An EOQ deteriorating inventory model with different types of demand and fully backlogged shortages

Abstract

The objective of this paper is to develop a deteriorating EOQ inventory model according to consideration of the price, stock dependent demand and fully backlogged shortages. In this model, it is described that the demand functions are: 1) a linear price with stock dependent; 2) price with negative power of constant; 3) exponential function of the price. The deterioration is considered as an instantaneous, i.e., when the item stock in retailer's house after any time deterioration will start. If there any shortages are allowed then it is fully backlogged. The corresponding inventory problem forms a nonlinear constraint optimisation problem. To optimise the problems, the Taylor series expansion is used and considered up to second order term to find the closed form of cycle length and total cost. To validate our result, a comparative approach between our result and some of other meta-heuristics algorithm is given. Also, a sensitivity analysis is being carried out to study the effect of changes of different inventory parameters while changing one parameter at a time and keeping the others value of parameters unchanged.