Model 29: Post Office Problem
Postal Optimality Analysis (Due to Gene Moore).
As part of a modernization effort U.S. Postal Service decided to upgrade,
streamline and make more efficient the process of handling and
distributing bulk mail (second, third and fourth class nonpreferential) in
the Chicago area. As part of this goal a new processing facility was
for the Chicago area. One part of this proposal was development of a low
cost operational plan for the manning of this facility once completed. The
plan would recognize the widely fluctuating hourly volume that is
characteristic of such a facility and would suggest a staffing pattern or
patterns that would accomplish the dual objective of receiving, unpacking,
weighing, sorting by destination, and shipping of mail designated as
nonpreferential, including second class (bulk rate), third class (parcel
post), and fourth class (books). It is most frequently designed as a single
purpose structure and is most typically located in or adjacent to the large
metropolitan areas which, in large measure, produce this type of mail in
significant volume. Although the trend in designing such facilities in the
recent past has been in the direction of increased utilization of automated
equipment (including highly sophisticated handling and sorting devices),
paid manpower continues to account for a substantial portion of total
Mail is received by the facility in mail bags and in containers, both of
which are shipped in trucks. It is also received in tied and wrapped
packages, which are sent directly to the facility on railroad flatcars.
Receipts of mail by the facility tend to be cyclical on a predictable basis,
throughout the 24 hour working day, resulting in the episodic build-up of an
``inventory'' of mail from one hour to the next, which inventory must be
processed at a given level of staffing and machine capacity. A policy
decision to have ``no idle time'' imposes a constraint on the optimal level
Once the facility is ready for operations, it will be necessary to implement
an operating plan which will include staffing requirements. A number of
assumptions regarding such a plan are necessary at the outset. Some of them
are based upon existing Postal Service policy while others evolve from
functional constraints. These assumptions are as follows.
- Pieces of mail are homogeneous in terms of processing effort.
- Each employee can process 1800 pieces per hour.
- Only full shifts are worked, i.e., it is impossible to introduce
additional labor inputs or reduce existing labor inputs at times other than
- Shift changes occur at midnight, 8:00 AM and 4:00 PM, which are the
first, second and third shifts, respectively.
- All mail arrivals occur on the hour.
- All mail must be processed the same day it is received, i.e., there
may not be any "inventory" carryover from the third shift to the following
day's first shift.
- Labor rates, including shift differential, are given in the
|1st (Midnight-8 AM)
|2nd (8 AM-4 PM)
|3rd (4 PM-Midnight)
- Hourly mail arrival is predictable and is given in the following
|Cumulative Mail Arrival
Formulate and solve the LP that determines the most cost effective hourly