Modeling a Four Echelon Omni-Channel Supply Chain for Seasonal Product under Stochastic Demand

Document Type : Research Paper


1 Ph.D. Candidate, Department of Industrial Engineering, School of Industrial Engineering, Alborz Campus, University of Tehran, Tehran, Iran.

2 Prof., Department of Industrial Engineering, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.

3 Associate Prof., Department of Industrial Engineering, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.


Objective: The present work proposes a mathematical model for a four-echelon supply chain network for a seasonal product with stochastic demand. The supply chain structure includes a supplier, a producer, a distributor, and a retailer with three sale channels.
Methods: The methodology introduced in this paper is a fundamental yet practical one that expands the knowledge of modeling for omnichannel supply chain and examines the outcomes in a real case study using a quantitative approach. In this case study, the retailer and the distributor are decision-makers, who decide the optimum order quantity. First, the centralized and decentralized models are identified. Second, the optimum order quantity for each model is determined, and finally, the results are verified using a numerical approach. Further, a sensitivity analysis is performed on the parameters that affect the profits obtained by members and the supply chain.
Results: Numerical examples show that the supply chain profit in the centralized model is more than the decentralized model, which correctly predicts the models and the estimated optimum order quantities.
Conclusion: The results of the sensitivity analysis show that the expected value of the members and the supply chain profit will increase when the final selling price and production capacity are increased. However, the increasing rate of profit obtained by increasing the selling price is higher than that of production capacity.


