Analysis of a Dominant Retailer Dual-Channel Supply Chain under Customers’ Channel Preference: The α-Branch and Bound Solution Algorithm

Document Type: Research Paper

Authors

Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Abstract

This paper investigates the Stackelberg equilibrium for pricing and ordering decisions in a dominant retailer dual-channel supply chain. In a dual-channel sales network, the products are sold through both a traditional, physical retailer and a direct Internet channel. It is assumed that the retailer is the leader and the powerful member of the supply chain has the market power and acts as a leader and proposes his/her inventory policies and dollar-markup and the manufacturer, as a follower, will decide on the wholesale price and the price of Internet channel as well as the inventory quantity of online store based on the retailer’s decisions. The situation is formulated as a bi-level programming problem, and it is converted to a single level model using Karush-Kuhn-Tucker (KKT) conditions. The single level problem is solved using the α-Branch and Bound (α-BB) algorithm. We investigate the significance of customers’ channel preference on adopting an online channel by the manufacturer. We show that an online channel is not always detrimental to a retailer, but in a Pareto-zone, a range or zone of customers’ channel preference, both supply chain members benefit from newly added sales channel.

Keywords

Main Subjects


Article Title [Persian]

تحلیل زنجیره تامین دوکاناله با یک خرده فروش قدرتمند و با لحاظ ترجیحات مشتری در [انتخاب] کانال: الگوریتم حل آلفا- انشعاب و تحدید

Authors [Persian]

  • رضا پاکدل مهربانی
  • عباس سیفی
دانشکده مهندسی صنایع و سیستمهای مدیریت، دانشگاه امیرکبیر(پلی تکنیک تهران)، تهران، ایران
Abstract [Persian]

این مقاله به بررسی تعادل استگلبرگ در تصمیم های قیمت گذاری و سفارش‌دهی در یک زنجیره تامین دوکاناله با وجود یک خرده فروش قدرتمند می‌پردازد. در یک زنجیره تامین دو کاناله، تولید کننده محصولات خود را از یک کانال فیزیکی و یک کانال مستقیم اینترنتی به فروش میرساند. فرض میشود که خرده فروش فیزیکی، قدرت بازار را در دست دارد و به عنوان رهبر در بازار عمل می‌نماید. این خرده فروش ابتدا حاشیه سود (به دلار) و سیاست موجودی خود را اعلام می‌نماید، سپس تولید کننده به عنوان پیرو، تصمیم‌های مرتبط با قیمت عمده فروشی، قیمت فروش کالا درکانال آنلاین و تعداد موجودی مورد نیاز در این کانال فروش را بر مبنای حاشیه سود توافق شده با خرده فروش و قیمت او تعیین می‌نماید. این مسئله به صورت برنامه ریزی دو سطحی مدل سازی شده است که با استفاده از شرایط بهینگی کروش- کان – تاکر به یک مسئله تک سطحی تبدیل می‌شود. در نهایت مسئله تک سطحی با استفاده از روش آلفا – انشعاب و تحدید حل می‌گردد. نتایج حل مدل نشانگر این موضوع است که ترجیح مشتری در انتخاب کانال خرید، تاثیر به سزایی بر نقطه تعادل بازی و همچنین بر تصمیم اولیه تولید کننده مبنی بر پذیرش یک کانال فروش آنلاین دارد. ما همچنین نشان می‌دهیم که کانال آنلاین همیشه به ضرر خرده فروش نیست بلکه در یک ناحیه پارتویی هر دو تولید کننده و خرده فروش در زنجیره تامین دوکاناله سود می‌برند.

Keywords [Persian]

