Timely order fulfillment is a ubiquitous customer service
criterion in the manufacturing and distribution sectors. This criterion is
commonly measured by the time-window fulfillment rate, which is defined as the
percentage of times that orders are completely fulfilled within a specific time
window. Many companies have set targets for their order fulfillment. For
example, around 1995, Hewlett-Packard targeted a 93% fulfillment rate within 3
days, and IBM PC and Compaq aimed at accomplishing 95% within 5 days (Hausman et
al., 1998).
In the academic
arena,
many operations management textbooks discuss two types of fulfillment or service
levels: fill rate and ready rate (Nahmias, 2001). Fill rate is commonly defined
as the fraction of quantity fulfilled over quantity requested, whereas ready
rate is frequency based, measuring the percentage of times in which the system
can fulfill all demands on time (i.e., instantly/off-shelf or within a specified
time window). Service levels are also measured on both an item and order basis.
An order-based service level focuses on the fulfillment of a whole order that
may be comprised of multiple items, whereas an item-based service level looks
only at the fulfillment of a particular item. The dominant order-based service
level is the order fill rate which corresponds to the probability of joint
demand fulfillment within a given time window. Because the quantities of
different items cannot be aggregated, whether an order is fulfilled or not
depends on whether all the requested items are completely met. Thus, the
item-based counterpart of order fill rate is actually the ready rate.
It is well known that controlling service levels for
individual items is computationally convenient, and that the order-based fill
rate can be approximated as a weighted average of item ready rates (Ballou,
1999). For instance, consider a two-item inventory system from which customers
order either one of the two items or both. Statistical analysis indicates that
the frequency of ordering each of the two items is 0.2, whereas that of ordering
both items is 0.6. If the ready rates of individual items (within a time window)
are all 0.95, then the weighted order fill rate is 0.95 X 0.4 + 0.95 X 0.95 X
0.6 = 0.92. If the target weighted fill rate is specified, then the service
levels for each item must be adjusted to achieve the desired order fill rate. In
a continuous review setting with Poisson demand arrivals, (Song, 1998) shows
analytically that such a weighted average constitutes a lower bound on the exact
order fill rate. In an intensive numerical study, she further shows that the
bound provides a good approximation. For this reason, we address the item-based
ready rate in this paper. |
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