Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 1, pp. 135-150.

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.

DOI : 10.1051/ro/2013058
Classification : 90B05, 90B30, 90C30
Mots-clés : production-inventory system, stock-dependent demand, variable holding cost, nonlinear programming 
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Alfares, Hesham K. Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 1, pp. 135-150. doi : 10.1051/ro/2013058. http://archive.numdam.org/articles/10.1051/ro/2013058/

[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] 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. | Zbl

[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] 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. | Zbl

[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. | Zbl

[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. | MR | Zbl

[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. | Zbl

[8] M. Goh, Some results for inventory models having inventory level dependent demand rate. Int. J. Prod. Econ. 27 (1992) 155-160.

[9] M. Goh, EOQ models with general demand and holding cost functions. Eur. J. Oper. Res. 73 (1994) 50-54. | Zbl

[10] R. Gupta and P. Vrat, Inventory model for stock-dependent consumption rate. Opsearch 23 (1986) 19-24. | MR | Zbl

[11] M.A. Koschat, Store inventory can affect demand: empirical evidence from magazine retailing. J. Retailing 84 (2008) 165-179.

[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. | MR | Zbl

[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. | MR

[14] A.P. Muhlemann and N.P. Valtis-Spanopoulos, Variable holding cost rate model. Eur. J. Oper. Res. 4 (1980) 132-135. | Zbl

[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. | MR | Zbl

[16] S.S. Sana, B.K. Sarkar, K. Chaudhuri and D. Purohit, The effect of stock, price and advertising on demand - An EOQ model. IJMIC 6 (2009) 81-88.

[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] 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. | Zbl

[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] 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. | MR | Zbl

[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. | MR

[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. | Zbl

[23] T.L. Urban, An extension of inventory models with discretely variable holding costs. Int. J. Prod. Econ. 114 (2008) 399-403.

[24] H.J. Weiss, Economic order quantity models with nonlinear holding costs. Eur. J. Oper. Res. 9 (1982) 56-60. | Zbl

[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. | Zbl

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