilevel model formulation and efficient solution algorithm”, Ind. Eng. Chem. Res. 53 (2014) 5564–5581; doi:10.1021/ie404272t.Google Scholar
Fong, D. K. H., Gempesaw, V. M. and Ord, J. K., “Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times”, European J. Oper. Res. 120 (2000) 97–107; doi:10.1016/S0377-2217(98)00394-4.Google Scholar
Giri, B. C., Bardhan, S. and Maiti, T., “Coordinating a three-layer supply chain with uncertain demand and random yield”, Int. J. Prod. Res. 54 (2016) 2499–2518 ; doi:10.1080/00207543.2015.1119324.Google Scholar
Govindan, K., “The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory”, European J. Oper. Res. 242 (2015) 402–423; doi:10.1016/j.ejor.2014.09.045.Google Scholar
Goyal, S. K. and Gunasekaran, A., “An integrated production-inventory-marketing model for deteriorating items”, Comput. Ind. Eng. 28 (1995) 755–762; doi:10.1016/0360-8352(95)00016-T.Google Scholar
Hohmann, S. and Zelewski, S., “Effects of vendor-managed inventory on the bullwhip effect”, IJISSCM 4 (2012) 1–17; doi:10.4018/jisscm.2011070101.Google Scholar
Huang, S. and Wan, Z., “A new nonmonotone spectral residual method for nonsmooth nonlinear equations”, J. Comput. Appl. Math. 313 (2017) 82–101; doi:10.1016/j.cam.2016.09.014.Google Scholar
Huynh, C. H. and Pan, W., “Operational strategies for supplier and retailer with risk preference under VMI contract”, Int. J. Prod. Econ. 169 (2015) 413–421; doi:10.1016/j.ijpe.2015.07.026.Google Scholar
Karray, S. and Martín-Herrán, G., “A dynamic model for advertising and pricing competition between national and store brands”, European J. Oper. Res. 193 (2009) 451–467 ; doi:10.1016/j.ejor.2007.11.043.Google Scholar
Kiesmller, G. P. and Broekmeulen, R. A. C. M., “The benefit of VMI strategies in a stochastic multi-product serial two echelon system”, Comput. Oper. Res. 37 (2011) 406–416 ; doi:10.1016/j.cor.2009.06.013.Google Scholar
Lee, J. Y. and Ren, L., “Vendor-managed inventory in a global environment with exchange rate uncertainty”, Int. J. Prod. Econ. 130 (2011) 169–174; doi:10.1016/j.ijpe.2010.12.006.Google Scholar
Luo, Z. Q., Pang, J. S. and Ralph, D., Mathematical programs with equilibrium constraints (Cambridge University Press, New York, NY, 1996); doi:10.1017/CBO9780511983658.Google Scholar
Mateen, A., Chatterjee, A. K. and Mitra, S., “VMI for single-vendor multi-retailer supply chains under stochastic demand”, Comput. Ind. Eng. 79 (2015) 95–102; doi:10.1016/j.cie.2014.10.028.CrossRefGoogle Scholar
Mohammaditabar, D., Ghodsypour, S. H. and Hafezalkotob, A., “A game theoretic analysis in capacity-constrained supplier-selection and cooperation by considering the total supply chain inventory costs”, Int. J. Prod. Econ. 181 (2015) 87–97; doi:10.1016/j.ijpe.2015.11.016.Google Scholar
Shah, N. H., Widyadana, G. A. and Wee, H. M., “Stackelberg game for two-level supply chain with price markdown option”, Int. J. Comput. Math. 91 (2014) 1054–1060 ; doi:10.1080/00207160.2013.819973.CrossRefGoogle Scholar
Sinha, A., Malo, P., Frantsev, A., Frantsev, A. and Deb, K., “Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm”, Comput. Oper. Res. 41 (2014) 374–385; doi:10.1016/j.cor.2013.07.010.Google Scholar
Stanger, S. H. W., “Vendor managed inventory in the blood supply chain in Germany: evidence from multiple case studies”, Strategic Outsourcing: An Int. J. 6 (2013) 25–47 ; doi:10.1108/17538291311316054.Google Scholar
Subramanyam, S. and Kumaraswamy, S., “EOQ formula under varying marketing policies and conditions”, AIIE Trans. 13 (1981) 312–314; doi:10.1080/05695558108974567.Google Scholar
Tsao, Y. C., Lu, J. C., An, N., Al-Khayyal, F., Lu, R. W. and Han, G., “Retailer shelf-space management with trade allowance: a Stackelberg game between retailer and manufacturers”, Int. J. Prod. Econ. 148 (2014) 133–144; doi:10.1016/j.ijpe.2013.09.018.Google Scholar
Wan, Z., Zhang, S. J. and Teo, K. L., “Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving”, Optim. Eng. 15 (2014) 267–292 ; doi:10.1007/s11081-012-9205-3.Google Scholar
Wang, K. J., Makond, B. and Liu, S. Y., “Location and allocation decisions in a two-echelon supply chain with stochastic demand – a genetic-algorithm based solution”, Expert Syst. Appl. 38 (2011) 6125–6131; doi:10.1016/j.eswa.2010.11.008.Google Scholar
Yang, D. and Jiao, R. J., “Simultaneous configuration of product families and supply chains for mass customization using leader-follower game theory”, in: Industrial Engineering and Engineering Management (IEEM), Malaysia, 9–12 December 2014, (IEEE, 2014) 707–711.Google Scholar
Yu, Y., Chu, F. and Chen, H., “A Stackelberg game and its improvement in a VMI system with a manufacturing vendor”, European J. Oper. Res. 192 (2009) 929–948 ; doi:10.1016/j.ejor.2007.10.016.Google Scholar
Yu, Y., Huang, G. Q. and Liang, L., “Stackelberg game-theoretic model for optimizing advertising, pricing and inventory policies in vendor managed inventory (VMI) production supply chains”, Comput. Ind. Eng. 57 (2009) 368–382; doi:10.1016/j.cie.2008.12.003.Google Scholar
Zhang, X. B., Huang, S. and Wan, Z., “Optimal pricing and ordering in global supply chain management with constraints under random demand”, Appl. Math. Model. 40 (2016) 10105–10130; doi:10.1016/j.apm.2016.06.054.Google Scholar
Zhang, X. B., Huang, S. and Wan, Z., “Stochastic programming approach to global supply chain management under random additive demand”, Oper. Res. Int. J. online (2016) 1–32 ; doi:10.1007/s12351-016-0269-2.Google Scholar
Zhou, Y. W., “A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information”, European J. Oper. Res. 181 (2007) 686–703; doi:10.1016/j.ejor.2006.08.001.Google Scholar