An inventory model with Weibull demand rate, finite rate of production and shortages

We develop here an inventory model with time-dependent two-parameter Weibull demand rate, allowing shortages in the inventory. The shortages are completely backlogged. The production rate is assumed to be finite and proportional to the demand rate. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. Sensitivity of the optimal solution with respect to changes in the values of the system parameters is also studied. Special features of time-dependent Weibull demand rate are discussed.