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The term "service level" is used in supply-chain management and in inventory management to measure the performance of inventory replenishment policies. [1] Under consideration, from the optimal solution of such a model also the optimal size of back orders can be derived.
A sequential single-echelon approach forecasts demand and determines required inventory for each echelon separately. Multi-echelon inventory optimization determines the correct levels of inventory across the network based on demand variability at the various nodes and the performance (lead time, delays, service level) at the higher echelons. [17]
Lead time is the delay between the time the reorder point (inventory level which initiates an order [8]) is reached and renewed availability. Service level is the desired probability of meeting demand during the lead time without a stockout. If the service level is increased, the required safety stock increases, as well.
In a base-stock system inventory position is given by on-hand inventory-backorders+orders and since inventory never goes negative, inventory position=r+1. Once an order is placed the base stock level is r+1 and if X≤r+1 there won't be a backorder. The probability that an order does not result in back-order is therefore:
The reorder point (ROP), also reorder level (ROL) or "optimal re-order level", [1] is the level of inventory which triggers an action to replenish that particular inventory. It is a minimum amount of an item which a firm holds in stock, such that, when stock falls to this amount, the item must be reordered.
If the inventory level is , each unit of demand above is lost in potential sales. This model is also known as the newsvendor problem or newsboy problem by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be ...
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The (Q,r) model addresses the question of when and how much to order, aiming to minimize total inventory costs, which typically include ordering costs, holding costs, and shortage costs. It specifies that an order of size Q should be placed when the inventory level reaches a reorder point r. The (Q,r) model is widely applied in various ...