Optimal inventory replenishment model with time-varying demand, Weibull distribution deterioration and shortages under a shortage followed by inventory policy

We consider here the inventory replenishment problem over a finite time horizon for a deteriorating item with general time-varying demand, Weibull distribution deterioration, equal replenishment cycles and shortages in every cycle. This paper provides the proof of uniqueness of the optimal replenishment schedule and checks the second-order optimality condition for the proposed model. Numerical examples and sensitivity analysis are also provided to illustrate the solution procedure.