Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T19:45:57.439Z Has data issue: false hasContentIssue false
  • English
  • Français

Production-inventory system with finite production rate,stock-dependent demand, and variable holding cost

Published online by Cambridge University Press:  10 January 2014

Hesham K. Alfares
Hesham K. Alfares*
Affiliation:
P.O. Box 5067, Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.. alfares@kfupm.edu.sa

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In general, traditional production-inventory systems are based on a number of simplifying– but somewhat unrealistic – assumptions, including constant demand rate, constant holdingcost, and instantaneous order replenishment. These assumptions have been individuallychallenged in numerous variations of production-inventory models. Finite production ratemodels, such as economic production quantity (EPQ) systems consider gradual orderreplenishment. Stock-dependent demand models assume the demand rate to be an elasticfunction of the inventory level. Variable holding cost models assume the holding cost perunit per time period to be a function of the time spent in storage. In this paper, thethree simplifying assumptions are simultaneously relaxed in a new production-inventorysystem with a finite production rate, stock-level dependent demand rate, and variableholding cost. Mathematical models and optimum solution procedures, including nonlinearprogramming, are presented for two functional forms of holding cost variability. The maincontribution of this paper is the formulation and solution of a new production-inventorymodel that more closely represents real-world situations. The realistic assumptions andefficient solution algorithms should make the model practical and useful for industrialapplications.

Keywords

Production-inventory systemstock-dependent demandvariable holding costnonlinear programming

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 1 , January 2014, pp. 135 - 150
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

References

Alfares, H.K., Inventory model with stock-level dependent demand rate and variable holding cost. Int. J. Prod. Econ. 108 (2007) 259–265. Google Scholar
Baker, R.C. and Urban, T.L., A deterministic inventory system with an inventory level dependent rate. J. Oper. Res. Soc. 39 (1988a) 823–831. Google Scholar
Baker, R.C. and Urban, T.L., Single-period inventory dependent demand models. Omega-The Int. J. Manag. Sci. 16 (1988b) 605–607. Google Scholar
Ferguson, M., Jayaraman, V. and Souza, G.V., Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables. Eur. J. Oper. Res. 180 (2007) 485–490. Google Scholar
Gayen, M. and Pal, A.K., A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost. Oper. Res. 9 (2009) 153–165. Google Scholar
Giri, B.C. and Chaudhuri, K.S., Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur. J. Oper. Res. 105 (1998) 467–474. Google Scholar
Giri, B.C., Goswami, A. and Chaudhuri, K.S., An EOQ model for deteriorating items with time-varying demand and costs. J. Oper. Res. Soc. 47 (1996) 1398–1405. Google Scholar
Goh, M., Some results for inventory models having inventory level dependent demand rate. Int. J. Prod. Econ. 27 (1992) 155–160. Google Scholar
Goh, M., EOQ models with general demand and holding cost functions. Eur. J. Oper. Res. 73 (1994) 50–54. Google Scholar
Gupta, R. and Vrat, P., Inventory model for stock-dependent consumption rate. Opsearch 23 (1986) 19–24. Google Scholar
Koschat, M.A., Store inventory can affect demand: empirical evidence from magazine retailing. J. Retailing 84 (2008) 165–179. Google Scholar
Min, J. and Zhou, Y.-W., A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint. Int. J. Syst. Sci. 40 (2009) 33–44. Google Scholar
Mahata, G.C. and Goswami, A., Fuzzy EOQ models for deteriorating items with stock dependent demand & non-linear holding costs. Int. J. Appl. Math. Comput. Sci. 5 (2009) 94–98. Google Scholar
Muhlemann, A.P. and Valtis-Spanopoulos, N.P., Variable holding cost rate model. Eur. J. Oper. Res. 4 (1980) 132–135. Google Scholar
Roy, A., An inventory model for deteriorating items with price dependent demand and time-varying holding cost. Adv. Model. Optim. 10 (2008) 25–37. Google Scholar
Sana, S.S., Sarkar, B.K., Chaudhuri, K. and Purohit, D., The effect of stock, price and advertising on demand – An EOQ model. IJMIC 6 (2009) 81–88. Google Scholar
Sarfaraz, A.R., A Deterministic and stochastic model for production lot size as a function of storage cost. Int. J. Modern Engrg. 9 (2009) 67–72. Google Scholar
Singh, S.R., Kumar, S. and Gaur, N.K., Inventory model with power demand, partial back logging, and incremental holding cost under inflation. Int. Trans. Appl. Sci. 1 (2009) 93–102. Google Scholar
N. Singh, S.R. Singh and B. Vaish, EPQ model for time varying production and demand rate with trade credit. Asia-Pacific Operational Research Societies Conference (APORS 2009), Jaipur, India pp. 6–9.
Teng, J.-T. and Yang, H.-L., Deterministic inventory lot-size models with time-varying demand and cost under generalized holding costs. Inform. Manag. Sci. 18 (2007) 113–125. Google Scholar
Tripathy, C.K., Pradhan, L.M. and Mishra, U., An EPQ model for linear deteriorating item with variable holding cost. Int. J. Comput. Appl. Math. 5 (2010) 209–215. Google Scholar
Urban, T.L., Inventory models with inventory-level-dependent demand: a comprehensive review and unifying theory. Eur. J. Oper. Res. 162 (2005) 792–804. Google Scholar
Urban, T.L., An extension of inventory models with discretely variable holding costs. Int. J. Prod. Econ. 114 (2008) 399–403. Google Scholar
Weiss, H.J., Economic order quantity models with nonlinear holding costs. Eur. J. Oper. Res. 9 (1982) 56–60. Google Scholar
Yang, H.-L., Teng, J.-T. and Chern, M.-S., An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages. Int. J. Prod. Econ. 123 (2010) 8–19. Google Scholar