Arcelus, F.J., Kumar, S., Srinivasan, G. (2008). Evaluating manufacturer’s buyback policies in a single-period two-echelon framework under price-dependent stochastic demand. Omega, 36, 808 – 824.
Cao, L., Li, L. (2015). The Impact of Cross-Channel Integration on Retailers’ Sales Growth. Journal of Retailing, 91(2), 198-216.
Chaharsooghi, S.K., heydari, J. (2010). Supply chain coordination for the joint determination of order quantity and reorder point using credit option. European Journal of Operational Research, 204, 86–95.
Chen, Z., Fang, L. & Su, S.I. (2019). The value of offline channel subsidy in bricks and clicks: an O2O supply chain coordination perspective. Electronic Commerce Research
Cong, J., Wang, H. (2017). Research on Three-Level Supply Chain Coordination Based on Revenue Sharing Contract and Option Contract. Xu, J., Hajiev, A., Nickle, S., Gen, M. (Editors). Advances in Intelligent Systems and Computing, 502, 1215-1226.
Du, R., Banerjee, A., Kim, S.L. (2013). Coordination of two-echelon supply chains using wholesale price discount and credit option. International Journal of Production Economics, 143, 327–334.
Ebrahimi, S., Hosseini‑Motlagh, S.M., Nematollahi, M. (2017). Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand. International Journal of Machine Learning and Cybernetics, 1, 1-14.
Ekhtiari, M., Zandieh, M., Alem Tabriz, A., Rabieh, M. (2019). Proposing a Bi-level Programming Model for Multi-echelon Supply Chain with an Emphasis on Reliability in Uncertainty. Industrial Management Journal, 11(2), 177-206. (in Persian)
Fathi, M. R., Nasrollahi, M., Zamanian, A. (2019). Mathematical Modeling of Sustainable Supply Chain Networks under Uncertainty and Solving It Using Metaheuristic Algorithms. Industrial Management Journal, 11(4), 621-652. (in Persian)
Gallino, S., Moreno, A. (2014). Integration of Online and Offline Channels in Retail: The Impact of Sharing Reliable Inventory Availability Information. Management Science, 60(6), 1434-1451.
Giri, B.C., Bardhan, S. (2017). Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production. International Journal of Production Economics, 191, 66-73.
Gulati, R., Garino, J. (2000). Get the right mix of bricks and clicks (cover story). Harvard Business Review, 78(3), 107-114.
He, Y., Zhao, X. (2012). Coordination in multi-echelon supply chain under supply and demand uncertainty. International Journal of ProductionEconomics, 139, 106–115.
Heydari, J. (2014). Supply chain coordination using time-based temporary price discounts. Computers & Industrial Engineering, 75, 96-101
Heydari, J., Rastegar, M., Glock, C.H. (2017). A two-level delay in payments contract for supply chain coordination: The case of credit-dependent demand. International Journal of Production Economics, 191, 26-36.
Honarvar, M. & Rezaee, H. (2019). Optimal Outsourcing Strategy Determination and Pricing Model in Dual-Channel Supply Chain under Uncertainty. Production and Operations management, 10(1), 155-174. (in Persian)
Hou, Y., Wei, F., Li, S.X., Huang, Z., Ashley, A. (2016). Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract. International Journal of Production Research, 55(1), 202-227
Huang, W., Swaminathan, J.M. (2009). Introduction of a second channel: Implications for pricing and profits. European Journal of Operational Research, 194, 258–279.
Hübner, A., Wollenburg, J., Holzapfel, A. (2016). Retail logistics in the transition from multi-channel to omni-channel. International Journal of Physical Distribution & Logistics Management, 46(6/7), 562 – 583.
Keren, B., Pliskin, J.S. (2006). A benchmark solution for the risk-averse newsvendor problem. European Journal of Operational Research, 174, 1643–1650.
Kozlenkova, I.V., Hult, G.T.M., Lund, D.J., Mena, J.A., Keke, P. (2015). The Role of Marketing Channels in Supply Chain Management. Journal of Retailing, 91 (4), 586–609.
Larke, R., Kilgour, M., O’Connor, H. (2018). Build touchpoints and they will come: transitioning to omnichannel retailing. International Journal of Physical Distribution & Logistics Management, 48(4), 465-483.
Luo, J. (2007). Buyer–vendor inventory coordination with credit period incentives. International Journal of Production Economics, 108, 143–152.
Mashreghi, H. & Amin Naseri, M. (2015). Supply chain coordination under demand uncertainty with rwvwnue sharing and buyback contrast. International Journal of Industrial Engineering & Production Management, 26(2), 186-202. (in Persian)
Melacini, M., Perotti, S., Rasini, M., Tappia, E. (2018). E-fulfilment and distribution in omni-channel retailing: a systematic literature review. International Journal of Physical Distribution & Logistics Management, 48(4), 391-414.
Modak, N.M. (2017). Exploring Omni-channel supply chain under price and delivery time sensitive stochastic demand. Supply Chain Forum: An International Journal, 18(4), 218-230
Modak, N.M., Kelle, P. (2019). Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand. European Journal of Operational Research, 272(1), 147-161.
Mohaghar, A., Garusi Mokhtarzadeh, N., Modarres Yazdi, M., HajiMaghsoudi, M. (2017). Designing a flexible supply network in a two levels supply chain and risk analyzing. Industrial Management Journal, 9(1), 189-216. (in Persian)
Mou, S., Robb, D.J., DeHoratius, N. (2017). Retail Store Operations: Literature Review and Research Directions. European Journal of Operational Research, 265(2), 399-422.
Naeimi Sedigh, A., Chaharsooghi, S.K., Sheikh Mohamadi, M. (2012). Designing a coordination model in a competitive supply chain using the cooperative and non-cooperative game theory approach. Journal of Modeling in Engineering, 10(29), 19-31. (in Persian)
Pang, Q., Chen, Y., Hu, Y. (2014). Coordinating Three-Level Supply Chain by Revenue-Sharing Contract with Sales Effort Dependent Demand. Discrete Dynamics in Nature and Society, 1, 1-10.
Piotrowicz, W., Cuthbertson, R. (2014). Introduction to the Special Issue Information Technology in Retail: Toward Omnichannel Retailing. International Journal of Electronic Commerce, 18(4), 5-16.
Sabet Motlagh, M., Mohaghar, A. (2016). Applying Genetic Algorithm for an integrated Supply and Production/Distribution Planning in assembly systems. Industrial Management Journal, 8(2), 163- 190. (in Persian)
Seifert, R.W., Zequeira, R.I., Liao, S. (2012). A three-echelon supply chain with price-only contracts and sub-supply chain coordination. International Journal of Production Economics, 138, 345–353.
Shah, N.H., Chaudhari, U., Cárdenas-Barrón, L.E. (2018). Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three echelon supply chain, International Journal of Systems Science: Operations & Logistics, 1, 1-12.
Takahashi, K., Aoi, T., Hirotani, D., Morikawa, K. (2011). Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery. International Journal of Production Economics, 133, 403–415.
Verhoef, P.C., Kannanb, P.K., Inman, J. (2015). From Multi-Channel Retailing to 
Omni-Channel Retailing: Introduction to the Special Issue on Multi-Channel Retailing. Journal of Retailing, 91 (2), 174–181.
Yang, S., Hong, K.S., Lee, C. (2014). Supply chain coordination with stock-dependent demand rate and credit incentives. International Journal of Production Economics, 157, 105-111.
Yu, X., Wang, S., Zhang, X. (2019). Ordering Decision and Coordination of a Dual-Channel Supply Chain with Fairness Concerns under an Online-to-Offline Model. Asia-Pacific Journal of Operational Research, 36 (2). DOI: 10.1142/S0217595919400049.
Zhang, J., Farris, P.W., Irvin, J.W., Kushwaha, T., Steenburgh, T.J., Weitz, B.A. (2010). Crafting Integrated Multichannel Retailing Strategies. Journal of Interactive Marketing, 24, 168–180.
Zhu, B., Wen, B., Ji, S., Qiu, R., (2020). Coordinating a dual-channel supply chain with conditional value-at-risk under uncertainties of yield and demand. Computers & Industrial Engineering, 139. DOI:10.1016/J.IJPE.2013.09.012.