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| {{Merge|service rate|date=September 2010}}
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| '''Service level''' measures the performance of a system. Certain goals are defined and the service level gives the percentage to which those goals should be achieved. [[Fill rate]] is different from service level.
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| Examples of service level:
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| * Percentage of calls answered in a [[call center]].
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| * Percentage of customers waiting less than a given fixed time.
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| * Percentage of customers that do not experience a [[stockout]].
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| ==Service level==
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| Service level is used in [[supply chain management]] and in [[inventory management]] to measure the performance of inventory replenishment policies.
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| 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.
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| In an inventory [[operations research|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 policy
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| under consideration, from the optimal solution of such a model also the optimal size of [[backorder]]s can be derived.
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| 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 metric|performance measures]]. The target values of these measures are set by the decision maker.
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| Several definitions of service levels are used in the literature as well as in practice. These 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 metric|performance measure]]s are the ''[[Performance indicator|Key Performance Indicators]]'' (KPI) of an inventory node which must be regularly monitored. If the [[Control (management)|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.
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| ==α service level (type 1)==
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| The α service level is an '''event-oriented''' performance criterion. It measures the [[probability]] that
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| ''all'' customer orders arriving within a given time interval will be completely delivered from stock on hand, i.e. without delay.
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| Two versions are discussed in the literature differing with respect to the time interval within which the customers arrive.
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| 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 <math>\alpha_p</math> service level):
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| <math>
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| \alpha_p = Prob\{Period~demand
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| \le \; {Inventory~on~hand~at~the~beginning~of~a~period}\}
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| </math>.
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| In order to determine the safety stock that guarantees a target <math>\alpha_p</math> service
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| level, the [[steady state|stationary]] probability distribution of the inventory on hand must be known. This version of α is also called ''ready rate''.
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| If an ''order cycle'' is considered as the standard period of reference, then α denotes the probability of no [[stockout]] within an order cycle which is equal to the proportion of all order cycles with no [[stockout]]s (cycle <math>\alpha_c</math> service level):
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| <math>
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| \alpha_c = Prob\{Demand~during~replenishment~lead~time
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| \le Inventory~on~hand~at~the~beginning~of~the~lead~time\}
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| </math>
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| 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 cannot stock out prior to reordering.
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| ==β service level (type 2)==
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| The β service level is a '''quantity-oriented''' performance measure describing the
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| proportion of total demand within a reference period which is delivered without delay from stock on hand:
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| <math>
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| \beta = 1- \frac{ Expected~backorders~per~time~period}
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| {Expected~period~demand}
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| </math>
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| This is equal to the probability that an arbitrary demand unit is delivered
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| without delay.
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| Because, contrary to the variations of the <math>\alpha</math> service level, the
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| <math>\beta</math> service level does not only reflect the [[stockout]] ''event'' but also the
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| ''amount backordered'', it is widely used in industrial practice.
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| Also, by the definitions, comparing service levels we always have <math>\alpha \le \beta</math> .
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| ==γ service level==
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| 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:
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| <math>
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| \gamma= 1- \frac{ Expected~backorder~level~per~time~period}
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| {Expected~period~demand}
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| </math>
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| The γ service level is rarely used in industrial practice.
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| ==See also==
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| * [[Inventory]]
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| * [[Service level agreement]]
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| * [[Stockout]]
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| ==Further reading==
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| * Tempelmeier, Horst, ''Inventory Management in Supply Networks'', Norderstedt (Books on Demand) 2006, ISBN 3-8334-5373-7
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| {{DEFAULTSORT:Service Level}}
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| [[Category:Distribution, retailing, and wholesaling]]
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| [[Category:Supply chain management]]
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