Studying the impact of quantity discount contract and cost-sharing contract on a two-echelon green supply chain profit

Document Type : Research Paper


1 University of Tehran

2 Industrial Engineering, Islamic Azad University, South Tehran Branch


The members of a chain always try to find new ways in order to raise their profit. Hence we intend to study two different scenarios in a single item two-echelon green supply chain including two manufacturers and one retailer to study the effects of two effective contracts on members’ profit. Two scenarios are discussed and in first one, first manufacturer proposes quantity discount contract to retailer and in second scenario retailer proposes cost sharing contract to second manufacturer. Then a numerical example and sensitivity analysis is implemented to review the mathematical relations in detail and assess the effect of some parameters on our decision variables and profits. The results show that cost sharing contract is more beneficial for retailer and second manufacturer than quantity discount contract.


Main Subjects

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.
Alfares, H.k., Turnadi, R. (2016). General Model for Single-item Lot-sizing with Multiple Suppliers, Quantity Discounts, and Backordering , Procedia CIRP, 56: 199-202.
Avni, G., Tamir, T. (2016). Cost-sharing scheduling games on restricted unrelated machines, Theoretical Computer Science, 646: 26-39.
Basiri, Z., Heydari, J. (2017). A mathematical model for green supply chain coordination with substitutable products, Journal of Cleaner Production, 145: 232-249.
Bohner , Ch., Minner, S. (2016). Supplier Selection under Failure Risk, Quantity and Business Volume Discounts, Computers & Industrial Engineering, In press.
Burke, G.J., Geunes, J., Romeijn, H.E., Vakharia, A. (2008). Allocating procurement to capacitated suppliers with concave quantity discounts, Operations Research Letters, 36: 103-109.
Çebi, F., Otay, I. (2016). A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead time, Information Sciences, 339: 143-157.
Chalkley, M., Malcomson, J.M., (2002), Cost sharing in health service provision: an empirical assessment of cost savings, Journal of Public Economics, 84: 219–249.
Chao, G.H., Iravani, S.M.R., Savaskan, R.C. (2009). Quality Improvement Incentives and Product Recall Cost Sharing Contracts, MANAGEMENT SCIENCE, 55: 1122-1138.
Chang, Ch.T., Chiou, Ch.Ch., Yang, Y.W., Chang, Sh.Ch., Wang, W. (2010). A three-echelon supply chain coordination with quantity discounts for multiple items, International Journal of Systems Science, 41: 561-573.

Ghosh, D., Shah, J. (2015). Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164: 319-329.

Heydari, J., Govindan, K., Jafari, A. (2017). Reverse and closed loop supply chain coordination by considering government role, Transportation Research Part D: Transport and Environment, 52: 379-398.
Hassanzadeh-Amin, S., Zhang, G., Akhtar, P. (2017). Effects of uncertainty on a tire closed-loop supply chain network, Expert Systems with Applications, 73: 82-91.
Chaharsooghi, S.K., Heydari, J., Nakhai Kamalabadi, I. (2011). Simultaneous coordination of order quantity and reorder point in a two-stage supply chain, Computers & Operations Research, 38(12), 1667-1677.
Heydari, J. (2014). Supply chain coordination using time-based temporary price discounts, Computers & Industrial Engineering, 75: 96-101.
Heydari, J., Norouzinasab, Y. (2015). A two-level discount model for coordinating a decentralized supply chain considering stochastic price-sensitive demand, Journal of Industrial Engineering International, 4(11): 531-542.
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.
Jackson, J.E., Munson, Ch.L. (2016). Shared resource capacity expansion decisions for multiple products with quantity discounts, European Journal of Operational Research, 253: 602-613.
Jiao, W., Zhang, J.L. (2017). The stochastic lot-sizing problem with quantity discounts, Computers & Operations Research, 80: 1-10.

Lau, A.H.L., Lau, H.Sh., Zhou, Y.W. (2008). Quantity discount and handling-charge reduction schemes for a manufacturer supplying numerous heterogeneous retailers, International Journal of Production Economics, 113: 425-445.

