Joint Replenishment Problem Under Demand Uncertainty

The strategy of inventory joint replenishment for a variety of items refers to jointly ordering various items from the same supplier to replenish inventory with the privileges of reducing the annual ordering times, obtaining discounts, saving expenses of inventory control as well as lowering the cost of items. When a group of goods are supplied by the same supplier (or from the same supply place), or when a group of goods are transported by vehicles, we are confronted with the problem of how to reasonably coordinate and arrange orders to minimize the cost. In the former researches, the issue of joint replenishment of various items has been conducted without considering demand rate or other replenishing problems. However in practice, there are interactive elements among various items, such as funds, inventory, transporting capacity, deterioration rate. Thus, when the demand rate is uncertain, it is necessary to establish a joint s replenishment model.First of all, the study on the joint replenishment model of stochastic demand with the shortage loss has been based on periodic replenishment strategy analyzing the loss model caused by out of stock with different rate of deterioration and taking minimum of ordering costs, inventory holding costs and the loss of out of stock as the objective function to establish the mathematical model. Meanwhile, the genetic algorithm has been used to calculate results and validated by means of numerical experiments.Secondly, the author has researched the issues of joint replenishment of fuzzy demand with a certain level of service. Then, guided by fuzzy programming ideas, the author has established a joint replenishment model of fuzzy demand, determined the total cost function, solved the result of this model by using genetic algorithms and provided us with encoding and decoding strategies, as well as genetic operators of selection, crossover and mutation. In the end, the results have been analyzed and validated through instance data. Finally, the algorithm and model have been applied in the inventory management system to verify the feasibility of the algorithm. From that, the author has obtained the best ordering cycle and the best ordering costs, which clearly demonstrates the excellent application of algorithm in this system.