We consider a spare parts inventory problem faced by a
manufacturer of an expensive electronic machine such as mainframe computer. The
manufacturer produces and sells the machine and provides service contracts to
geographically dispersed customers. To support the service process, the
manufacturer operates a central warehouse and many field depots that are in
close proximity to the customers. Both types of facilities stock spare parts,
which are highly reliable and very expensive. Furthermore, the warehouse acts as
a repair facility and replenishes stock at
the
field depots. When a machine fails, the customer reports the failure and the
part that failed to the field depot serving the customer. If the field depot has
the spare part on-hand and a technician is available, the technician travels to
the customer site to fix the machine. Otherwise, the repair is delayed until
either a technician is available to fix the machine or the spare part becomes
available at the field depot. In either case, the delay is very costly to the
customer.
A measure of the service quality used by the manufacturer
is the response time, defined as the time it takes for a technician to arrive at
the customer site with a spare part to fix the machine after the customer
reports a failure. To provide high-quality service, the manufacturer prefers to
keep the response time to each customer short. However, the spare parts are
expensive and electronic components have high depreciation and obsolescence
costs. Therefore, it is imperative that the manufacturer maintains the inventory
level as low as possible at the central warehouse and the field depots.
Since the cost of providing a technician to each field
depot is dominated by the inventory cost of holding the expensive parts and the
failure rates of the parts are quite low, a technician is usually available for
service whenever a repair is required. Also, since the field depots are
typically close to the customer sites, the technician's travel time is
negligible. Thus, the ability to meet the response time constraint depends
mainly on the inventory policy at the field depots and the central warehouse. If
the required spare part is in stock at the field depot, the customer is served
immediately and the response time is negligible. On the other hand, if the depot
is out of stock of the specific part requested, the response time includes the
time until the field depot receives the part from the central warehouse and the
time it takes for the technician to bring it to the customer, which includes the
repair time as well as the travel time to and from the central warehouse.
The problem described and analyzed in this paper was
motivated by a project conducted by the authors for a large electronics
manufacturing company. The model constructed and analyzed for our client was
characterized by hundreds of parts and customers, very low part failure rates,
tight response times, many field depots around the US and a base stock policy
for each part at each field depot. To control the quality of service, the
company prefers to keep the average response time to each customer below a
threshold level, say 4 hours. Our model therefore has an objective of
determining an inventory policy to minimize system-wide inventory holding costs
such that the average response time is no greater than the threshold
