Document Type: Original Article

Authors

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

2 Iran University of Science & Technology, Tehran, Iran.

Abstract

In this paper, an inventory model for deterioration items in a two-echelon supply chain including one retailer and one manufacturer is proposed by considering the stock and price dependent demand and capacity constraint for holding inventories. First, the model is presented as a leader-follower game in which the manufacturer announces wholesale prices. Second, the retailer decides for the order quantity and price of the items based on the wholesale prices. Then, by introducing the integrated model of the supply chain, a cost-sharing contract is applied to coordinate the manufacturer and the retailer. On the other hand, by using the convergence properties of the model and proving non-concavity of the problem, a meta-heuristic algorithm, namely iterative local search (ILS) is proposed to solve the models. The results show the determinant role of the capacity constraint on the optimal decisions and the ability of the proposed contract to coordinate the supply chain. Moreover, it is shown that the proposed algorithm outperforms the well-known interior point algorithm as the results of the initiations embedded in it for the special problem.

Keywords

Kaasgari, M.A., Imani, D.M. and Mahmoodjanloo, M., (2017). "Optimizing a vendor managed inventory (VMI) supply chain for perishable products by considering discount: Two calibrated meta-heuristic algorithms", Computers & Industrial Engineering, Vol. 103, pp. 227-241. 

Akçay, Y., Natarajan, H.P. and Xu, S.H., (2010). "Joint dynamic pricing of multiple perishable products under consumer choice", Management Science, Vol. 56, No. 8, pp. 1345-1361. 

Bakker, M., Riezebos, J. and Teunter, R.H., (2012). "Review of inventory systems with deterioration since 2001", European Journal of Operational Research, Vol. 221, No. 2, pp. 275-284.

Chen, L.H. and Ouyang, L.Y., (2006). "Fuzzy inventory model for deteriorating items with permissible delay in payment", Applied Mathematics and Computation, Vol. 182, No. 1, pp. 711-726. 

Chen, Z., Fu, K. and Bidanda, B., (2018). "Instant production-replenishment and coordination mechanism for short life cycle and deteriorating item with stock-dependent demand", International Journal of Systems Science: Operations & Logistics, Vol. 5, No. 1, pp. 45-59. 

Chen, L.T. and Wei, C.C., (2012). "Multi-period channel coordination in vendor-managed inventory for deteriorating goods", International Journal of Production Research, Vol. 50, No. 16, pp. 4396-4413. 

Chen, T.H., 2017. Optimizing pricing, replenishment and rework decision for imperfect and deteriorating items in a manufacturer-retailer channel. International Journal of Production Economics, Vol. 183, pp. 539-550. 

Chen, T.H. and Chang, H.M., (2010). "Optimal ordering and pricing policies for deteriorating items in one-vendor multi-retailer supply chain", The International Journal of Advanced Manufacturing Technology, Vol. 49, pp. 341-355. 

Chen, T.H., (2017). "Optimizing pricing, replenishment and rework decision for imperfect and deteriorating items in a manufacturer-retailer channel", International Journal of Production Economics, Vol. 183, pp. 539-550.

Frazelle, E., (2002). Supply chain strategy: the logistics of supply chain management. McGrraw Hill.

Ghosh, S.K., Sarkar, T. and Chaudhuri, K., (2015). "A multi-item inventory model for deteriorating items in limited storage space with stock-dependent demand", American Journal of Mathematical and Management Sciences, Vol. 34, No. 2, pp. 147-161. 

Giri, B.C. and Bardhan, S., (2012). "Supply chain coordination for a deteriorating item with stock and price‐dependent demand under revenue sharing contract", International Transactions in Operational Research, Vol. 19, No. 5, pp. 753-768. 

Kanda, A. and Deshmukh, S.G., (2008). "Supply chain coordination: perspectives, empirical studies and research directions", International journal of production Economics, Vol. 115, No. 2, pp. 316-335. 

Katayama, K. and Narihisa, H., (1999). Iterated local search approach using genetic transformation to the traveling salesman problem. In Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation-Volume 1 (pp. 321-328). Morgan Kaufmann Publishers Inc. 

Lin, F., Yang, Z.C. and Jia, T., (2016). Optimal pricing and ordering policies for non-instantaneous deteriorating items with price dependent demand and maximum lifetime, In Proceedings of the 6th International Asia Conference on Industrial Engineering and Management Innovation (pp. 411-421). Atlantis Press, Paris.

Lin, C. and Lin, Y., (2007). "A cooperative inventory policy with deteriorating items for a two-echelon model", European Journal of Operational Research, Vol. 178, No. 1, pp. 92-111.

