Quadratic Approximation for an Inflationary Bi-objective Integrated Vendor-buyer Inventory Model with Imperfect Manufacturing Process and Fixed and Variable Lead Time Crash Costs

Document Type : Research Paper


Department of Industrial Engineering, Kharazmi University, Tehran, Iran


In this paper, we develop an integrated bi-objective model of two-stage supply chain composed of a vendor and a buyer under an imperfect production process. The stochastic inflationary condition wherein the first objective is minimizing the expected costs of the proposed supply chain model and the second objective is minimizing buyer’s shortage variance. We assume lead time and ordering cost are controllable parameters and lead time crashing cost is considered as a function of both order quantity and reduced lead time. An effective solution procedure is developed to determine the optimal policy of the proposed model. Finally, a numerical example and sensitivity analysis are proposed to show the performance of the model.


Main Subjects

Banerjee, A. (1986). A joint economic lot size model for purchaser and vendor. Decision Science, Vol. (17), pp. 292-311.
Gholami-Qadikolaei, A., Mirzazadeh, A., Tavakkoli-Moghaddam A. (2013). A stochastic multiobjective multiconstraint inventory model under inflationary condition and different inspection scenarios, Proc-IMechE-Part B- Journal of Engineering Manufacture, Vol. (227), pp. 1057-1074.
Gholami-Qadikolaei, A., Mirzazadeh, A., Tavakkoli-Moghaddam, R. (2015). Lead time and ordering cost reductions in budget and storage space restricted probabilistic inventory models with imperfect items, RAIRO-Operations Research, Vol. (49), pp. 215-242.
Gholami-Qadikolaei, A., Mohammadi, M., Mirzazadeh, A. (2012). A continuous review inventory system with controllable lead time and defective items in partial and perfect lead time demand distribution information environments, International Journal of Management science and Engineering Management, Vol. (7), pp. 205-212.
Ghoreishi, M., Weber, G. W., Mirzazadeh, A. (2014). An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation and selling price demand and customer returns, Annals of Operations Research, Vol. (226), pp. 221-238.  
Giri, B. C., Sharma, S. (2017). Integrated model for an imperfect production-inventory system with a generalized shipment policy, errors in quality inspection and ordering cost reduction, International Journal of System Science, Vol. (4), pp. 260-274.
Glock, C. H. (2012). Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand, International Journal of Production Economics, Vol. (136), pp. 37-44.
Goyal, S. K. (1988).  A joint economic-lot-size model for purchaser and vendor: A comment. Decision Science, Vol. (19), pp. 236-241.
Goyal, S. K. (1976). An integrated inventory model for a single supplier single customer problem. International Journal of Production Research, Vol. (15), pp. 107-111.
Ha, D., Kim, S. L. (1997). Implementation of JIT purchasing: An integrated approach. Production Planning and Control, Vol. (8), pp. 152-157.
Hadley, G. A. (1964). Comparison of order quantities computed using the average annual cost and discounted cost. Management Science, Vol. (10), pp. 427-467.
Hans, S., Raafat, N. I., Paul, B. L. (2006). Joint economic lot size in distribution system with multiple shipment policy. International Journal of Production Economics, pp. 302-316.
Hariga, M. A., Al-Ahmari. (2013). An integrated retail space allocation and lot sizing models under vendor managed inventory and consignment stock arrangement. Computers and Industrial Engineering, Vol. (64), pp. 45-55.
Ho, C. H. (2009). A minimax distribution free procedure for an integrated inventory model with defective goods and stochastic lead time demand. International Journal of Information and Management Science, Vol. (20), pp. 161-171.
Huang, C. K. (2002). An integrated vendor-buyer cooperative inventory model for items with imperfect quality. Production Planning and Control, Vol. (13), pp. 355-361.
Kumar, N., Kumar, S. (2016). Inventory model for non-instantaneous deteriorating items, stock dependent demand, partial backlogging and inflation over a finite time horizon. International Journal of Supply and Operations Management, Vol. (3), pp. 1168-1191
Liao, C.  J., Shyu, C. H. (1991). An analytical determination of lead time with normal demand. International Journal of Production Management, Vol. (11), pp. 72-78.
Lin, Y. J. (2009). An integrated vendor-buyer inventory model with backorder price discount and effective investment to reduce ordering cost. Computers and Industrial Engineering. Vol. (56), pp. 1597-1606.
Lo, S. T., Wee, H. M., Huang, W. C. (2007). An integrated production-inventory model with imperfect production processes and weibull distribution deterioration under inflation. International Journal of production Economics, 2007, 106, 248-260
Mirzazadeh, A., SeyedEsfehani, M. M., FatemiGhomi, S. M. T. (2009). An inventory model under uncertain inflationary condition, finite production rate and inflation-dependent demand rate for deteriorating items with shortages. International Journal of Systems Science, Vol. (40), pp. 21-31.
Mirzazadeh, A. (2011). A comparison of the mathematical modelling methods in the inventory systems under uncertain conditions. International Journal of Engineering Science and Technololgy, Vol. (3), 6131-6142.
Nasrabadi, M., Mirzazadeh, A. (2016). The inventory system management under uncertain conditions and time value of money. International Journal of Supply and Operations Management, Vol. (3), pp. 1192-1214.
Ouyang, L. Y., Wu, K. S., Ho, C. H. (2004). Integrated vendor-buyer cooperative models with stochastic demand in controllable lead time. International Journal of Production Economics. Vol. (92), pp. 255-266.
Pan, C. H. J., Yang, J. S. (2002). A study of an integrated inventory with controllable lead time. International Journal of Production Research, Vol. (40), pp. 1263-1273.
Pan, C. H. J., Hsiao, Y. C. (2005). Integrated inventory models with controllable lead time and backorder discount considerations. International Journal of Production Economics, Vol. (94), pp. 387-397. 
Porteus, E. L. (1985). Investing in reduced setups in the EOQ model. Management Science, Vol. (31), pp. 998-1010.
Salameh, M. k., Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics. Vol. (64), pp. 59-64.
Sarkar, B. R., Jamal, A. M., Wang, S. (2000). Supply chain models for perishable products under inflation and permissible delay in payment. Computers and Operations Research, Vol. (27), pp. 59-75.
Wan, N., and Chen, X. (2017). The role of put option contracts in supply chain management under inflation. International Transactions in Operational Research (,https://doi.org/10.1111/itor.12372)
Yang, P. C., Wee, H. M. (2003). An integrated multi-lot-size production inventory model for deteriorating item. Computers and Operations Research, Vol. (30), pp. 671-682.
Yedess, Y., Chelbi, A., Rezg, N. (2012). Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process. Journal of Intelligent manufacturing. Vol. 23(4), pp. 1254-1256.