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
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\{Period~demand \le \; {Inventory~on~hand~at~the~beginning~of~a~period}\} . In order to determine the safety stock that guarantees a target \alpha_p service level, the
stationary probability distribution of the inventory on hand must be known. This version of α is also called the
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
stockouts (cycle \alpha_c service level): \alpha_c = Prob\{Demand~during~replenishment~lead~time \le Inventory~on~hand~at~the~beginning~of~the~lead~time\} 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.
β service level (type 2) The β service level is a
quantity-oriented performance measure describing the proportion of total demand within a reference period which is delivered without delay from stock on hand: \beta = 1- \frac{ Expected~backorders~per~time~period} {Expected~period~demand} 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. Because, contrary to the variations of the \alpha service level, the \beta 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 \alpha \le \beta 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: \gamma= 1- \frac{ Expected~backorder~level~per~time~period} {Expected~period~demand} The γ service level is rarely used in industrial practice. ==Service rate==