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 proposed 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 operating expense. 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 of staffing. 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.
  1. Pieces of mail are homogeneous in terms of processing effort.
  2. Each employee can process 1800 pieces per hour.
  3. 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.
  4. Shift changes occur at midnight, 8:00 AM and 4:00 PM, which are the first, second and third shifts, respectively.
  5. All mail arrivals occur on the hour.
  6. 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.
  7. Labor rates, including shift differential, are given in the following table:
  8. Shift $/hr. Daily Rate
    1st (Midnight-8 AM) 3.90 31.20
    2nd (8 AM-4 PM) 3.60 28.80
    3rd (4 PM-Midnight) 3.80 30.40

  9. Hourly mail arrival is predictable and is given in the following table.
  10. Cumulative Mail Arrival
    1st Shift 2nd Shift 3rd Shift
    Hr. Pieces Hr. Pieces Hr. Pieces
    0100 56,350 0900 242,550 1700 578,100
    0200 83,300 1000 245,000 1800 592,800
    0300 147,000 1100 249,900 1900 597,700
    0400 171,500 1200 259,700 2000 901,500
    0500 188,650 1300 323,400 2100 908,850
    0600 193,550 1400 369,950 2200 928,450
    0700 210,700 1500 421,400 2300 950,500
    0800 220,500 1600 485,100 2400 974,000

    Formulate and solve the LP that determines the most cost effective hourly staff.