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{{Unreferenced|date=February 2014}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
'''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.


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]].


==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. Under 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 metric|performance measures]]. The target values of these measures are set by the decision maker.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


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.
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


===α service level (type 1)===
'''source'''
The α service level is an '''event-oriented''' performance criterion. It measures the [[probability]] that
:<math forcemathmode="source">E=mc^2</math> -->
''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.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
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):


<math>
==Demos==
\alpha_p = Prob\{Period~demand
                      \le \; {Inventory~on~hand~at~the~beginning~of~a~period}\}


</math>.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


In order to determine the safety stock that guarantees a target <math>\alpha_p</math> service
level, the [[steady state|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 [[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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** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


<math>
==Test pages ==
\alpha_c = Prob\{Demand~during~replenishment~lead~time
\le  Inventory~on~hand~at~the~beginning~of~the~lead~time\}
</math>


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.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
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===β service level (type 2)===
*[[Inputtypes|Inputtypes (private Wikis only)]]
The β service level is a '''quantity-oriented''' performance measure describing the
*[[Url2Image|Url2Image (private Wikis only)]]
proportion of total demand within a reference period which is delivered without delay from stock on hand:
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
<math>
\beta = 1- \frac{ Expected~backorders~per~time~period}
{Expected~period~demand}
</math>
 
This is equal to the probability that an arbitrary demand unit is delivered without delay. This approach usually involves calculating a loss integral, whose values are tabulated for the normal distribution.<ref>Donald Bowersox, David Closs, M. Bixby Cooper, Supply Chain Logistics Management, McGraw-Hill 2012</ref>
 
Because, contrary to the variations of the <math>\alpha</math> service level, the
<math>\beta</math> service level does not only reflect the [[stockout]] ''event'' but also the
''amount backordered'', it is widely used in industrial practice.
 
Also, by the definitions, comparing service levels we have <math>\alpha \le \beta</math> whenever the probability of zero demand equals 0.
 
===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:
 
<math>
\gamma= 1- \frac{ Expected~backorder~level~per~time~period}
{Expected~period~demand}
</math>
 
The γ service level is rarely used in industrial practice.
 
==Service rate==
*In business, service rate is a [[performance metric]] used to measure the [[customer service]] in a [[supply (economics)|supply]] organization. One example of a service rate measures the number of units filled as a percentage of the total ordered and is known as fill rate. If customer orders total 1000 units, and you can only meet 900 units of that order, your fill rate is 90%.
 
*In statistics, notably in queuing theory, service rate denotes the rate at which customers are being served in a system. It is the reciprocal of the service time. For example, a supermarket cash desk with an average service time of 30 seconds per customer would have an average service rate of 2 per minute. In statistics the Greek letter <math>\mu</math> is used for the service rate.
 
==See also==
* [[Inventory]]
* [[Service level agreement]]
* [[Stockout]]
 
==References==
{{Reflist}}
 
==Further reading==
* Tempelmeier, Horst, ''Inventory Management in Supply Networks'', Norderstedt (Books on Demand) 2006, ISBN 3-8334-5373-7
 
{{DEFAULTSORT:Service Level}}
[[Category:Distribution, retailing, and wholesaling]]
[[Category:Supply chain management]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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