Leng, M., Parlar, M. (2010). Game-theoretic analyses of decentralized assembly supply chains: Non-cooperative equilibria vs. coordination with cost-sharing contracts, European Journal of Operational Research, 204: 96-104.
Lee, J.Y., Cho, R.K., Paik, S.K. (2016). Supply chain coordination in vendor-managed inventory systems with stockout-cost sharing under limited storage capacity, European Journal of Operational Research, 248: 95-106.
Mahdavi Mazdeh, M., Emadikhiav, M., Parsa, I. (2015). A heuristic to solve the dynamic lot sizing problem with supplier selection and quantity discounts, Computers & Industrial Engineering, 85: 33-43.
Munson, C.L., Hu, J. (2010). Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision, European Journal of Operational Research, 201: 581-592.
Nie, T., Due, Sh. (2017). Dual-fairness supply chain with quantity discount contracts, European Journal of Operational Research, 258: 491-500.
Ovaskainen, V., Hujala, T., Hänninen, H., Mikkola, J. (2017). Cost sharing for timber stand improvements: Inducement or crowding out of private investment?, Forest Policy and Economics, 74: 40-48.
Paratha Sarathi, G., Sarmah, S.P., Jenamani., M. (2014). An integrated revenue sharing and quantity discounts contract for coordinating a supply chain dealing with short life-cycle products, Applied Mathematical Modelling, 38: 4120-4136.
Paydar, M.M., Babaveisi, V., Safaei, A.S. (2017). An engine oil closed-loop supply chain design considering collection risk, Computers & Chemical Engineering, 104: 38–55.
Roma, P., Perrone, G. (2016). Cooperation among competitors: A comparison of cost-sharing mechanisms, International Journal of Production Economics, 180: 172-182.
Tamjidzad, Sh., Mirmohammadi, S.H. (2017). Optimal (r, Q) policy in a stochastic inventory system with limited resource under incremental quantity discount, Computers & Industrial Engineering, 103: 59-69.
Taleizadeh AA, Niaki ST, Aryanezhad MB (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 AA, Aryanezhad MB, Niaki STA (2008b) Optimizing Multi-Products Multi-Constraints Inventory Control Systems with Stochastic Replenishments, Journal of Applied Science, 6(1):1-1.
Taleizadeh AA, Moghadasi H, Niaki STA, Eftekhari AK (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 AA, Niaki STA, Aryanezhad MB (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 AA, Niaki STA, Aryanezhad MB, 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 AA, Barzinpour F, Wee HM (2011) Meta-heuristic Algorithms to Solve the Fuzzy Single Period Problem, Mathematical and Computer Modeling, 54(5-6): 1273-1285.
Taleizadeh AA, Pentico DW, Jabalameli MS, Aryanezhad MB (2013a) An Economic Order Quantity Model with Multiple Partial Prepayments and Partial Backordering, Mathematical and Computer Modeling, 57 (3-4): 311–323.
Taleizadeh AA, Pentico DW (2013b) An Economic Order Quantity Model with Known Price Increase and Partial Backordering. European Journal of Operational Research, 28 (3): 516-525.
Taleizadeh AA (2014) An Economic Order Quantity Model with Partial Backordering and Advance Payments for an Evaporating Item, International Journal of Production Economic. 155, 185–193.
Xie, J., Liang, L., Liu, L., Ieromonachou, P. (2017). Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, International Journal of Production Economics, 183: 528–538.
Zhao, H., Lin, B., Mao, W., Ye, Y. (2014). Differential Game Analyses of Logistics Service Supply Chain Coordination by Cost Sharing Contract, Journal of Applied Mathematics, 2014: 1-10.
Zhou, Y., Bao, M., Chen, X., Xu, X. (2016). Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns, Journal of Cleaner Production, 133: 402-413.
Zissis, D., Loannou, G., Burnetas, A. (2015). Supply chain coordination under discrete information asymmetries and quantity discounts, Omega, 53: 21-29.