An Integrated Inventory Model with Controllable Lead time and Setup Cost Reduction for Defective and Non-Defective Items

Document Type : Research Paper

Authors

1 The Gandhigram Rural Institute – Deemed University, Gandhigram

2 The Gandhigram Rural Institute – Deemed University, Gandhigram

Abstract

In this paper, the study deals with the lead time and setup reduction problem in the vendor-purchaser integrated inventory model. The cost of capital (i.e., opportunity cost) is one of the key factors in making the inventory and investment decisions. Lead time is an important element in any inventory system. The proposed model is presents an integrated inventory model with controllable lead time with setup cost reduction for defective and non defective items under investment for quality improvement. In this analysis, the proposed model, we assumed that the setup cost and process quality is logarithmic function. Setup cost reduction for defective and non defective items, is the main focus for the proposed model. The objective of the proposed model is to minimize the total cost of both the vendor-purchaser. The mathematical model is derived to investigate the effects to the optimal decisions when investment strategies in setup cost reductions are adopted. This paper attempts to determine optimal order quantity, lead time, process quality and setup cost reduction for production system such that the total cost is minimized. A solution procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.

Keywords


Banerjee, A. (1986). A joint economic-lot-size model for purchaser and vendor, Decision Sciences, Vol.17, pp. 292-311.
Ben-Daya, M., and Raouf, A. (1994). Inventory models involving lead time as decision variable, Journal of the Operational Research Society, Vol. 45, pp.579-582.
Chang, H.C., Ouyang, L.Y., Wu, K.S. and Ho, C.H. (2006). Integrated vendor- buyer cooperative inventory models with controllable lead time and ordering cost reduction, European Journal of Operational Research, Vol. 170, pp.481-495.
Coates, E.R. (1996). Manufacturing setup cost reduction, Computers and Industrial Engineering, Vol. 31, pp. 111-114.
Glock C.H. (2012). Lead time reduction strategies in a single vendor-single buyer integrated inventory model with lot size-dependent lead time and stochastic demand. International Journal of Production Economics, Vol. 136, pp. 37-44.
Glock C.H. (2012a ). The joint economic lot size problem: A review. International Journal of Production Economics, Vol. 135, pp. 671-686.
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.
Goyal, S.K. (1988). A joint economic-lot-size model for purchaser and vendor: A comment, Decision Sciences, Vol.19, pp.236-241.
Goyal, S.K. and Nebebe, F. (2000). Determination of economic production-shipment policy for a single-vendor single-buyer system, European Journal of Operations Research, Vol. 121, pp. 175-178.
Goyal, S.K. and Srinivasan, G. (1992). The individually responsible and rational decision approach to economic lot sizes for one vendor and many purchasers: a comment, Decision Sciences, Vol.23, pp. 777-784.
Hall, R.W., zero Inventories, Dow Jones Irwin, Homewood, IL, 1983.
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 Sciences, Vol.20, pp.161-171.
Hong, J.D. and Hayya, J.C. (1995). Joint investment in quality improvement and setup reduction, Computers and Operations Research, Vol. 22, pp. 567-574.
Hoque, M.A. (2013). A vendor-buyer integrated production inventory model with normal distribution of lead time. International Journal of Production Economics, Vol. 144, pp.409- 417.
Hoque, M.A. and Goyal, S.K. (2006). A heuristic solution procedure for an integrated inventory system under controllable lead-time with equal or unequal size batch shipments between a vendor and a buyer, International Journal of Production Economics, Vol. 102, pp. 217-225.
Hsu, S.L. and Lee, C.C. (2009). Replenishment and lead time decisions in manufacturer retailer chains, Transportation Research Part E, Vol.45, pp. 398-408.
Hwang, H., Kim, D.B. and Kim, Y.D. (1993). Multiproduct economic lot size models with investments costs for setup reduction and quality improvement, International Journal of Production Research, Vol. 31, pp. 691-703.
Keller, G. and Noori, H. (1988). Impact of investing in quality improvement on the lot size model, Omega, Vol. 15, pp. 595-601.
Kim, K.L., Hayya, J.C. and Hong, J.D. (1992). Setup reduction in economic production quantity model, Decision Science, Vol. 23, pp. 500-508.
