A credit mechanism in coordinating quality level, pricing and replenishment decisions with deteriorating items

Document Type: Research Paper


School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


In this paper, we present a two-level supply chain (SC) consisting of a single manufacturer that suppling one type of deteriorating product to a single retailer that the market demand rate for the product is time-varying and depends on two endogenous variables that include the retail price and product quality. The objective of this paper is to determine simultaneously pricing policy and ordering for the retailer, as well as product quality optimizing strategy for the manufacturer. Firstly, the problem is formulated under a decentralized structure with a manufacturer-Stackelberg game where each member optimizes his/her decisions regardless of the others’ profitability. Next, a centralized structure was presented and optimized based upon the whole SC profitability. Although the centralized model improves the quality level of the product and profitability of the entire SC, it may reduce the profitability of each SC members. Then, this paper is developed with an incentive scheme based on credit policy to coordinate this system. Moreover, Numerical examples and sensitivity analysis are presented to indicate the effectiveness of the contract. The results show that the credit contract can lead to perfect coordination, while the coordinated system is more robust than the centralized system. This paper extends the understanding of supply chain coordination in the context of deteriorating items that indisputably have a reciprocal relationship with market time-varying demand in many real-life cases.


Main Subjects

Aggarwal, S. and C. Jaggi (1995). "Ordering policies of deteriorating items under permissible delay in payments." Journal of the operational research society 46(5): 658-662.

Banker, R. D., et al. (1998). "Quality and competition." Management science 44(9): 1179-1192.

Cachon, G. P. (2003). "Supply chain coordination with contracts." Handbooks in operations research and management science 11: 227-339.

Cachon, G. P. and M. A. Lariviere (2005). "Supply chain coordination with revenue-sharing contracts: strengths and limitations." Management science 51(1): 30-44.

Chaharsooghi, S. K. and J. Heydari (2010). "Supply chain coordination for the joint determination of order quantity and reorder point using credit option." European Journal of Operational Research 204(1): 86-95.

Du, R., et al. (2013). "Coordination of two-echelon supply chains using wholesale price discount and credit option." International Journal of Production Economics 143(2): 327-334.

Gholamian, M. R. and M. Ebrahimzadeh-Afruzi (2019). "Credit and discount incentive options for two-level supply chain coordination, under uncertain price-dependent demand." Operational Research: 1-25.

Goyal, S. K. (1985). "Economic order quantity under conditions of permissible delay in payments." Journal of the operational research society: 335-338.

Heydari, J., et al. (2017). "A two-level delay in payments contract for supply chain coordination: The case of credit-dependent demand." International Journal of Production Economics.

Ho, C.-H. (2011). "The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit." Computers & Industrial Engineering 60(1): 117-126.

Ho, C.-H., et al. (2008). "Optimal pricing, shipment and payment policy for an integrated supplier–buyer inventory model with two-part trade credit." European Journal of Operational Research 187(2): 496-510.

Hsieh, T.-P. and C.-Y. Dye (2017). "Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand." European Journal of Operational Research 262(1): 136-150.

Jaggi, C. K., et al. (2011). "Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions." International Journal of Systems Science 42(7): 1185-1196.

Jamal, A., et al. (2000). "Optimal payment time for a retailer under permitted delay of payment by the wholesaler." International Journal of Production Economics 66(1): 59-66.

Kovach, J. J., et al. (2018). "Salesforce incentives and remanufacturing." Production and Operations Management 27(3): 516-530.

Liu, G., et al. (2015). "Joint dynamic pricing and investment strategy for perishable foods with price-quality dependent demand." Annals of Operations Research 226(1): 397-416.

Maiti, T. and B. Giri (2015). "A closed loop supply chain under retail price and product quality dependent demand." Journal of Manufacturing Systems 37: 624-637.

Moorthy, K. S. (1988). "Product and price competition in a duopoly." Marketing science 7(2): 141-168.

Nair, A. and R. Narasimhan (2006). "Dynamics of competing with quality-and advertising-based goodwill." European Journal of Operational Research 175(1): 462-474.

Noori-Daryan, M., et al. (2019). "Analyzing pricing, promised delivery lead time, supplier-selection, and ordering decisions of a multi-national supply chain under uncertain environment." International Journal of Production Economics 209: 236-248.

Panda, S., et al. (2013). "Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand." International Journal of Systems Science 44(1): 127-138.

SeyedEsfahani, M. M., et al. (2011). "A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer–retailer supply chains." European Journal of Operational Research 211(2): 263-273.

Taylor, T. A. (2002). "Supply chain coordination under channel rebates with sales effort effects." Management science 48(8): 992-1007.

Tibrewala, R., et al. (2018). "Buy-back policy for supply chain coordination: a simple rule." International Journal of Operational Research 31(4): 545-572.

Tsay, A. A. (1999). "The quantity flexibility contract and supplier-customer incentives." Management science 45(10): 1339-1358.

Vörös, J. (2006). "The dynamics of price, quality and productivity improvement decisions." European Journal of Operational Research 170(3): 809-823.

Wang, W.-C., et al. (2014). "Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime." European Journal of Operational Research 232(2): 315-321.

Xie, G., et al. (2011). "Quality investment and price decision in a risk-averse supply chain." European Journal of Operational Research 214(2): 403-410.

Xiong, H., et al. (2011). "A composite contract based on buy back and quantity flexibility contracts." European Journal of Operational Research 210(3): 559-567.

Ye, Y.-S., et al. (2016). "The price of anarchy in competitive reverse supply chains with quality-dependent price-only contracts." Transportation Research Part E: Logistics and Transportation Review 89: 86-107.

Zhai, Y., et al. (2017). "Production lead-time hedging and coordination in prefabricated construction supply chain management." International Journal of Production Research 55(14): 3984-4002.