# A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract

Supply chain (SC) coordination is one of the major issues which has been considered in the investigations of supply chains. In this study, a two-echelon supply chain with one retailer and one supplier is considered. Demand is stochastic and has a normal distribution and lead time is assumed determin...

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Main Authors: , , Article fas 2019-04-01 Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī http://jims.atu.ac.ir/article_9613_ac8cd0284b5d5c52b4c0830fe31bc353.pdf
id doaj-bf7954e0fbc14a43aa8ff5a6c1dfb52a Article doaj-bf7954e0fbc14a43aa8ff5a6c1dfb52a2020-11-25T03:50:07ZfasAllameh Tabataba'i University PressMuṭāli̒āt-i Mudīriyyat-i Ṣan̒atī2251-80292019-04-01175228733810.22054/JIMS.2018.17520.1626A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount ContractMina Nouri Harzvili Seyyed-Mahdi Hosseini-MotalghMohammadreza NematollahiSupply chain (SC) coordination is one of the major issues which has been considered in the investigations of supply chains. In this study, a two-echelon supply chain with one retailer and one supplier is considered. Demand is stochastic and has a normal distribution and lead time is assumed deterministic. The retailer uses a periodic review inventory system for his replenishment decisions and faces partial shortages. Review period and order-up-to-level are decision variables of the retailer. First, the optimized values of the variables in both decentralized and centralized decision-making structures are obtained. Although Centralized decision making increases the whole SC’s profitability, it reduces the profitability of the retailer in comparison with the decentralized model; In order to make centralized decisions and to encourage the retailer to change his decisions, a coordination model is proposed. Quantity discount contract is used as an incentive scheme in the coordinated model. For calculating the exact value of the discount factor in this contract, the both member’s profit is considered. Furthermore, to fairly share the extra profit achieved by the coordinated model, a profit-sharing strategy, based on the bargaining power of the members, is proposed. A set of numerical experiments and sensitivity analysis, which is performed with respect to several key parameters of the study, reveal that, from economic viewpoint, the proposed coordination model for the supplier-distributor channel, can increase the channel profit up to its optimal profit level and guarantee the improvement of channel members’ profit in comparison with their profit under the decentralized model. From inventory management viewpoint, the proposed discount contract reduces the distributor’s inventory shortage risk. Moreover, results of evaluating the proposed model under high levels of demand uncertainty shows that the proposed model is capable of coordinating the SC under various conditions such as demand frequencies and high quantities of standard deviation of the demand http://jims.atu.ac.ir/article_9613_ac8cd0284b5d5c52b4c0830fe31bc353.pdftwo-echelon decentralized supply chain supply chain coordination periodic review inventory systems quantity discount contract profit-sharing strategy DOAJ fas Article DOAJ Mina Nouri Harzvili Seyyed-Mahdi Hosseini-Motalgh Mohammadreza Nematollahi Mina Nouri Harzvili Seyyed-Mahdi Hosseini-Motalgh Mohammadreza Nematollahi A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī two-echelon decentralized supply chain supply chain coordination periodic review inventory systems quantity discount contract profit-sharing strategy Mina Nouri Harzvili Seyyed-Mahdi Hosseini-Motalgh Mohammadreza Nematollahi Mina Nouri Harzvili A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract mathematical model for coordinating decisions in periodic review inventory systems and sharing the profit in a two-echelon decentralized supply chain, by considering quantity discount contract Allameh Tabataba'i University Press Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī 2251-8029 2019-04-01 Supply chain (SC) coordination is one of the major issues which has been considered in the investigations of supply chains. In this study, a two-echelon supply chain with one retailer and one supplier is considered. Demand is stochastic and has a normal distribution and lead time is assumed deterministic. The retailer uses a periodic review inventory system for his replenishment decisions and faces partial shortages. Review period and order-up-to-level are decision variables of the retailer. First, the optimized values of the variables in both decentralized and centralized decision-making structures are obtained. Although Centralized decision making increases the whole SC’s profitability, it reduces the profitability of the retailer in comparison with the decentralized model; In order to make centralized decisions and to encourage the retailer to change his decisions, a coordination model is proposed. Quantity discount contract is used as an incentive scheme in the coordinated model. For calculating the exact value of the discount factor in this contract, the both member’s profit is considered. Furthermore, to fairly share the extra profit achieved by the coordinated model, a profit-sharing strategy, based on the bargaining power of the members, is proposed. A set of numerical experiments and sensitivity analysis, which is performed with respect to several key parameters of the study, reveal that, from economic viewpoint, the proposed coordination model for the supplier-distributor channel, can increase the channel profit up to its optimal profit level and guarantee the improvement of channel members’ profit in comparison with their profit under the decentralized model. From inventory management viewpoint, the proposed discount contract reduces the distributor’s inventory shortage risk. Moreover, results of evaluating the proposed model under high levels of demand uncertainty shows that the proposed model is capable of coordinating the SC under various conditions such as demand frequencies and high quantities of standard deviation of the demand two-echelon decentralized supply chain supply chain coordination periodic review inventory systems quantity discount contract profit-sharing strategy http://jims.atu.ac.ir/article_9613_ac8cd0284b5d5c52b4c0830fe31bc353.pdf AT minanouriharzvili amathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract AT seyyedmahdihosseinimotalgh amathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract AT mohammadrezanematollahi amathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract AT minanouriharzvili mathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract AT seyyedmahdihosseinimotalgh mathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract AT mohammadrezanematollahi mathematicalmodelforcoordinatingdecisionsinperiodicreviewinventorysystemsandsharingtheprofitinatwoechelondecentralizedsupplychainbyconsideringquantitydiscountcontract 1724492236715982848