Bassem Hossam Roushdy
Inventory Control for a Joint Replenishment Problem with Stochastic Demand
—Most papers model Joint Replenishment Problem (JRP) as a (݇ܶ, ܵ) where ݇ܶ is a multiple value for a common review period ܶ,and ܵ is a predefined order up to level. In general the (ܶ, ܵ) policy is characterized by a long out of control period which requires a large amount of safety stock compared to the ሺܴ, ܳሻ policy. In this paper a probabilistic model is built where an item, call it itemሺ݅ሻ, with the shortest order time between interval ሺܶሻ is modeled under (ܴ, ܳ) policy and its inventory is continuously reviewed, while the rest of items (j) are periodically reviewed at a definite time corresponding to item ሺ݅ሻ. An order up to level policy for items (j) is applied in synchronization with itemሺ݅ሻ. For the sake of inventory out of control period reduction for items ሺ݆ሻ, an inventory review is done on the inventory position for items ሺ݆ሻ one period before replenishment, at ሺ݇௝ െ 1ሻ period. A lower control value ሺݏ௝ ሻ is determined using an iterative method, if the inventory position is above this value then an order is done at the ݇௝ period, otherwise it is made at ሺ݇௝ െ 1ሻ period. Another iterative method is used to find the optimum order up to level ܵ௝ for this policy.