publication . Article . 2014

Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate

Tsoularis, A;
Open Access English
  • Published: 01 Jan 2014
  • Country: United Kingdom
Abstract
It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal contro...
Related Organizations
Download from
36 references, page 1 of 3

Alfares, H.K. (2007) 'Inventory model with stock-dependent demand rate and variable holding cost', International Journal of Production Economics, Vol. 108, No. 1-2, pp.259-265. [OpenAIRE]

Aoki, M. and Yoshikawa, H. (2002) 'Demand saturation-creation and economic growth', Journal of Economic Behavior and Organization, Vol. 48, No. 2, pp.127-154.

Baker, R.C. and Urban, T.L. (1988) 'A deterministic inventory system with an inventory-level-dependent demand rate', The Journal of the Operational Research Society, Vol. 39, No. 9, pp.823-831.

Balakrishnan, A., Pangburn, M.S. and Stavrulaki, E. (2004) 'Stack them high, let'em fly”: lotsizing policies when inventories stimulate demand', Management Science, Vol. 50, No. 5, pp.630-644. [OpenAIRE]

Bensoussan, A., Sethi, S.P., Vickson, R. and Derszko, N. (1984) 'Stochastic production planning with production constraints', SIAM Journal of Control and Optimization, Vol. 22, No. 6, pp.920-935. [OpenAIRE]

Berling, P. and Martinez-de-Albéniz, V. (2011) 'Optimal inventory policies when purchase price and demand are stochastic', Operations Research, Vol. 59, No. 1, pp.109-124.

Berman, O. and Perry, D. (2006) 'An EOQ model with state-dependent demand rate', European Journal of Operational Research, Vol. 171, No. 1, pp.255-272.

Chen, Y., Lu, Y. and Xu, M. (2012) 'Optimal inventory control policy for periodic-review inventory systems with inventory-level-dependent demand', Naval Research Logistics, Vol.59, No. 6, pp.430-440.

Datta, T.K. and Paul, K. (2001) 'An inventory system with stock-dependent, price-sensitive demand rate', Production Planning and Control, Vol. 12, No. 1, pp.13-20.

Dohi, T., Kaio, N. and Osaki, S. (1995) 'Optimal production planning under diffusion demand pattern', Mathematical and Computer Modelling, Vol. 21, No. 11, pp.35-46. [OpenAIRE]

Feichtinger, G. and Hartl, R. (1985) 'Optimal pricing and production in an inventory model', European Journal of Operational Research, Vol. 19, No. 1, pp.45-56.

Fleming, W.H and Rishel, R.W. (1975) Deterministic and Stochastic Optimal Control, Springer Verlag, New York. [OpenAIRE]

Fleming, W.H and Souganidis, P.E. (1986) 'Asymptotic series and the method of vanishing viscosity', Indiana University Mathematics Journal, Vol. 35, No. 2, pp.425-447.

Fleming, W.H., Sethi, S.P. and Soner, H.M. (1987) 'An optimal stochastic production planning problem with randomly fluctuating demand', SIAM Journal of Control and Optimization, Vol. 25, No. 6, pp.1494-1502.

Gallego, G. and Van Ryzin, G. (1994) 'Optimal dynamic pricing of inventories with stochastic demand over finite horizons', Management Science, Vol. 40, No. 8, pp.999-1020.

36 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue