This paper develops a pricing and inventory model of a supply chain composing one supplier and two manufacturers in which the supplier sells its product to two competing manufacturers. Each manufacturer faces a deterministic demand that depends on his/her own and the other competitor sale price. Selling price for the supplier is time dependent and increment function.Both amelioration and deterioration effects are seen simultaneously for this model. In this paper, it is assumed that shortages are not allowed in whichthe objective ismaximizing the total profit of supplier and manufacturers in two stages. In first stage, the total profit of supplier is maximized and then in the second stage, two manufacturers maximize their total profits with regard to the optimal decision variables obtained in the first stage. A case study of trout fish breeding is presented andnumerical example is solved by Mathematica optimization tool. Sensitivity analysis is finally conducted to study the effect of various parameters on the optimal solution.

Abad, P.L., (1996). Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Management Science, 42(8), pp.1093-1104.

Basiri, Z. and Heydari, J., 2017. A mathematical model for green supply chain coordination with substitutable products. Journal of Cleaner Production.

Bernstein, F. and Federgruen, A., (2003). Pricing and replenishment strategies in a distribution system with competing retailers. Operations Research, 51(3), pp.409-426.

Bertrand, J., (1883). iBook review of theoriemathematique de la richessesociale and of recherchessur les principles mathematiques de la theorie des richessesj. Journal de Savants, 67.

Bhunia, A.K. and Maiti, M., (1999). An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand. Applied Mathematical Modelling, 23(4), pp.301-308.

Caldart, A.A. and Oliveira, F., 2010. Analysing industry profitability: A “complexity as cause” perspective. European Management Journal, 28(2), pp.95-107.

Chen, X. and Simchi-Levi, D., (2012). Pricing and inventory management. The Oxford handbook of pricing management, pp.784-822.

Chen, X., Pang, Z. and Pan, L., (2014). Coordinating inventory control and pricing strategies for perishable products. Operations Research, 62(2), pp.284-300.

Choi, S.C., (1991). Price competition in a channel structure with a common retailer. Marketing Science, 10(4), pp.271-296.

Chung, K.J. and Liao, J.J., (2006). The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity. International Journal of Production Economics, 100(1), pp.116-130.

Cohen, M.A., (1977). Joint pricing and ordering policy for exponentially decaying inventory with known demand. Naval Research Logistics Quarterly, 24(2), pp.257-268.

Dong, L., Narasimhan, C. and Zhu, K., (2009). Product line pricing in a supply chain. Management Science, 55(10), pp.1704-1717.

Dye, C.Y. and Ouyang, L.Y., (2005). An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging. European Journal of Operational Research, 163(3), pp.776-783.

Feng, L., Zhang, J. and Tang, W., 2016. Optimal inventory control and pricing of perishable items without shortages. IEEE Transactions on Automation Science and Engineering, 13(2), pp.918-931.

Heydari, J. and Norouzinasab, Y., 2016. Coordination of pricing, ordering, and lead time decisions in a manufacturing supply chain. Journal of Industrial and Systems Engineering, 9, pp.1-16.

Ingene, C.A. and Parry, M.E., (1995). Channel coordination when retailers compete. Marketing Science, 14(4), pp.360-377.

Jiang, L., Wang, Y. and Yan, X., (2014). Decision and coordination in a competing retail channel involving a third-party logistics provider. Computers & Industrial Engineering, 76, pp.109-121.

Kang, S. and Kim, I.T., (1983). A study on the price and production level of the deteriorating inventory system. The International Journal of Production Research, 21(6), pp.899-908.

Lee, E. and Staelin, R., (1997). Vertical strategic interaction: Implications for channel pricing strategy. Marketing Science, 16(3), pp.185-207.

Mahata, G.C. and De, S.K., (2016). An EOQ inventory system of ameliorating items for price dependent demand rate under retailer partial trade credit policy. OPSEARCH, pp.1-28.

Maihami, R. and Kamalabadi, I.N., (2012). Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. International Journal of Production Economics, 136(1), pp.116-122.

