Abstract
The paper studies a two-echelon supply chain comprising of one manufacturer and two competing retailers with sales price dependent demand and random arrival of the customers. The manufacturer acts as the supplier who specifies wholesale price for the retailers and the retailers compete with each other announcing different sales prices. We analyse a single-period newsvendor type model to determine the optimal order quantity, considering the competing retailers’ strategies.The unsold items at the retailers are buyback to the manufacturer at less price than the sales prices.On the other hand, the retailers face shortages as the demand is uncertain in nature. The profit functions of manufacturer and two retailers are analyzed and compared following Stakelberg, Bertrand, Cournot–Bertrand and integrated approaches. Moreover, distribution-free model is analyzed for integrated profit of the chain. A numerical example is given to illustrate the theoretical results developed in each case. Computational results show that it is always beneficial in integrated system for the members of the chain.
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Alfares, K. H., & Elmora, H. H. (2005). The distribution-free newsboy problem: Extensions to the shortage penalty case. International Journal of Production Economics, 91–94, 465–477.
Arcelus, I. F., Pakkala, M. P. T., & Srinivasan, G. (2006). On the interaction between retailers inventory policies and manufacturer trade deals in response to supply-uncertainty occurrences. Annals of Operations Research, 143, 45–58.
Artalejo, R. J., Krishnamoorthy, A., & Lopez-Herrero, J. M. (2006). Numerical analysis of(s, S) inventory systems with repeated attempts. Annals of Operations Research, 141, 67–83.
Berg, K. (2013). Complexity of solution structures in nonlinear pricing. Annals of Operations Research, 206, 23–37.
Bertsimas, D., & Thiele, A. (2004). A robust optimization approach to supply chain management. Integer Programming and Combinatorial Optimization, 3064, 86–100.
Cardenas-Barron, L. E., Trevino-Garza, G., & Wee, H. M. (2012). A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Systems with Applications, 39, 3888–3895.
Cardenas-Barron, L. E., Chung, K. J., & Trevino-Garza, G. (2014). Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris. International Journal of Production Economics, 155, 1–7.
Cardenas-Barron, L. E., & Sana, S. S. (2014). A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams’ initiatives. International Journal of Production Economics, 155, 249–258.
Cardenas-Barron, L. E., & Trevino-Garza, G. (2014). An optimal solution to a three echelon supply chain network with multi-product and multi-period. Applied Mathematical Modelling, 38, 1911–1918.
Cardenas-Barron, L. E., Wee, H. M., & Blos, M. F. (2011). Solving the vendor-buyer integrated inventory system with arithmetic-geometric inequality. Mathematical and Computer Modelling, 53, 991–997.
Choi, S. C. (1991). Price competition in a channel structure with a common retailer. Marketing Science, 10, 271–296.
Ertek, G., & Griffin, P. M. (2002). Supplier- and buyer-driven channels in a two-stage supply chain. IIE Transactions, 34, 691–700.
Fernandez, E., Puerto, J., & Rodrguez-Cha, M. A. (2013). On discrete optimization with ordering. Annals of Operations Research, 207, 83–96.
He, Y., Zhao, X., Zhao, L., & He, J. (2009). Coordinating a supply chain with effort and price dependent stochastic demand. Applied Mathematical Modelling, 33, 2777–2790.
Ishii, Y. (2000). International cournot duopoly and R & D subsidies under demand uncertainty. Journal of economics, 72, 203–222.
Iyer, G. (1998). Coordinating channels under price and nonprice competition. Marketing Science, 17, 338–355.
Kalpakam, S., & Shanthi, S. (2006). A continuous review perishable system with renewal demands. Annals of Operations Research, 143, 211–225.
Khouja, M. (1999). The single-period(news-vendor)problem: Literature review and suggestions for future research. Omega, 27, 537–553.
Kim, S. Y., & Staelin, R. (1999). Manufacturer allowances and retailer pass through rates in a competitive environment. Marketing Science, 18, 59–76.
Lau, A. H. L., & Lau, H. S. (1988). The newsboy problem with price-dependent demand distribution. IEE Transactions, 20, 168–175.
Lau, A., & Lau, H. S. (2005). Some two-echelon supply-chain games: improving from deterministic-symmetric-information to stochastic asymmetric- formation models. European Journal of Operational Research, www.sciencedirect.com.
