Optimal inventory model under stock and time dependent demand for time varying deterioration rate with shortages

Effect of deterioration plays a vital role in present environment of market. In this paper, a deterministic inventory model for deteriorating items having stock and time dependent demand under the effect of deterioration has been studied. A two parameter Weibull distribution has been used to represent the deterioration rate. The present model has been solved analytically to minimize the total cost of the system. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions which could minimize the retailer’s total cost per unit time has been discussed. Some numerical examples have been carried out to illustrate the developed model.