Mondal, B., Bhunia, A.K. and Maiti, M., (2003). An inventory system of ameliorating items for price dependent demand rate. Computers & industrial engineering, 45(3), pp.443-456.

Moon, I., Giri, B.C. and Ko, B., 2005. Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting. European Journal of Operational Research, 162(3), pp.773-785.

Mukhopadhyay, S., Mukherjee, R.N. and Chaudhuri, K.S., (2004). Joint pricing and ordering policy for a deteriorating inventory. Computers & Industrial Engineering, 47(4), pp.339-349.

Padmanabhan, G. and Vrat, P., (1995). EOQ models for perishable items under stock dependent selling rate. European Journal of Operational Research, 86(2), pp.281-292.

Padmanabhan, V. and Png, I.P., (1997). Manufacturer's return policies and retail competition. Marketing Science, 16(1), pp.81-94.

Pang, Z., (2011). Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operations Research Letters, 39(5), pp.375-379.

Rabbani, M., Zia, N.P. and Rafiei, H., 2015. Coordinated replenishment and marketing policies for non-instantaneous stock deterioration problem. Computers & Industrial Engineering, 88, pp.49-62.

Rajan, A., Rakesh and Steinberg, R., (1992). Dynamic pricing and ordering decisions by a monopolist. Management Science, 38(2), pp.240-262.

Sana, S.S., Sarkar, B.K., Chaudhuri, K. and Purohit, D., (2009). The effect of stock, price and advertising on demand-an EOQ model. International Journal of Modelling, Identification and Control, 6(1), pp.81-88.

Taleizadeh, A.A., Mohammadi, B., Cárdenas-Barrón, L.E. and Samimi, H., (2013). An EOQ model for perishable product with special sale and shortage. International Journal of Production Economics, 145(1), pp.318-338.

Taleizadeh, A.A., Noori-daryan, M. and Cárdenas-Barrón, 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, pp.285-295.

Teng, J.T., Chang, C.T. and Goyal, S.K., (2005). Optimal pricing and ordering policy under permissible delay in payments. International Journal of Production Economics, 97(2), pp.121-129.

Valliathal, M. and Uthayakumar, R., 2010. The production—inventory problem for ameliorating/deteriorating items with non-linear shortage cost under inflation and time discounting. Applied Mathematical Sciences, 4(6), pp.289-304.

Valliathal, M. and Uthayakumar, R., 2011. Optimal pricing and replenishment policies of an EOQ model for non-instantaneous deteriorating items with shortages. The International Journal of Advanced Manufacturing Technology, 54(1-4), pp.361-371.

Wee, H.M., (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, 59(1), pp.511-518.

Wee, H.M., Lo, S.T., Yu, J. and Chen, H.C., (2008). An inventory model for ameliorating and deteriorating items taking account of time value of money and finite planning horizon. International Journal of Systems Science, 39(8), pp.801-807.

Woynarovich, A., Hoitsy, G. and Moth-Poulsen, T., (2011). Small-scale rainbow trout farming. Food and Agriculture Organization of the United Nations.

Xiao, T. and Xu, T., (2013). Coordinating price and service level decisions for a supply chain with deteriorating item under vendor managed inventory. International Journal of Production Economics, 145(2), pp.743-752.

Yao, Z., Leung, S.C. and Lai, K.K., (2008). Manufacturer’s revenue-sharing contract and retail competition. European Journal of Operational Research, 186(2), pp.637-651.

Yu, J.C., Lin, Y.S. and Wang, K.J., (2013). Coordination-based inventory management for deteriorating items in a two-echelon supply chain with profit sharing. International Journal of Systems Science, 44(9), pp.1587-1601.

Zhang, J., Wei, Q., Zhang, Q. and Tang, W., (2016). Pricing, service and preservation technology investments policy for deteriorating items under common resource constraints. Computers & Industrial Engineering, 95, pp.1-9.

Zhu, S.X., 2015. Integration of capacity, pricing, and lead-time decisions in a decentralized supply chain. International Journal of Production Economics, 164, pp.14-23.