Joint Replenishment Problem Under Fuzzy Environment

The Joint Replenishment Problem 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 problem has been conducted considering certainty demand rate or certainty costs problems. However in practice, many factors are nondeterministic from the uncertainty environment of Joint Replenishment Problem, thus these uncertain factors should be considered in Joint Replenishment Problem.Firstly, the Joint Replenishment Problem with fuzzy demand was studied. Use the trapeziform fuzzy number to represent the fuzzy demand and fuzzy programming model was constructed. A Genetic Algorithm (GA) was presented to solve the JRP model with fuzzy programming model and discussed the genetic operations. Numerical examples and program flow chart were given to illustrate the theory of the problem.Secondly, the Joint Replenishment Problem with fuzzy major ordering cost and fuzzy resource constraint was studied. The fuzzy variable is represented with triangular fuzzy number. Fuzzy programming model was constructed with fuzzy expected definition and possibility theory. Two methods which Combing GA and fuzzy simulation and converting the fuzzy model into the crisp model are used to solve the fuzzy programming model. Finally a numerical example is provided.Finally, the algorithm and model have been applied in the inventory management system to verify the feasibility of the algorithm.