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.

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.
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 following table:

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

Hourly mail arrival is predictable and is given in the following table.

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