Volume 2 Issue 1 pp. 61-86 Winter, 2011


An inventory model for deteriorating items with varying demand pattern and unknown time horizon


Ibraheem Abdul and Atsuo Murata


The primary assumptions with many multi-period inventory lot-sizing models are fixed time horizon and uniform demand variation within each period. In some real inventory situations, however, the time horizon may be unknown, uncertain or imprecise in nature and the demand pattern may vary within a given replenishment period. This paper presents an economic order quantity model for deteriorating items where demand has different pattern with unknown time horizon. The model generates optimal replenishment schedules, order quantity and costs using a general ramp-type demand pattern that allows three-phase variation in demand. Shortages are allowed with full backlogging of demand and all possible replenishment scenarios that can be encountered when shortages and demand pattern variation occur in multi-period inventory modeling are also considered. With the aid of numerical illustrations, the advantages of allowing for variation in demand pattern within replenishment periods, whenever they occur, are explored. The numerical examples show that the length of the replenishment period generated by the model varies with the changes in demand patterns.


DOI: 10.5267/j.ijiec.2010.05.002

Keywords: Inventory, ramp-type demand, deterioration, time horizon, shortages
References

Bahari-Kashani, H. (1989). Replenishment schedule for deteriorating items with time proportional demand. Journal of the Operational Research Society, 40, 75-81.

Cheng, M., & Wang, G. (2009). A note on the inventory model for deteriorating items with trapezoidal type demand rate. Computers & Industrial Engineering, 56, 1296-1300.

Chu, P., & Chen, P. S. (2002). A note on inventory replenishment policies for deteriorating items in an exponentially declining market. Computers and Operations Research, 29, 1827–1842.

Chung, K-J., & Ting, P-S. (1993). A heuristic for replenishment of deteriorating items with a linear trend in demand, Journal of the Operational Research Society, 44, 1235-1241.

Conn, A. R., Scheiberg, K., & Vincete, L. N. (2009). Global convergence of general derivative-free trust-region algorithms to first- and second-order critical points, SIAM Journal on Optimization, 20 (1), 387-415.

Covert, R.P., & Philip, G.C. (1973). An EOQ model for items with Weibull distribution deterioration”, AIIE Transactions, 5, 323–326.

Dave, V., & Patel, K. (1981). (T, Si) Policy inventory model for deteriorating items with time proportional demands. Journal of the Operational Research Society, 32, 137-142.

Deng, P.S., Lin, R. H-J., & Chu, P. (2007). A note on the inventory models for deteriorating items with ramp-type demand rate. European Journal of Operational Research, 178, 112–120.

Donaldson, W. A. (1977). Inventory replenishment policy for a linear trend in demand – An analytical solution. Operations Research Quarterly, 28 (3), 671-681.

Dye, C-Y., Chang, H-J., & Teng, J-T. (2006). A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging. European Journal of Operational Research, 172, 417–429.

Ghare, P.M., & Schrader, G.F. (1963). A model for exponential decaying inventory. Journal of Industrial Engineering, 14, 238-243.

Giri, B. C., & Chaudhuri, K. S. (1997). Heuristic models for deteriorating items with shortages and time-varying demand and costs. International Journal of System Science, 28 (2), 153-159.

Giri, B.C, Jalan, A.K, & Chaudhuri K.S. (2003). Economic order quantity model with Weibull deterioration distribution, shortage and ramp-type demand. International Journal of Systems Science, 34 (4), 237–243.

Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134, 1-16.

Hariga, M. A. (1995). An EOQ model for deteriorating items with shortages and time-varying demand. Journal of the Operational Research Society, 46, 398-404.

Hariga, M. A. (1996). Optimal EOQ models for deteriorating items with time-varying demand. Journal of the Operational Research Society, 47, 1228-1246.

Hill, R. M. (1995). Inventory model for increasing demand followed by level demand. Journal of the Operational Research Society, 46, 1250–1259.

Kar, S., Roy, T. K., & Maiti, M. (2006). Multi-item fuzzy inventory model for deteriorating items with finite time horizon and time dependent demand. Yugoslav Journal of Operations Research, 16 (2), 161-176.

Khanra, S., & Chaudhuri, K. S. (2003). A note on an order-level inventory model for a deteriorating item with time dependent quadratic demand. Computers & Operations Research, 30, 1901–1916.

Kim, D.H. (1995). A heuristic for Replenishment of deteriorating items with a linear trend in demand. International Journal for Production Economics, 39, 265 – 270.

Mandal, B., & Pal, A. K. (1998). Order level inventory system with ramp-type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics, 1, 49–66.

Manna, S. K., & Chaudhuri, K. S. (2006). An EOQ model with ramp-type demand rate, time dependent deterioration rate, unit production cost and shortages. European Journal of Operational Research, 171, 557–566.

Nocedal, J., & Wright, S. J. (1999). Numerical Optimization. New-York: Springer-Verlag Inc.

Panda, S., Senapati, S., & Basu, M. (2008). Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand. Computers and Industrial Engineering, 54, 301–314.

Rau, H. & Ouyang, B.C. (2008). An optimal batch size for integrated production–inventory policy in a supply chain. European Journal of Operational Research, 185, 619–634.

Roy, A., Maiti, M. K., Kar, S., & Maiti, M. (2007). Two storage inventory model with fuzzy deterioration over a random planning horizon. Mathematical and Computer Modeling, 46, 1419–1433.

Sachan, R.S. (1984). On (T, Si) policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society, 35, 1013-1019.

Sadjadi, S. J., & Ponnambalam, K. (1999). Advances in trust region algorithms for constrained optimization. Applied Numerical Mathematics, 29 (3), 423-443.

Shah, Y.K., & Jaiswal, M.C. (1977). An order-level inventory model for a system with constant rate of deterioration. Opsearch, 14, 174–184.

Silver, E.A. (1979). A simple inventory replenishment decision rule for a linear trend in demand. Journal of the Operational Research Society, 30, 71-75.

Silver, E.A., & Meal, H.C. (1973). A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment. Production and Inventory Management, 14, 64-74.

Wu, K-S., & Ouyang, L-Y. (2000). A replenishment policy for deteriorating items with ramp-type demand rate. Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, 24 (4), 279–286.

Wu, K-S. (2001). An EOQ inventory model for items with Weibull distribution deterioration, ramp-type demand rate and partial backlogging. Production Planning and Control, 12(8), 787–793.