  • زنجیره تامین خرده فروشی
  • زنجیره تامین دو کاناله
  • تکمیل کانال
  • آلفا- انشعاب و تحدید
Adjiman, C. S., Dallwig, S., Floudas, C. A., & Neumaier, A. (1998). A global optimization method, αBB, for general twice-differentiable constrained NLPs—I: Theoretical advances. Computers & Chemical Engineering, 22(9), 1137-1158.
Al-Khayyal, F. A., & Falk, J. E. (1983). Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2), 273-286.
Androulakis, I. P., Maranas, C. D., & Floudas, C. A. (1995). αBB: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization, 7(4), 337-363.
Batarfi, R., Jaber, M. Y., & Zanoni, S. (2016). Dual-channel supply chain: A strategy to maximize profit. Applied Mathematical Modelling, 40(21-22), 9454-9473.
Bernstein, F., & Federgruen, A. (2004). Dynamic inventory and pricing models for competing retailers. Naval Research Logistics (NRL), 51(2), 258-274.
Cai, G. G. (2010). Channel selection and coordination in dual-channel supply chains. Journal of Retailing, 86(1), 22-36.
Cattani, K., Gilland, W., Heese, H. S., & Swaminathan, J. (2006). Boiling frogs: Pricing strategies for a manufacturer adding a direct channel that competes with the traditional channel. Production and Operations Management, 15(1), 40-56.
Chen, F. Y., Yan, H., & Yao, L. (2004). A newsvendor pricing game. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 34(4), 450-456.
Chen, J., Zhang, H., & Sun, Y. (2012). Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain. Omega, 40(5), 571-583.
Chen, K.-Y., Kaya, M., & Özer, Ö. (2008). Dual sales channel management with service competition. Manufacturing & Service Operations Management, 10(4), 654-675.
Chen, S., Wang, X., Wu, Y., & Zhou, F. (2017). Pricing policies of a dual-channel supply chain considering channel environmental sustainability. Sustainability, 9(3), 382-396
Analysis of a Dominant Retailer Dual-Channel Supply Chain under … 591
Chen, Y. C., Fang, S.-C., & Wen, U.-P. (2013). Pricing policies for substitutable products in a supply chain with Internet and traditional channels. European Journal of Operational Research, 224(3), 542-551.
Chiang, W.-y. K., Chhajed, D., & Hess, J. D. (2003). Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design. Management Science, 49(1), 1-20.
Colson, B., Marcotte, P., & Savard, G. (2005). Bilevel programming: A survey. 4OR, 3(2), 87-107.
David, A., & Adida, E. (2015). Competition and coordination in a two‐channel supply chain. Production and Operations Management, 24(8), 1358-1370.
Dumrongsiri, A., Fan, M., Jain, A., & Moinzadeh, K. (2008). A supply chain model with direct and retail channels. European Journal of Operational Research, 187(3), 691-718.
Hua, G., Wang, S., & Cheng, T. E. (2010). Price and lead time decisions in dual-channel supply chains. European Journal of Operational Research, 205(1), 113-126.
Kacen, J. J., Hess, J. D., & Chiang, W.-y. K. (2013). Bricks or clicks? Consumer attitudes toward traditional stores and online stores. Global Economics and Management Review, 18(1), 12-21.
Li, B., Chen, P., Li, Q., & Wang, W. (2014). Dual-channel supply chain pricing decisions with a risk-averse retailer. International Journal of Production Research, 52(23), 7132-7147.
Liang, T.-P., & Huang, J.-S. (1998). An empirical study on consumer acceptance of products in electronic markets: A transaction cost model. Decision support systems, 24(1), 29-43.
Modak, N. M., & Kelle, P. (2018). Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand. European Journal of Operational Research.
592 (IJMS) Vol. 12, No. 4, Autumn 2019
Mukhopadhyay, S. K., Zhu, X., & Yue, X. (2008). Optimal contract design for mixed channels under information asymmetry. Production and Operations Management, 17(6), 641-650.
Panda, S., Modak, N., Sana, S., & Basu, M. (2015). Pricing and replenishment policies in dual-channel supply chain under continuous unit cost decrease. Applied Mathematics and Computation, 256(1), 913-929.
Petruzzi, N. C., & Dada, M. (1999). Pricing and the newsvendor problem: A review with extensions. Operations Research, 47(2), 183-194.
Tsay, A. A., & Agrawal, N. (2004). Channel conflict and coordination in the e‐commerce age. Production and Operations Management, 13(1), 93-110.
Xiao, T., Choi, T.-M., & Cheng, T. (2014). Product variety and channel structure strategy for a retailer-Stackelberg supply chain. European Journal of Operational Research, 233(1), 114-124.
Xu, H., Liu, Z. Z., & Zhang, S. H. (2012). A strategic analysis of dual-channel supply chain design with price and delivery lead time considerations. International Journal of Production Economics, 139(2), 654-663.
Xu, J., Qi, Q., & Bai, Q. (2018). Coordinating a dual-channel supply chain with price discount contracts under carbon emission capacity regulation. Applied Mathematical Modelling, 56, 449-468.
Yan, R., Guo, P., Wang, J., & Amrouche, N. (2011). Product distribution and coordination strategies in a multi-channel context. Journal of Retailing and Consumer Services, 18(1), 19-26.
Zhang, R., Liu, B., & Wang, W. (2012). Pricing decisions in a dual channels system with different power structures. Economic Modelling, 29(2), 523-533.
Zhao D, Wang F, Qi Y. (2009) Channel coordination of a dominant-retailer supply chain model with option contract. Proceedings of the 1st International Workshop on Education
Analysis of a Dominant Retailer Dual-Channel Supply Chain under … 593
Technology and Computer Science, Vol 02, Wuhan, Hubei, 7–8 March 2009, pp. 471–475.