Int. J. of Industrial and Systems Engineering   »   2015 Vol.21, No.1



Title: Inventory model with stock dependent demand and different holding cost functions


Authors: R.P. Tripathi; Dinesh Singh


Department of Mathematics, Graphic Era University, 566/6, Bell Road, Clement Town, Dehradun (Uttarakhand), 248002, India
Department of Mathematics, S.G.R.R. PG College, Dehradun (Uttarakhand), 248001, India


Abstract: This study develops inventory models in which demand rate is stock level dependent and three different holding cost functions: 1) constant holding cost; 2) exponential time dependent; 3) stock level dependent. Mathematical models have been developed for these three different situations to determine optimal order quantities, cycle time and optimal total inventory cost. Truncated Taylor's series expansion is used for exponential terms for finding closed form numerical solutions. The results are illustrated with the help of numerical examples. The sensitivity analysis of the optimal solution with respect to the variation of the parameters of the model is also discussed.


Keywords: inventory modelling; stock dependent demand; holding cost functions; total inventory costs; mathematical modelling; order quantities; cycle time; optimisation.


DOI: 10.1504/IJISE.2015.070875


Int. J. of Industrial and Systems Engineering, 2015 Vol.21, No.1, pp.68 - 82


Available online: 21 Jul 2015



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