Service level in model of inventory location with stochastic demand

Abstract

In this paper we consider the influence of the safety factor on the decision of the inventory location. This decision is done based on the model which centralizes or decentralizes the safety stock. In this model we have to choose between the location of the inventory in the regional warehouses or the location in the central warehouse. The decision is made due to the minimizing the holding costs and the supply costs of the safety stock from the central warehouse to the customer. The main assumption is that the customers have the stochastic demands on the inventory items. Moreover, the customers’ demands have the known distribution with the known parameters. The complex analysis of the influences of possible probabilistic demands' distributions on the safety factors is conducted. The numerical computations for the safety factors used in the facility location model are also presented. In numerical examples we take into considerations the demands’ distributions the most often used in practice like the normal, the Poisson, the Gamma and the exponential distribution. Some graphs for the safety factors of these distributions are also drawn. Moreover for the mentioned demands’ distributions the model of the safety stock location depends on the specific factors. Among other things these factors are the mean and the variance of the demand, the number of the regional warehouses, the assumed service level, and some cost factors like the holding costs and the transportation costs. Some graphs which illustrated the dependence of the model elements on some listed before parameters are presented and their influence on the location decision is studied also.