Service level
Encyclopedia
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. Fill rate
is different than service level.
Examples
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 policy
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 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 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.
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
service level):
.
In order to determine the safety stock that guarantees a target
service
level, 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 stockout
within an order cycle which is equal to the proportion of all order cycles with no stockout
s (cycle
service level):
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.
proportion of total demand within a reference period which is delivered without delay from stock on hand:
This is equal to the probability that an arbitrary demand unit is delivered
without delay.
Because, contrary to the variations of the
service level, the
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 always have
.
The γ service level is rarely used in industrial practice.
Fill rate
Fillrate or fill rate can refer to:* Fillrate, a measure of graphics performance* Service rate, a logistics measure of ordering performance* Fill rate, a logistics measure of inventory effectiveness at meeting demands...
is different than service level.
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 stockoutStockoutA stockout, or out-of-stock event is an event that causes inventory to be exhausted. Reorder points are often specified in such a way as to reduce the likelihood of stockouts during replenishment, due to the vendor's lead time, which cause interruptions to sales or deliveries.Stockouts are...
.
Service level
Service level is used in supply chain managementSupply chain management
Supply chain management is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers...
and in inventory management to measure the performance of inventory systems.
Under stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
conditions it is unavoidable that in some periods the inventory on hand is not sufficient to deliver the complete demand
Demand
- Economics :*Demand , the desire to own something and the ability to pay for it*Demand curve, a graphic representation of a demand schedule*Demand deposit, the money in checking accounts...
and, as a consequence, that part of the demand is filled only after an inventory-related waiting time.
In an inventory optimization
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
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
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 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 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.
α service level (type 1)
The α service level is an event-oriented performance criterion. It measures the probabilityProbability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
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
service level):.In order to determine the safety stock that guarantees a target
servicelevel, the stationary
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...
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
Stockout
A stockout, or out-of-stock event is an event that causes inventory to be exhausted. Reorder points are often specified in such a way as to reduce the likelihood of stockouts during replenishment, due to the vendor's lead time, which cause interruptions to sales or deliveries.Stockouts are...
within an order cycle which is equal to the proportion of all order cycles with no stockout
Stockout
A stockout, or out-of-stock event is an event that causes inventory to be exhausted. Reorder points are often specified in such a way as to reduce the likelihood of stockouts during replenishment, due to the vendor's lead time, which cause interruptions to sales or deliveries.Stockouts are...
s (cycle
service level):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)
The β service level is a quantity-oriented performance measure describing theproportion of total demand within a reference period which is delivered without delay from stock on hand:
This is equal to the probability that an arbitrary demand unit is delivered
without delay.
Because, contrary to the variations of the
service level, the service level does not only reflect the stockoutStockout
A stockout, or out-of-stock event is an event that causes inventory to be exhausted. Reorder points are often specified in such a way as to reduce the likelihood of stockouts during replenishment, due to the vendor's lead time, which cause interruptions to sales or deliveries.Stockouts are...
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:The γ service level is rarely used in industrial practice.
Further reading
- Tempelmeier, Horst, Inventory Management in Supply Networks, Norderstedt (Books on Demand) 2006, ISBN 3-8334-5373-7