Models For Multi-Echelon Distribution Inventory System With Random Leadtime And Stochastic Demand

The inventory cost is a primary component of the supply chain cost, and the method for multi-echelon inventory optimization and control must be adopted for the sake of the entire supply chain optimization and control. How to effectively control the multi-echelon inventory system is one of the key factors to improve the operational efficiency of supply chains. At present, papers on multi-echelon inventory systems have solved some problems, but they still have limitations. Firstly, they assumed that leadtimes are constants. In practice, as the unknowable incidents exist in production, transportation and distribution processes, leadtimes usually are uncertain. Secondly, the existing inventory approximation models adopt normal or Poisson distribution to approximate the leadtime demand of retailers. However, in some of cases the normal approximations will give a relatively high probability mass for negative values. The mean and variance of Poisson distribution is the same, so it is improper that the leadtime demand is approximated by Poisson distribution and it can not represent the alteration of the leadtime demand. Thirdly, most studies concentrate on two-echelon supply chains, but a supply chain generally is a there-echelon or over there-echelon system. This paper at first discusses a two-echelon distribution inventory system with a central warehouse and multiple retailers, where the retailers face stochastic compound Poisson demand process and random leadtimes. The system is controlled by continuous review installation stock (R, Q) policies. This paper presents an improved approximated method that the leadtime demand of warehouse is approximated by the normal distribution, and the leadtimes demand of retailers are approximated based on negative binomial distribution. An average cost per unit time model for the two-echelon inventory distribution system with stochastic demand and random leadtimes is developed. The objective is to minimize the average cost of two-echelon distribution inventory. To get the optimal solution, a search algorithm is given. The model is illustrated by numerical examples and sensitivity analyses are conducted. The results show that when the parameters of the gamma distribution are changed, with the increase of the mean value and variance of retailers'leadtimes, the optimal order point and average total cost per unit time will also increase. It indicates that random leadtimes greatly affect the system performance and approximated optimal order strategy. In addition, this paper extends above-mentioned two-echelon inventory model to the multi-echelon inventory model, and it sketches how this can be done with the illustration of three-echelon inventory system.