# Performance Indicators, Service Levels, Waiting time

In the literature several variations of inventory-related performance measures are discussed which may differ not only with respect to their scope and to the number of considered products but also with respect to the time interval they are related to. These performance measures are the "Key Performance Indicators" (KPI) of an inventory node which must be regularly monitored. If the controlling of the performance of an inventory node is neglected, the decision maker will not be able to optimize the processes within a supply chain.

In the sequel we first discuss several performance measures related to a single product. After that we consider the situation when the performance of an inventory node is an aggregate construct related to the simultaneous delivery of a group of products. Primarily because of their complexity, product group-specific performance measures are rarely discussed in the literature. Nevertheless, criteria of this kind are relevant in assemble-to-order production systems when upon arrival of a customer order the product is assembled from several components. In addition, in the case when a customer order includes several lines defining demands for different products, the customer may require the simultaneous delivery of all products within a single delivery event. In these situations performance measures based on isolated products are over-optimistic.

### $\alpha$ service level

The $\alpha$ service level is an event-oriented performance criterion. It measures the probability that all customer orders arriving within a given time interval will be completely delivered from stock on hand, i.e. without delay.

Two versions are discussed in the literature differing with respect to the time interval within which the customers arrive. With reference to a demand period, $\alpha$ denotes the probability that an arbitrarily arriving customer order will be completely served from stock on hand, i.e. without an inventory-related waiting time (period $\alpha_p$ service level):

### Performance measures related to a group of products

Further information are available in the book.

### Customer-class specific performance measures

Further information are available in the book.

### The effect of the inventory policy on the transportation system

Further information are available in the book.

### The Effect of Inventory Performance on Subsequent Logistical Processes

Compute the optimum transportation capacity for a given inventory policy. Further information are available in the book.

### The Key Performance indicator "Inventory Run-Out time"

In industrial practice, the performance of a company's logistics system is often measured with the indicator "inventory run-out-time". This is also a popular measure used by financial analysts. The run-out-time is equal to the average inventory on hand divided by the average demand per period. This criterion suggests that a company with a long run-out-time performs poorer than a company with a short run-out-time. In a benchmark study, a company with a short run-out-time would thus be evaluated as superior.

For the analysis of the logistical performance, the number of average period demands is a misleading criterion. In order to improve performance by reducing the holding costs, it is necessary to look at the causes of inventory. In a hierarchical planning system, inventory may be built up as a consequence of decisions made on several planning levels.