Reducing Letter Delays in Post Offices

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.

Work-Conserving Tandem Queues

“…As every customer departs earlier under the optimal allocation, there are fewer customers in system at every time t, which is the result in [8]. These results readily extend to any number of queues in tandem; see Section 6.…”

“…In Section 2, we show by a SPA that α = 0 is optimal for our model, in the same strong sense as in [8]; stochastic assumptions such as PIE are irrelevant. This allocation corresponds to the optimal policy in [8]. Under PIE, we show that the average waiting time in system for α = 1 can be much larger than the same quantity for α = 0.…”

“…Earlier research [8] analyzed the allocation of workers to sort letters at a post office so as to reduce letter delays. They assumed work conservation; whenever there is work to do (letters to sort), workers are allocated so that they are all busy.…”

Sequencing the processing of incoming mail to match an outbound truck delivery schedule

“…Oliver and Samuel [1] reported several mathematical models for the analysis and evaluation of the time in system of ÿrst-class letter mail in a P&DC. Scheduling policies were developed to take into account the peak ows that exceed the processing rate.…”

Using different response-time requirements to smooth time-varying demand for service

“…A deterministic fluid model tends to be appropriate when the aggregate demand is made up of a relatively large number of small demands, as is likely to occur in a message communication service. A seminal contribution on deterministic fluid approximations was Oliver and Samuel [12]. Segal [15] has recently proposed a mathematical programming approach with a discrete-time deterministic model to determine a good order of service (queue discipline) in each period.…”