A Game Theoretical Study on Pricing and Production Decisions of Firms

Document Type : Research Paper


1 Industrial Engineering, Islamic Azad University, South Tehran Branch

2 University of Tehran


Today, products’ lead time adjustment has become one of the main challenges for organizations managers and service companies. Products’ lead time has an undeniable impact on firms’ inventory control way in order to meet required customer demand. In addition, pricing on manufactured good way, in order to achieve most profit and decrease the side expenditures, is of issues of importance in this context. In this research, market demand, is considered Sensitive to product sales price and amount of inventory-on-hand and We have addressed to analyze the behavior of firms by assuming Being unauthorized of Shortage. It should be noted that in both scenarios, firms’ decision making review about appropriate lead time optimal policies, products’ price and amount of inventory as the problem decision variables with the aim of maximizing profits and minimizing costs are addressed. In first scenario, only a single firm behavior analysis is considered and in second scenario, two firm’s behavior Study when changing in price level, lead time and inventory at exclusive market have been addressed by using Nash equilibrium. In the following, by expressing numerical examples, we have addressed to the problem results analysis and have determined optimal points. Sensitivity analysis clearly Shows Market potential and inventory attraction parameters influence on the decision variables. Eventually, it was found that among two proposed scenarios, single firm’s scenario is more profitable than the two firms’ scenario. This research can be helpful for planners and industrial managers to optimize existing conditions, achieving maximum profit.


