Constrained probabilistic multi-source inventory model by decreasing holding cost with Weibull and Lindley-Weibull distributions

Abstract

The main goal of this work is to minimize the expected total cost for a multi-item, multi-source (MIMS) probabilistic continuous review inventory model with constraint on the expected decreasing holding cost utilizing the Lagrange multiplier technique. The demand is a continuous random variable. The optimal order quantity and the optimal reorder point for the i^th item and s^th source which achieve the objective are obtained when lead time demand follows Weibull and Lindley-Weibull distributions. Also, an application is analyzed and reach the goal of minimizing the expected total cost.