Mantrala, M. K., & Raman, K. (1999). Demand uncertainty and suppliers return policies for a multi-store style-good retailer. European Journal of Operational Research, 115, 270–284.
Messinger, P. R., & Narasimhan, C. (1995). Has power shifted in the grocery channel? Marketing Science, 14, 189–223.
Mostard, J., de Koster, R., & Teunter, R. (2005). The distribution-free newsboy problem with resalable returns. International Journal of Production Economics, 97, 329–342.
Ouyang, L. Y., & Chuang, B. R. (1999). (Q, R, L) inventorymodel involving quantity discounts and a stochastic backorder rate. Production Planning and Control, 10, 426–433.
Ozler, A., Tan, B., & Karaesmen, F. (2009). Multi-product newsvendor problem with value-at-risk consideration. International Journal of Production Economics, 117, 244–255.
Parlar, M., & Wang, Q. (1994). Discounting decisions in a supply–buyer relationship with a linear buyer-demand. IIE Transactions, 26, 34–41.
Petruzzi, N. C., & Dada, M. (1999). Pricing and the news vendor problem: A review with extension. Operations Research, 47, 183–194.
Sarkar, B., & Chaudhuri, K. (2015). Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint. Journal of Manufacturing Systems, 34, 74–82.
Sana, S. S. (2011). The stochastic EOQ model with random sales price. Applied Mathematics and Computation, 218, 239–248.
Sana, S. S. (2012). Price sensitive demand with random sales price—A newsboy problem. International Journal of Systems Science, 43, 491–498.
Scarf, H. (1958). A min-max solution of an inventory problem. In K. Arrow, S. Karlin, & H. Scarf (Eds.), Studies in the mathematical theory of inventory and production (pp. 201–209). California: Stanford University Press.
Silver, E. A., Pyke, D. F., & Peterson, R. P. (1998). Inventory management and production planning and scheduling (3rd ed.). New York: Wiley.
Soni, H., & Shah, N. H. (2011). Optimal policy for fuzzy expected value production inventory model with imprecise production preparation-time. International Journal of Machine Learning and Cybernetics, 2, 219–224.
Taleizadeh, A. A., Niaki, S. T. A., & Makui, A. (2012). Multiproduct multiple-buyer single vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint. Expert Systems with Applications, 39, 5338–5348.
Taleizadeh, A. A., Kalantari, S. S., & Cardenas-Barron, L. E. (2015). Determining optimal price, replenishment lot size and number of shipments for an EPQ model with rework and multiple shipments. Journal of Industrial and Management Optimization, 11, 1059–1071.
Taleizadeh, A. A., Noori-daryan, M., & Cardenas-Barron, L. E. (2015). Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items. International Journal of Production Economics, 159, 285–295.
Teng, J. T., Cardenas-Barron, L. E., Lou, K. R., & Wee, H. M. (2013). Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives. International Journal of Systems Science, 44, 986–994.
Tsay, A. A., & Agrawal, N. (2000). Channel Dynamics Under Price and Service Competition. Manufacturing and Service Operations Management, 2, 372–391.
Wang, C. X. (2010). The loss-averse newsvendor game. International Journal of Production Economics, 124, 448–452.
Wang, C. H. (2010). Some remarks on an optimal order quantity and reorder point when supply and demand are uncertain. Computers and Industrial Engineering, 58, 809–813.
Weng, Z. K. (1995). Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships. European Journal of Operational Research, 86, 300–314.
Wu, C., Petruzzi, N. C., & Chhajed, D. (2007). Vertical integration with price-setting competitive newsvendors. Decision Sciences, 38, 581–610.
Xiao, T., Jin, J., Chen, G., Shi, J., & Xie, M. (2010). Ordering, wholesale pricing and lead-time decisions in a three-stage supply chain under demd uncertainty. Computers and Industrial Engineering, 59, 840–852.
Yue, J., Chen, B., & Wang, M. (2006). Expected value of distribution information for the newsvendor problem. Operations Research, 54, 1128–1136.
Zhang, G. (2010). The multi-product newsboy problem with supplier quantity discounts and a budget constraint. European Journal of Operational Research, 206, 350–360.
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Roy, A., Sana, S.S. & Chaudhuri, K. Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model. Ann Oper Res 260, 481–500 (2018). https://doi.org/10.1007/s10479-015-1996-0
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DOI: https://doi.org/10.1007/s10479-015-1996-0