Lin, F., Yang, Z.C. and Jia, T., (2016). Optimal pricing and ordering policies for non-instantaneous deteriorating items with price dependent demand and maximum lifetime. In Proceedings of the 6th International Asia Conference on Industrial Engineering and Management Innovation (pp. 411-421). Atlantis Press, Paris.

Lin, Y.H., Lin, C. and Lin, B., (2010). "On conflict and cooperation in a two-echelon inventory model for deteriorating items", Computers & Industrial Engineering, Vol. 59, No. 4, pp. 703-711. 

Maity, K. and Maiti, M., (2009). "Optimal inventory policies for deteriorating complementary and substitute items", International Journal of Systems Science, Vol. 40, No. 3, pp.267-276. 

Mandal, N.K., Roy, T.K. and Maiti, M., (2006). "Inventory model of deteriorated items with a constraint: A geometric programming approach", European Journal of Operational Research, Vol. 173, No. 1, pp. 199-210. 

Martin, O.C. and Otto, S.W., (1995). "Partitioning of unstructured meshes for load balancing", Concurrency: Practice and Experience, Vol. 7, No. 4, pp. 303-314.

Pakhira, N., Maiti, M.K. and Maiti, M., (2018). "Fuzzy Optimization for Multi-item Supply Chain with Trade Credit and Two-Level Price Discount under Promotional Cost Sharing", International Journal of Fuzzy Systems, pp. 1-12. 

Pandey, R., Singh, S., Vaish, B. and Tayal, S., (2017). "An EOQ model with quantity incentive strategy for deteriorating items and partial backlogging", Uncertain Supply Chain Management, Vol. 5, No. 2, pp. 135-142. 

Roy, T. and Chaudhuri, K.S., (2009). "A production‐inventory model under stock‐dependent demand, Weibull distribution deterioration and shortage", International Transactions in Operational Research, Vol. 16, No. 3, pp. 325-346.

Saha, S. and Goyal, S.K., (2015). "Supply chain coordination contracts with inventory level and retail price dependent demand", International Journal of Production Economics, Vol. 161, pp. 140-152.

Sana, S.S., (2010). "An EOQ model for perishable item with stock dependent demand and price discount rate", American Journal of Mathematical and Management Sciences, Vol. 30, pp. 299-316.

Sana, S.S., (2015). "An EOQ model for stochastic demand for limited capacity of own warehouse", Annals of Operations Research, Vol. 233, No. 1, pp. 383-399. 

Sana, S.S., (2011). "An EOQ model of homogeneous products while demand is salesmen’s initiatives and stock sensitive", Computers & Mathematics with Applications, Vol. 62, No. 2, pp. 577-587. 

Sarkar, B., Mandal, B. and Sarkar, S., (2017). "Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages", Journal of Industrial & Management Optimization, Vol. 13, No. 1, pp. 187-206. 

Singh, T., Sahoo, N.C. and Sahoo, C.K., (2016). "An EOQ model for deteriorating items with inventory dependent demand and initial order quantity dependent deterioration", International Journal of Management Concepts and Philosophy, Vol. 9, No. 4, pp. 306-329.

Teng, J.T. and Chang, C.T., (2005). "Economic production quantity models for deteriorating items with price-and stock-dependent demand", Computers & Operations Research, Vol. 32, No. 2, pp. 297-308. 

Teng, J.T., Krommyda, I.P., Skouri, K. and Lou, K.R., (2011). "A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme", European Journal of Operational Research, Vol. 215, No. 1, pp. 97-104.

Tiwari, S., Jaggi, C.K., Gupta, M. and Cárdenas-Barrón, L.E., (2018). "Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity", International Journal of Production Economics, Vol. 200, pp. 278-290.

Urban, T.L., (2005). "Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory", European Journal of Operational Research, Vol. 162, No. 3, pp.792-804.

Wang, K.J., Lin, Y.S. and Jonas, C.P., (2011). "Optimizing inventory policy for products with time-sensitive deteriorating rates in a multi-echelon supply chain", International Journal of Production Economics, Vol. 130, No. 1, pp. 66-76. 

Wee, H.M., (1993). "Economic production lot size model for deteriorating items with partial back-ordering", Computers & Industrial Engineering, Vol. 24, No. 3, pp. 449-458.

Wu, B. and Sarker, B.R., (2013). "Optimal manufacturing and delivery schedules in a supply chain system of deteriorating items", International Journal of Production Research, Vol. 51, No. 3, pp. 798-812.

Yan, C., Banerjee, A. and Yang, L., (2011). "An integrated production-distribution model for a deteriorating inventory item", International Journal of Production Economics, Vol. 133, Vol. 1, pp. 228-232.