# Service level

Service level measures the performance of a system. Certain goals are defined and the service level gives the percentage to which they should be achieved.

Examples
* Percentage of calls answered in a call center.
* Percentage of customers waiting less than a given fixed time.
* Percentage of customers that do not experience a stock out.

Service Level (Inventory Management)

Service level is used in supply chain management and in inventory management to measure the performance of inventory systems.

Under stochastic conditions it is unavoidable that in some periods the inventory on hand is not sufficient to deliver the complete demand and, as a consequence, that part of the demand is filled only after an inventory-related waiting time. In an inventory optimization model, the amount of late deliveries can be influenced through the introduction of penalty costs (backorder costs) into the objective function. In addition to the optimal parameters of the inventory policyunder consideration, from the optimal solution of such a model also the optimal size of backorders can be derived.Unfortunately, this optimization approach requires that the planner know the optimal value of the backorder costs. As these costs are difficult to quantify in practice, the logistical performance of an inventory node in a supply network is measured with the help of technical performance measures. The target values of these measures are set by the decision maker.

Several definitions of service levels are used in the literature as well as in practice. These may differ not only withrespect 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.

α Service Level (Type 1)

The α 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", α 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):

$alpha_p = Prob\left\{Period~demand le ; \left\{Inventory~on~hand~at~the~beginning~of~a~period\right\}\right\}$

.

In order to determine the safety stock that guarantees a target $alpha_p$ servicelevel, the stationary probability distribution of the inventory on hand must be known. This version of α is also called "ready rate".

If an "order cycle" is considered as the standard period of reference, then α denotes the probability of no stock-out within an order cycle which is equal to the proportion of all order cycles with no stock-outs (cycle $alpha_c$ service level):

$alpha_c = Prob\left\{Demand~during~replenishment~lead~timele Inventory~on~hand~at~the~beginning~of~the~lead~time\right\}$

This second definition, which is often used in operations management textbooks, is based on the idea of not running out of stock during the time between re-ordering and order arrival (the leadtime). That is, the probability of demand during that leadtime being less than or equal to the amount of stock you had left when you ordered. It assumes your reorder point is positive, that orders are in unit increments and inventory is monitored continuously so you can not stock out prior to reordering.

β Service Level (Type 2, also known as "fill rate")

The β service level (fill rate) is a quantity-oriented performance measure describing the
proportion of total demand within a reference period which is delivered withoutdelay from stock on hand:

This is equal to the probability that an arbitrary demand unit is deliveredwithout delay.

Because, contrary to the variations of the $alpha$ service level, the service level does not only reflect the stock-out "event" but also the"amount backordered", it is widely used in industrial practice.

Also, by the definitions, comparing service levels we always have .

γ Service Level

The γ service level, a time- and quantity-related performance criterion, serves to reflect not only the amount of backorders but also the waiting times of the demands backordered. The γ service level is defined as follows:

$gamma= 1- frac\left\{ Expected~backorder~level~per~time~period\right\}\left\{Expected~period~demand\right\}$

The γ service level is rarely used in industrial practice.

Further performance indicators

* Duration of a stockout situation

* Customer order waiting time

* Inventory
* Service level agreement

* Tempelmeier, Horst, "Inventory Management in Supply Networks", Norderstedt (Books on Demand) 2006, ISBN 3-8334-5373-7

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