A class of inventory and distribution policies for scheduled deliveries of perishable products subject to variable demand is modeled as a Markov chain with a manageable number of states. From its stationary distribution, such measures as probability of shortage, the average age of the inventory, and the average number discarded per time period are obtained. Easily computable bounds on these measures that indicate how they behave as functions of demand, and inventory policy parameters are developed.
Each year over two million hospitalized Americans depend upon the timely availability of the right type of blood products at 6,000 hospital blood banks (HBB's) in the United States. If the right blood products are not available at the HBB when required, then medical complications or postponements of elective surgery can result which translates to extra days of hospitalization and expense. On the other hand, since most blood products may only be administered to a patient of the same blood type within 21 days of collection, overstocking at HBB's leads to low utilization, which increases costs and is wasteful of the scarce blood resource. The Long Island blood distribution system was set up as a prototype of a regional blood center and the hospital blood banks that it services collaborating to preplan regional blood flow. It maximizes blood availability and utilization according to a Programmed Blood Distribution System (PBDS) model and strategy that has been shown to be generally applicable. PBDS schedules blood deliveries according to statistical estimates of the needs of each HBB and monitors actual requirements to adjust deliveries when indicated by control chart techniques. In addition, it provides a daily forecasting of short-term shortages and surpluses for the next several days that results in controlled movement of blood to and from adjoining regions. Finally, the system is able to adjust the regional strategy so that availability is reduced uniformly at all HBB's during periods of seasonal, regional shortages. PBDS has drastically improved utilization and availability of blood on Long Island: wastage has been reduced by 80%, and delivery costs by 64%. This prototype is acting as a model for other regional blood centers in the United States and for other national blood services as a basis for planning and controlling blood flow in a geographic area. It usually replaces preexisting procedures where a regional blood center collects blood based upon gross estimates and reacts to requests for blood by individual HBB's on the basis of experience and on the currently prevailing inventory situation.
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