Volume 4 Issue 1 pp. 81-92 Winter, 2013


Three stage supply chain model with two warehouse, imperfect production, variable demand rate and inflation


S.R. Singh, Vandana Gupta Preety Gupta




This study develops an integrated production inventory model from the perspectives of vendor, supplier and buyer. The demand rate is time dependent for the vendor and supplier and buyer assumes the stock dependent demand rate. As per the demand, supplier uses two warehouses (rented and owned) for the storage of excess quantities. Shortages are allowed at the buyer’s part only and the unfulfilled demand is partially backlogged. The effect of imperfect production processes on lot sizing is also considered. This complete model is studied under the effect of inflation. The objective is to minimize the total cost for the system. A solution procedure is developed to find a near optimal solution for the model. A numerical example along with sensitivity analysis is given to illustrate the model.




DOI: 10.5267/j.ijiec.2012.10.005

Keywords: Supply chain model, Two warehouse, Partially backlogging, Imperfect items, Variable demand rate and inflation

References

References Baker, R.C., & Urban, T.L. (1988). A deterministic inventory system with an inventory level-dependent demand rate. Journal of the Operational Research , 39, (9), 823-831.

Balkhi, Z.T., & Benkherouf, L. (2004). On an inventory model for deteriorating items with stock dependent and time-varying demand rates. Computers and Operations Research, 31(2), 223-240.

Bhunia, A. K., & Maiti, M. (1998). A two warehouses inventory model for deteriorating items with a linear trend in demand and shortages. Journal of Operation Research, 49(1), 287–292.

Chern, M.S., Yang, H.L., Teng, J.T., & Papachristos, S. (2008). Partial backlogging inventory lot size models for deteriorating items with fluctuating demand under inflation. European Journal of Operational Research, 191(1), 127–141.

Chen, L.H., & Kang, F.S. (2010). Coordination between vendor and buyer considering trade credit and items of imperfect quality. International Journal of Production Economics, 123(1), 52–61.

Chung, K.J., & Hou, K.L. (2003). An optimal production runtime with imperfect production processes and allowable shortages. Computers and Operations Research, 20(1), 483–490.

Chung, K.J., Her, C.C., & Lin, S.D. (2009). A two-warehouse inventory model with imperfect quality production processes. Computers & Industrial Engineering, 56(1), 193–197.

Chung, K.J., & Huang, Y.F. (2006). Retailer’s optimal cycle times in the EOQ model with imperfect quantity and a permissible credit period. Quality & Quantity, 40(1), 59-77.

Das, B., Maity, K., & Maiti, M. (2007). A two warehouse supply-chain model under possibility/necessity/credibility measures. Mathematical and Computer Modelling, 46(3-4), 398–409.

Geraldine, S., & Yves, P. (2010). An integrated model for warehouse and inventory planning. European Journal of Operation Research, 204(1), 35-50.

Goswami, A., & Chaudhuri, K. S. (1992). An economic order quantity model for items with two levels of storage for a linear trend in demand. Journal of Operational Research, 43(2), 157–167.

Ho, C.H, Ouyang, L.Y., & Su, C.H. (2006). Analysis of optimal vendor-buyer integrated inventory policy involving defective items. International Journal of Advanced Manufacturing Technology, 29(11–12), 1232-1245.

Hsu, P.H. (2012). Optimal production policy with investment on imperfect production processes. African Journal of Business Management, 6(1), 67-79.

Hartley, V. R. (1976). Operations research – a managerial emphasis California. Good Year Publishing Company, 315–317.

Khouja, M., & Mehrez, A. (1994).An Economic Production Lot Size Model with Imperfect Quality and Variable Production Rate. Journal of Operational Research, 45(12), 1405-1417.

Lee, C.C., & Hsu, S.L. (2009). Two Warehouse production model for deteriorating inventory items with time-dependent demands. European Journal of Operational Research, 194(3), 700-710.

Lin, C.S. (1999). Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials. Mathematical and Computer Modelling, 29(2), 81-89.

Mandal, M., & Maiti, M. (1997). Inventory model for damageable items with stock-dependent demand and shortages. Opsearch, 34(3), 155-166.

Maddah, B., & Jaber, M.Y. (2008). Economic order quantity for items with imperfect quality. International Journal of Production Economics, 112(2), 808–815.

Porteus, E. L. (1986). Optimal lot sizing, process quality improvement and setup cost reduction. Operations Research, 18(1), 137–144.

Rosenblatt, M.J., & Lee, H.L. (1986). Economic production cycles with imperfect production processes. IIE Transactions, 18(1), 48–55.

Sarkar, B., & Moon, I. (2011). An EPQ model with inflation in an imperfect production system. Applied Mathematics and Computation, 217(13), 6159-6167.

Yang, H.L. (2004). Two warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operation Research, 157(2), 344-356.

Yang, H.L. (2006). Two warehouse partial backlogging inventory models for deteriorating items under inflation. International Journal of Production Economics, 103(2), 362-370.

Yang, H. L., Teng, J. T., & Chern, M. S. (2010). An inventory model under inflation for deteriorating items with stock dependent consumption rate and partial backlogging shortages. International Journal of Production Economics, 123(1), 8-19.

Salameh, M.K., & Jaber, M.Y. (2000). Economic production quantity model for items with imperfect quantity. International Journal of Production Economics, 64(1–3), 59-64.

Wee, H.M., Yu, J., & Chen, M.C. (2007). Optimal inventory model for items with imperfect quality and shortage backordering. Omega Naval Research Logistics, 35(1), 7–11.