Reducing Letter Delays in Post Offices

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Abstract
This paper reports a number of mathematical models and experiments that have been designed for the analysis and evaluation of delays of first-class letter mail in a post office. The flow pattern of mail consists of a number of serial and parallel processing stages. A letter takes a particular path through this flow network, which depends on its final destination, consequently, the delay of letter mail depends on its address as well as the inventories of other mail and the processing rates met enroute. While mail flow into a post office may contain many random elements, it is generally the case that input rates are predictable and strongly time-dependent. Scheduling policies must take into account the peak flows that temporarily exceed available processing rates and, in addition, must observe certain specified restrictions on the cost of processing, sorting, and storage operations. The effect of various transportation facilities between processing stages and from one post office to another must also be considered. The mathematical analysis deals with the minimization of letter delay through a network of processing and storage stages where there are capacity restrictions on individual and/or serial and parallel stage combinations. Analytical and graphical procedures are developed and numerical results are reported. The paper also reports a series of full-scale experiments performed at one of the larger United States Post Offices where theoretical procedures and decision rules were applied and tested. Delay reductions for first-class letter mail are believed to be of the order of 25 per cent.

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