Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation

In many inventory systems, the effects of deterioration of physical goods have drawn much attention of various researchers in recent years. The more the deterioration is, the more the order quantity would be. According to such consideration, taking the deterioration rate into account is necessary. Thus, in this paper, I develop the two-warehouse partial backlogging inventory model introduced in Yang (2006) to incorporate three-parameter Weibull deterioration distribution. The objective is to derive the optimal replenishment policy that minimizes the net present value of total relevant cost per unit time. Two alternative models are compared based on the minimum cost approach. The study shows that the optimal solution not only exists but also is unique. Model 2 is still less expensive to operate than Model 1 in the proposed model. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.