An EOQ model for time-dependent deteriorating items with alternating demand rates allowing shortages by considering time value of money

Authors

  • Antara Kundu University of Calcutta, Department of Applied Mathematics, Calcutta, India
  • Priya Chakrabarti Institute of Engineering and Management, Calcutta, India
  • Tripti Chakrabarti University of Calcutta, Department of Applied Mathematics, Calcutta, India

DOI:

https://doi.org/10.2298/YJOR130120022K

Keywords:

EOQ, deterioration, shortages, two-component demand

Abstract

The present paper deals with an economic order quantity (EOQ) model of an inventory problem with alternating demand rate: (i) For a certain period, the demand rate is a non linear function of the instantaneous inventory level. (ii) For the rest of the cycle, the demand rate is time dependent. The time at which demand rate changes, may be deterministic or uncertain. The deterioration rate of the item is time dependent. The holding cost and shortage cost are taken as a linear function of time. The total cost function per unit time is obtained. Finally, the model is solved using a gradient based non-linear optimization technique (LINGO) and is illustrated by a numerical example.

References

Baker, R. C., and Urban, T. L., A deterministic inventory system with an inventory-level dependent demand rate, J. Opl. Res. Soc., 39 (9) (1988) 823-831.

Basu, M., and Sinha, S., An ordering policy for deteriorating items with two component demand and price breaks allowing shortages, Opsearch, 44, 1 (2007).

Chakrabarti, T., and Sen, S., An order inventory model with variable rate of deteriorating and alternating replenishing rates considering shortage, Journal of Operations Research Society of India, 44, 1 (2007) 17-26.

Chakrabarti, T., and Sen, S., An EOQ model for deteriorating items with quadratic time varying demand and shortages in all cycles, Journal of Mathematics and System Sciences, 44 (1) (2008) 141-148.

Chung, K. J., and Hwang, Y. F., The optimal cycle time for EOQ inventory model under permissible delay in payments, International Journal of Production Economics, 84 (2003) 307-318.

Dye, C. Y., A deteriorating inventory model with stock dependent demand and partial backlogging under conditions of permissible delay in payments, Opsearch, 39 (2002) 3 & 4.

Gupta, R., and Vrat, P., Inventory model for stock-dependent consumption rate, Opsearch, 23 (1) (1986) 19-24.

Ghare, P. M., and Scharder, G. F., A model for exponentially decaying inventory, J. Indust. Engg, 14 (1963) 238-243.

Jamal, A. M. M., Sarkar, B. R., and Wang, S., An ordering policies for deteriorating items with allowable shortages and permissible delay in payment, J. Oper. Res. Soc., 48 (1997) 826-833.

Khanra, S., Sana, S. S., and Chaudhuri, K. S., An EOQ model for perishable item with stock and price dependent demand rate, International Journal of Mathematics in Operational Research, 2 (3) (2010) 320-335.

Levin, R. I., Melaughlin, C. P., Lamone, R. P., and Kottas, J. F., Production/Operations Management: Contemporary Policy for Managing Operating Systems, McGraw-Hill, New York, (1972) 373.

Mandal, B. N., and Phaugdar, S., A note on an inventory model with stock-dependent consumption rate, Opsearch, 26 (1) (1989) 43-46.

Mandal, B. N., and Phaujdar, S., An inventory model for deteriorating items and stock dependent consumption rate, J. Opl. Res. Soc., 40 (5) (1989) 483-488.

Pal, A. K., and Mandal, B., An EOQ model for deteriorating inventory with alternating demand rates, Korean J Cop & Appl Math, 4 (2) (1997) 397-407.

Rao, K. S., and Sarma, K. V. S., An order-level inventory model under L2 system with power pattern demand, International Journal of Management and Systems, 20 (2004) 31-40.

Rau, H., Wu, M. Y., and Wee, H. M., Deteriorating item inventory model with shortage due to supplier in an integrated supply chain, International Journal of System Science, 35 (5) (2004) 293-303.

Reddy, G. S. N., and Sarma, K. V. S., A periodic review inventory problem with variable stock dependent demand, Opsearch, 38 (3) (2001) 332-341.

Silver, E. A., Operations research in inventory management, Opns. Res., 29 (1981) 628-645.

Silver, E. A., and Peterson, R., Decision Systems for Inventory Management and Production Planning, 2nd edn. Wiley, New York, 1985.

Subbaiah, K. V., Rao, K. S., and Satyanarayana, B., Inventory models for perishable items having demand rate dependent on stock level, Opsearch, 41 (4) (2004) 223-236.

Skouri, K., and Papachritos, S., Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging, International Journal of Production Economics, 81-82 (2003) 525-531.

Teng, J. T., and Chang, C. T., Economic production quantity models for deteriorating items with price and stock dependent demand, Computers and Operational Research, 32 (2005) 297-308.

Wee, H. M., A replenishment policy for items with a price dependent demand and varying rate of deterioration, Production Planning and Control, 8 (5) (1997) 494-499.

Downloads

Published

2013-06-01

Issue

Vol. 23 No. 2 (2013)

Section

Research Articles

License

Copyright (c) 2013 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.