Research On Joint Replenishment Problem Under Uncertainty

The Joint Replenishment Problem (JRP) is a process in which coordinating a group of items may be jointly ordered from a single supplier. In the traditional inventory replenishment model researchers always assume some key factors as a known constant, such as the major ordering cost, the minor ordering cost of each item, holding inventory cost per unit and time of each item etc., and then decide which items would be jointly ordered according to requirements. But in reality, some factors may be uncertain, for example, demand may be fluctuated by market volatility, the order lead time may be restrained by transportation conditions. It forms an uncertainty environment of joint replenishment. When a complex joint replenishment inventory system is designed, we should take these uncertain factors into consideration. When the demand or the order lead time of items is uncertain, the joint replenishment has become the joint replenishment problem in uncertain environments.The existence of uncertain factors could make the decision-making system of joint replenishment to contain stochastic parameters. Which policy would be used is the key to establish a joint replenishment problem model, the paper compared the previous models of the joint replenishment problem in uncertain environment with certain environment, and presents an expected value model of the inventory system in stochastic demand environment, which use the (T, S) policy under periodic review, the purpose of this expected value model is to acquire the least total cost. For the inventory system in stochastic demand and the lead time environment, using the same policy, an expanded expected value model is presented. These models are general for handling uncertain factors.In order to seek the solution of uncertain model, the paper discusses the theory of the genetic algorithm and stochastic simulation, and presents a way of handling stochastic parameters of the model, which uses stochastic simulation, lastly designs a hybrid genetic algorithm based on stochastic simulation, and the genetic operation, such as coding, mutation, selection and crossover etc. In addition hybrid iterative algorithm is designed to process the model of the inventory system in stochastic demand and the lead time environment.Finally, simulation data is as example and the nearly optimum solution is calculated by using algorithm, which illustrate the feasibility and validity of this model and algorithm.