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

Hesham K. Alfares

RAIRO - Operations Research - Recherche Opérationnelle (2014)

  • Volume: 48, Issue: 1, page 135-150
  • ISSN: 0399-0559

Abstract

top
In general, traditional production-inventory systems are based on a number of simplifying – but somewhat unrealistic – assumptions, including constant demand rate, constant holding cost, and instantaneous order replenishment. These assumptions have been individually challenged in numerous variations of production-inventory models. Finite production rate models, such as economic production quantity (EPQ) systems consider gradual order replenishment. Stock-dependent demand models assume the demand rate to be an elastic function of the inventory level. Variable holding cost models assume the holding cost per unit per time period to be a function of the time spent in storage. In this paper, the three simplifying assumptions are simultaneously relaxed in a new production-inventory system with a finite production rate, stock-level dependent demand rate, and variable holding cost. Mathematical models and optimum solution procedures, including nonlinear programming, are presented for two functional forms of holding cost variability. The main contribution of this paper is the formulation and solution of a new production-inventory model that more closely represents real-world situations. The realistic assumptions and efficient solution algorithms should make the model practical and useful for industrial applications.

How to cite

top

Alfares, Hesham K.. "Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost." RAIRO - Operations Research - Recherche Opérationnelle 48.1 (2014): 135-150. <http://eudml.org/doc/275091>.

@article{Alfares2014,
abstract = {In general, traditional production-inventory systems are based on a number of simplifying – but somewhat unrealistic – assumptions, including constant demand rate, constant holding cost, and instantaneous order replenishment. These assumptions have been individually challenged in numerous variations of production-inventory models. Finite production rate models, such as economic production quantity (EPQ) systems consider gradual order replenishment. Stock-dependent demand models assume the demand rate to be an elastic function of the inventory level. Variable holding cost models assume the holding cost per unit per time period to be a function of the time spent in storage. In this paper, the three simplifying assumptions are simultaneously relaxed in a new production-inventory system with a finite production rate, stock-level dependent demand rate, and variable holding cost. Mathematical models and optimum solution procedures, including nonlinear programming, are presented for two functional forms of holding cost variability. The main contribution of this paper is the formulation and solution of a new production-inventory model that more closely represents real-world situations. The realistic assumptions and efficient solution algorithms should make the model practical and useful for industrial applications.},
author = {Alfares, Hesham K.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {production-inventory system; stock-dependent demand; variable holding cost; nonlinear programming},
language = {eng},
number = {1},
pages = {135-150},
publisher = {EDP-Sciences},
title = {Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost},
url = {http://eudml.org/doc/275091},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Alfares, Hesham K.
TI - Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 1
SP - 135
EP - 150
AB - In general, traditional production-inventory systems are based on a number of simplifying – but somewhat unrealistic – assumptions, including constant demand rate, constant holding cost, and instantaneous order replenishment. These assumptions have been individually challenged in numerous variations of production-inventory models. Finite production rate models, such as economic production quantity (EPQ) systems consider gradual order replenishment. Stock-dependent demand models assume the demand rate to be an elastic function of the inventory level. Variable holding cost models assume the holding cost per unit per time period to be a function of the time spent in storage. In this paper, the three simplifying assumptions are simultaneously relaxed in a new production-inventory system with a finite production rate, stock-level dependent demand rate, and variable holding cost. Mathematical models and optimum solution procedures, including nonlinear programming, are presented for two functional forms of holding cost variability. The main contribution of this paper is the formulation and solution of a new production-inventory model that more closely represents real-world situations. The realistic assumptions and efficient solution algorithms should make the model practical and useful for industrial applications.
LA - eng
KW - production-inventory system; stock-dependent demand; variable holding cost; nonlinear programming
UR - http://eudml.org/doc/275091
ER -

