Sequencing the processing of incoming mail to match an outbound truck delivery schedule☆
Section snippets
Introduction and motivation
In the United States postal service (USPS) system, mail collected from mailboxes is gathered at an associate office (AO) or a processing and distribution center (P&DC). The AO forwards the collected mail to the pre-assigned P&DC without any operation. In a P&DC, the mail goes through a certain number of operations. After all the necessary operations are completed, mail is dispatched to either an AO or another P&DC depending on its destination. If the final destination of the mail is in the
Problem definition
When we treat the entire P&DC as a single machine, the problem of sequencing mail processing can be briefly described as follows:
Sequencing mail at a P&DC (SMPDC): Mail comes from origin i=1,…,m, where m is the number of origins. Associated with each origin i is an arrival time ri and a number of mail trays ai. Each mail tray from origin i takes pi units of machine time. After being processed, the mail is delivered to destination j=1,…,n, where n is the number of destinations. Associated with
Solution methodologies
To understand better the nature of the problem SMPDC we first formulate it as a mixed integer programming problem. With the introduction of the following decision variables:
zik: start time of processing kth mail tray from origin i,
yikj: portion of completed kth mail tray from origin i at time dj,
SMPDC can be formulated as
Performance evaluation
This section is devoted to the performance evaluation of the dispatching rules and heuristics presented in Section 3. To test the effectiveness of these methods on SMPDC (the single machine problem), computational experiments are carried out and LP relaxation (P2) is used as a benchmark. To test the effectiveness of these methods on the original multi-center multi-machine P&DC system, simulation experiments are carried out and FIFO is used as a benchmark.
Summary and future work
In this paper, we introduce the problem of sequencing the processing of incoming mail encountered at a typical P&DC. We first focus on a simplified version of the original system and propose some dispatching rules and heuristics for this version. The efficiency of these rules and heuristics are tested via computational experiments. The same rules are tested on the original system via simulation experiments. The experimental results show that the performance of the revised greedy algorithm is
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This research was supported by a Grant from Lockheed Martin Systems Integration to the University at Buffalo (SUNY).