Stochastic Models of Internal Mail Delivery Systems

Article Abstract:

This paper develops two stochastic models of an internal mail delivery system in which a single clerk picks up, sorts and delivers mail to a closed loop of offices. The two models differ in whether deliveries are made at scheduled times or not. For a model in which all mail picked up each round is sorted before the next delivery, we assume that mail is generated in the system by a stationary Poisson process and derive an expression for the expected delay between generation of a letter and its ultimate delivery. These results are then extended to systems in which letters are generated according to a stationary compound Poisson process and to multiple clerk delivery systems. A second model in which mail is delivered at scheduled times only is shown to be equivalent to a classical storage process. For this model, we derive bounds on the expected number of letters left unsorted at the start of a scheduled delivery and the expected delivery delay. This model is also generalized to multiclerk systems. (Reprinted by Permission of Publisher.)

Performance/Cost Relationship, Systems, Operations Research

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(S-1, S) Policies for Perishable Inventory

Article Abstract:

We consider (S-1,s) policies for a single item whose lifetime is fixed and known with certainty. Demands are generated by a stationary Poisson process and there is a positive leadtime for replenishment. We believe this study gives the only analysis for perishables with a positive order leadtime. The analysis involves the derivation of the stationary distribution of the S-dimensional stochastic process corresponding to the time elapsed since the last S orders were placed. This distribution is then used to obtain an expression for the expected cost rate of operating the system in steady state as a function of S. A computer program has been developed to compute optimal S values and expected annual costs. We report a computation for a variety of system parameters which show some of the unusual features of the problem. Finally, we show how this model can be used in the context of a problem of optimizing availability of operating equipment subject to scheduled maintenance as well as random failure. (Reprinted by permission of Publisher.)

Manufacturing, Production, Inventory Control, Optimization, Policy, Scheduling, Management Science

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Storing crossmatched blood: a perishable inventory model with prior allocation

Article Abstract:

A model for determining shortages and outdates of crossmatched blood is presented. Blood crossmatching, which involves testing patients' blood samples against inventory samples to ensure compatibility, may result in outdated blood units because physicians tend to order more blood than will be used by patients. The blood inventory control model uses such generally accepted parameters as the amount of crossmatched blood that is used by patients, and the number of days after which unused crossmatched blood is released. The model is a decision support tool that provides blood bank managers with a way of conducting sensitivity analyses associated with controllable blood inventory parameters.

Health and allied services, not elsewhere classified, Blood collection and preservation, Logistics, Blood banks

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