Main Subjects

Ahmadi-Javid, A., Hoseinpour, P. 2015. A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints. Transportation Research Part E: Logistics and Transportation Review. 82, 238-255.
Alfares, H.K., Ghaithan, A.M., 2016. Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Computers & Industrial Engineering, 94, 170-177.
Amit, R. K., Mehta, P., Tripathi, R. R. 2015. Optimal shelf-space stocking policy using stochastic dominance under supply-driven demand uncertainty. European Journal of Operational Research. 246, 339-342.
Chao, X., Yang, B., Xu, Y. 2012. Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost. Operations Research Letters. 40, 99-107.
Chua, G. A., Liu, Y. 2015. On the effect of demand randomness on inventory, pricing and profit. Operations Research Letters. 43, 514-518.
Chung, W., Talluri, S., Narasimhan, R. 2014. Optimal Pricing and Inventory Strategies with Multiple Price Markdowns over Time. European Journal of Operational Research. 243, 130–141.
Ding, X. S., Zhang, J. H., Chen, X. 2012. A joint pricing and inventory control problem under an energy buy-back program. Operations Research Letters. 40, 516-520.
El-Wakeel, M. F. 2012. Constrained backorders inventory system with varying order cost: Lead time demand uniformly distributed. Journal of King Saud University-Science. 24, 285-288.
Hammami, R., Nouira, I., Frein, Y. 2015. Carbon emissions in a multi-echelon production-inventory model with lead time constraints. International Journal of Production Economics. 164, 292–307.
Heydari, J., Norouzinasab, Y. 2016. Coordination of pricing, ordering, and lead time decisions in a manufacturing supply chain. Journal of Industrial and Systems Engineering. 9, 1-16.
Inderfurth, K., Kiesmüller, G. P. 2015. Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times. European Journal of Operational Research, 245, 109-120.
Jian, M., Fang, X., Jin, L. Q., Rajapov, A. 2015. The impact of lead time compression on demand forecasting risk and production cost: A newsvendor model. Transportation Research Part E: Logistics and Transportation Review. 84, 61-82.
Ju, W., Gabor, A. F., van Ommeren, J. C. W. 2015. An approximate policy for a dual-sourcing inventory model with positive lead times and binomial yield. European Journal of Operational Research. 244, 490-497.
Kaminsky, P., Kaya, O. 2008. Inventory positioning, scheduling and lead-time quotation in supply chain. International Journal of Production Economics. 114, 276-293
Lee, C., Park, K. S. 2016. Inventory and transshipment decisions in the rationing game under capacity uncertainty. Omega. 65, 82-97.
Lin, D. Y., Wu, M. H. 2016. Pricing and inventory problem in shrimp supply chain: A case study of Taiwan's white shrimp industry. Aquaculture. 456, 24-35.
Lin, J., Hung, K. C., Tang, D. 2014. Solution process for inventory models with crashable lead time. Applied Mathematics and Computation. 227, 335-340.
Naseri, F., Hafezalkotob, A. 2016. Cooperative network flow problem with pricing decisions and allocation of benefits: A game theory approach. Journal of Industrial and Systems Engineering. 9, 73-87.
Noori-daryan, M., Taleizadeh, A., A. 2016. Coordinating Pricing and Ordering Decisions in a Multi-Echelon Pharmacological Supply Chain under Different Market Power using Game Theory. Journal of Industrial and Systems Engineering. 9, 35-56.
Pang, Z. 2011. Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operations Research Letters. 39, 375-379.
Qin, Y. Wang, J. Wei, C. 2014. Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously. International Journal of Production Economics. 152, 42–48.
Roldán, R., F., Basagoiti, R., Coelho, L., C. 2016. A survey on the inventory-routing problem with stochastic lead times and demands. Journal of Applied Logic. http://dx.doi.org/10.1016/j.jal.2016.11.010
Sarkar, B., Gupta, H., Chaudhuri, K, Goyal, S. K. 2014. An integrated inventory model with variable lead time, defective units and delay in payments. Applied Mathematics and Computation. 237, 650-658.
Song, H. M., Yang, H., Bensoussan, A. 2013. Optimizing production and inventory decisions in a supply chain with lot size, production rate and lead time interactions. Applied Mathematics and Computation. 224, 150-165.
Taleizadeh A.A., Niaki S.T., Aryanezhad M.B. (2008a) Multi-Product Multi-Constraint Inventory Control Systems with Stochastic Replenishment and Discount under Fuzzy Purchasing Price and Holding Costs, American Journal of Applied Science, 8(7):1228-1234.
Taleizadeh A.A., Aryanezhad M.B., Niaki S.T.A. (2008b). Optimizing Multi-Products Multi-Constraints Inventory Control Systems with Stochastic Replenishments, Journal of Applied Science, 6(1):1-1.
Taleizadeh A.A., Moghadasi H., Niaki S.T.A., Eftekhari A.K. (2009). An EOQ-Joint Replenishment Policy to Supply Expensive Imported Raw Materials with Payment in Advance, Journal of Applied Science, 8(23): 4263-4273.
Taleizadeh A.A., Niaki S.T.A., Aryanezhad M.B. (2010a). Replenish-up-to Multi Chance-Constraint Inventory Control System with Stochastic Period Lengths and Total Discount under Fuzzy Purchasing Price and Holding Costs, International Journal of System Sciences, 41(10): 1187-1200.
Taleizadeh A.A., Niaki S.T.A., Aryanezhad M.B., Fallah-Tafti A. (2010b). A Genetic Algorithm to Optimize Multi-Product Multi-Constraint Inventory Control Systems with Stochastic Replenishments and Discount, International Journal of Advanced Manufacturing Technology, 51, (1-4): 311-323.
Taleizadeh A.A., Barzinpour F., Wee H.M. (2011). Meta-heuristic Algorithms to Solve the Fuzzy Single Period Problem, Mathematical and Computer Modeling, 54(5-6): 1273-1285.
Taleizadeh A.A., Pentico D.W., Aryanezhad M.B., Ghoreyshi M., (2012). “An Economic Order Quantity Model with Partial Backordering and a Special Sale Price,” European Journal of Operational Research, 221 (3): 571-583.
Taleizadeh A.A., Pentico D.W., Jabalameli M.S., Aryanezhad M.B. (2013a). An Economic Order Quantity Model with Multiple Partial Prepayments and Partial Backordering, Mathematical and Computer Modeling, 57 (3-4): 311–323.
Taleizadeh A.A., Pentico D.W. (2013b). An Economic Order Quantity Model with Known Price Increase and Partial Backordering. European Journal of Operational Research, 28 (3): 516-525.
Taleizadeh A.A., Wee H.M., Jalali-Naini S.Gh.R., (2013c). “Economic Production Quantity Model with Repair Failure and Limited Capacity,” Applied Mathematical Modeling, 37(5): 2765-2774.
Taleizadeh A.A. (2014a). An Economic Order Quantity Model with Partial Backordering and Advance Payments for an Evaporating Item, International Journal of Production Economic. 155, 185–193.
Taleizadeh A.A., Cardenas-Barron L.E., Mohammadi, B. (2014b). Multi Product Single Machine EPQ model with Backordering, Scraped Products, Rework and Interruption in Manufacturing Process. International Journal of Production Economic, 150, 9-27.
Taleizadeh A.A., Nematollahi M.R., (2014c). An Inventory Control Problem for Deteriorating Items with Backordering and Financial Engineering Considerations, Applied Mathematical Modeling, 38, 93–109.
Taleizadeh A.A., Pentico D.W. (2014d). An Economic Order Quantity Model with Partial Backordering and All-units Discount. International Journal of Production Economic. 155, 172–184.
Wang, H., Chi, C. 2009. The Impact of Revenue Sharing Contracts on a Retailer's Shelf-Space and Pricing Decisions. Management and Service Science. 2009,1-4.
Wang, H., Yan, H. 2009. Inventory Policies for a Batch-Replenishment Supplier with Alternative Delivery Lead-time Choices. IFAC Proceedings Volumes. 42, 1568-1572.
Wang, X., Disney, S. M. 2017. Mitigating variance amplification under stochastic lead-time: The proportional control approach. European Journal of Operation Research. 256, 151-162.
Wu, Z., Zhai, X., Liu, Z., 2015. The inventory billboard effect on the lead time decision. International Journal of Production Economics.170, 45-53.
Xie, Y., Liang, X., Ma, L. and Yan, H. 2016. Inventory rationing and markdown strategy in the presence of lead-time sensitive customers. Operations Research Letters, 44(4), 525-531.
Yang, J. Q., Zhang, X. M., Fu., H.Y., Liu, C. 2017. Inventory competition in a dual-channel supply chain with delivery lead time consideration. Applied Mathematical Modelling. 42, 675-692.
Zhang, J., Y., Lu, L., Tang, W. 2015. Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand. International Journal of Production Economics.  170, Part A, 136-145.