In this research work we propose a
mathematical model of an inventory system with time dependent three-parameter
Weibull deterioration and price-dependent
demand rate. The model incorporates shortages and deteriorating items are
considered in which inventory is depleted not only by demand but also by decay,
such as, direct spoilage as in fruits, vegetables and food products, or deterioration
as in obsolete electronic components. Furthermore, the rate of deterioration is
taken to be time-proportional, and a power law form of the price dependence of
demand is considered. This price-dependence of the demand function is
nonlinear, and is such that when price of a commodity increases, demand
decreases and when price of a commodity decreases, demand increases. The
objective of the model is to minimize
the total inventory costs. From the numerical example presented to
illustrate the solution procedure of the model, we obtain meaningful results.
We then proceed to perform sensitivity analysis of our model. The sensitivity
analysis illustrates the extent to which the optimal solution of the model is
affected by slight changes or errors in its input parameter values.
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