References

top
  1. [1] H.K. Alfares, Inventory model with stock-level dependent demand rate and variable holding cost. Int. J. Prod. Econ.108 (2007) 259–265. 
  2. [2] R.C. Baker and T.L. Urban, A deterministic inventory system with an inventory level dependent rate. J. Oper. Res. Soc. 39 (1988a) 823–831. Zbl0659.90040
  3. [3] R.C. Baker and T.L. Urban, Single-period inventory dependent demand models. Omega-The Int. J. Manag. Sci. 16 (1988b) 605–607. 
  4. [4] M. Ferguson, V. Jayaraman and G.V. Souza, Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables. Eur. J. Oper. Res.180 (2007) 485–490. Zbl1106.90009
  5. [5] M. Gayen and A.K. Pal, A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost. Oper. Res.9 (2009) 153–165. Zbl1172.90307
  6. [6] B.C. Giri and K.S. Chaudhuri, Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur. J. Oper. Res.105 (1998) 467–474. Zbl0955.90003MR1660209
  7. [7] B.C. Giri, A. Goswami and K.S. Chaudhuri, An EOQ model for deteriorating items with time-varying demand and costs. J. Oper. Res. Soc.47 (1996) 1398–1405. Zbl0871.90026
  8. [8] M. Goh, Some results for inventory models having inventory level dependent demand rate. Int. J. Prod. Econ.27 (1992) 155–160. 
  9. [9] M. Goh, EOQ models with general demand and holding cost functions. Eur. J. Oper. Res.73 (1994) 50–54. Zbl0809.90039
  10. [10] R. Gupta and P. Vrat, Inventory model for stock-dependent consumption rate. Opsearch23 (1986) 19–24. Zbl0593.90022MR838017
  11. [11] M.A. Koschat, Store inventory can affect demand: empirical evidence from magazine retailing. J. Retailing84 (2008) 165–179. 
  12. [12] J. Min and Y.-W. Zhou, 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. Zbl1279.90012MR2489975
  13. [13] G.C. Mahata and A. Goswami, Fuzzy EOQ models for deteriorating items with stock dependent demand & non-linear holding costs. Int. J. Appl. Math. Comput. Sci.5 (2009) 94–98. MR2531997
  14. [14] A.P. Muhlemann and N.P. Valtis-Spanopoulos, Variable holding cost rate model. Eur. J. Oper. Res.4 (1980) 132–135. Zbl0421.90026
  15. [15] A. Roy, An inventory model for deteriorating items with price dependent demand and time-varying holding cost. Adv. Model. Optim.10 (2008) 25–37. Zbl1157.90328MR2369401
  16. [16] S.S. Sana, B.K. Sarkar, K. Chaudhuri and D. Purohit, The effect of stock, price and advertising on demand – An EOQ model. IJMIC6 (2009) 81–88. 
  17. [17] A.R. Sarfaraz, A Deterministic and stochastic model for production lot size as a function of storage cost. Int. J. Modern Engrg.9 (2009) 67–72. 
  18. [18] S.R. Singh, S. Kumar and N.K. Gaur, Inventory model with power demand, partial back logging, and incremental holding cost under inflation. Int. Trans. Appl. Sci.1 (2009) 93–102. Zbl1220.90028
  19. [19] 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. 
  20. [20] J.-T. Teng and H.-L. Yang, Deterministic inventory lot-size models with time-varying demand and cost under generalized holding costs. Inform. Manag. Sci.18 (2007) 113–125. Zbl1171.90330MR2346726
  21. [21] C.K. Tripathy, L.M. Pradhan and U. Mishra, An EPQ model for linear deteriorating item with variable holding cost. Int. J. Comput. Appl. Math.5 (2010) 209–215. MR2658412
  22. [22] T.L. Urban, Inventory models with inventory-level-dependent demand: a comprehensive review and unifying theory. Eur. J. Oper. Res.162 (2005) 792–804. Zbl1067.90009
  23. [23] T.L. Urban, An extension of inventory models with discretely variable holding costs. Int. J. Prod. Econ.114 (2008) 399–403. 
  24. [24] H.J. Weiss, Economic order quantity models with nonlinear holding costs. Eur. J. Oper. Res.9 (1982) 56–60. Zbl0471.90041
  25. [25] H.-L. Yang, J.-T. Teng and M.-S. Chern, 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. Zbl1101.90006

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.