Liao, C.J., and Shyu, C.H. (1991). An analytical determination of lead time with normal demand, International Journal of Operations & Production Management, Vol.11, pp.72-78.
Moon, I. (1994). Multiproduct economic lot size models with investments costs for setup reduction and quality improvement: Review and extensions, International Journal of Production Research, Vol. 32, pp. 2795-2801.
Moon,I., and Choi,S. (1998). A note on lead time and distributional assumptions in continuous review inventory models, Computers & Operations Research, Vol. 25, pp. 1007-1012.
Nasri, F., Affisco, J.F. and Paknejad, M.T. (1990). Setup cost reduction in an inventory model with finite range stochastic lead times, International Journal of Production Research, Vol. 28, pp. 199-212.
Ouyang, L.Y. and Chang, H.C. (1999). Impact of investing in quality improvement on (Q, r, L) model involving the imperfect production process, Production Planning Control, Vol. 11, pp.598-607.
Ouyang, L.Y., Chen, C.K. and Chang, H.C. (1999a ). Lead time and ordering cost reductions in continuous review inventory systems with partial backorders, Journal of the Operational Research Society, Vol. 50, pp. 1272-1279.
Ouyang, L.Y., Wu, K.S. and 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.
Ouyang, L.Y., Wu, K.S. and Ho, C.H. (2007). An integrated vendor buyer inventory model with quality improvement and lead time reduction, International Journal of Production Economics, 108, 349-358.
Ouyang, L.Y., and Chuang, B.R. (1999b ). (Q, R, L,) inventory model involving quantity discounts and a stochastic backorder rate, Production Planning & Control, Vol. 10, pp. 426- 433.
Ouyang, L.Y., and Chuang, B.R. (1999c ). A minimax distribution free procedure for stochastic inventory models with a random backorder rate, Journal of the Operations Research Society of Japan, Vol. 42, pp.342-351.
Ouyang, L.Y., and Chuang, B.R. (2000). Stochastic inventory models involving variable lead time with a service level constraint, Yugoslav Journal of Operations Research, Vol. 10, pp.81-98.
Ouyang, L.Y., Chuang, B.R., and Wu, K.S. (1999d ). Optimal inventory policies involving variable lead time with defective items, Journal of the Operational Research Society of India, Vol.36, pp. 374-389.
Paknejad, M. J. and Affisco, J. F. (1987). The effect of investment in new technology on optimal batch quantity, Proceedings of the Northeast Decision Sciences Institute, DSI, RI, USA, 118-120.
Pan, J.C.H. and Yang, J.S. (2004). Just-in-time: an integrated inventory model involving deterministic variable lead time and quality improvement investment, International Journal of Production Research, Vol. 42, pp. 853-863.
Pan, J.C.H. and Yang, J.S.A. (2002). Study of an integrated inventory with controllable lead time, International Journal of Production Research, Vol. 40, pp. 1263-1273.
Pandey, A., Masin, M. and Prabhu, V. (2007). Adaptive logistic controller for integrated design of distributed supply chains, Journal of Manufacturing Systems, Vol.26, pp. 108-115.
Porteus, E.L. (1985). Investing in reduced setups in the EOQ model, Management Sciences, Vol. 31, pp. 998-1010.
Porteus, E.L. (1986). Optimal lot sizing process quality improvement and setup cost reduction, Operations Research, Vol. 34, pp.137-144.
Rosenblatt, M.J. and Lee, H.L. (1986). Economic production cycles with imperfect production processes, IIE Transactions, Vol.18, pp. 48-55.
Schonberger, R. (1982). Japanese Manufacturing Techniques, the Free, New York.
Tang, J., Yung, K.L. and Ip, A. W.H. (2004). Heuristics-based integrated decisions for logistics network systems, Journal of Manufacturing Systems, Vol.23, pp.1-13.
Teng, J.T., Crdenas, B.L.E. and Lou, K.R. (2011). The economic lot-size of the integrated vendor-buyer inventory system derived without derivatives: a simple derivation, Applied Mathematics and Computation, Vol. 217, pp. 5972-5977.
Tersine, R. (1994). Principle of Inventory and Material Management, Fourth Edition. Prentice-Hall, USA.
Tsou, C.S., Fang, H.H., Lo, H.C., Huang, C.H. (2009). A study of cooperative advertisings in a manufacturer-retailer supply chain, International Journal of Information and Management Sciences, Vol. 20, pp. 15-26.
Woo, Y.Y., Hsu, S.L. and Wu, S.H. (2001). An integrated inventory model for a single vendor and multiple buyers with ordering cost reduction, International Journal of Production Economics, Vol. 73, pp. 203-215.
Zhang, T., Liang, L., Yu, Y. and Yan, Y. (2007). An integrated vendor-managed inventory model for a two-echelon system with order cost reduction, International Journal of Production Economics, Vol. 109, pp. 241-253.