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

https://doi.org/10.1016/j.cor.2003.11.029Get rights and content

Abstract

This paper considers the problem of sequencing the processing of incoming mail in a processing and distribution center (P&DC) to match a given outbound truck delivery schedule. Mail arrives at a P&DC from local associate offices or remote P&DCs following an incoming schedule. The mail from an origin has different proportions to different destinations. For each destination, there are trucks scheduled with limited capacities. The objective of the problem is to determine the sequence in which the incoming mail should be processed so that the total unused truck capacity is minimized. Since, we are not concerned with detailed scheduling/routing decisions inside the P&DC, we treat the P&DC system as a single machine. Dispatching rules and heuristics are proposed for this single machine problem and tested via computational experiments. Simulation experiments are performed to test the efficiency of these methods for the original multi-center multi-machine system.

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,

ui1k1i2k2=1ifthek1thmailtrayfromorigini1isprocessedbeforethek2thmailtrayfromorigini2,0otherwise,

SMPDC can be formulated as(P1)minj=1nljs.t.zi1k1+pi1⩽zi2k2+K(1−ui1k1i2k2),∀i1,i2∈M,k1∈Ai1,k2∈Ai2,yikj⩽(dj

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

References (8)

There are more references available in the full text version of this article.

Cited by (28)

  • Problem on the integration between production and delivery with parallel batching machines of generic job sizes and processing times

    2020, Computers and Industrial Engineering
    Citation Excerpt :

    Polynomial-time heuristics have been proposed, which prioritize the production time window. In Wang, Batta, and Szczerba (2005) is considered the scheduling of the received orders integrated with the delivery schedule of the trucks. Furthermore, the vehicles have different capacities, and the orders have identical sizes and different processing times.

View all citing articles on Scopus

This research was supported by a Grant from Lockheed Martin Systems Integration to the University at Buffalo (SUNY).

View full text