Staff Scheduling at USPS Mail
Processing & Distribution Centers
A Case Study Using
Integer Programming
General Observation
Companies and organizations that
build, or make use of the latest
technology in their business
practices, rarely make use of the
latest technology in planning and
scheduling!
Service Area in City
DU
DU
DU
DU
DU
DU
DU
P&DC
DU
DU
DDC
DU
DU
DU
DU
DU
DU
P&DC: Processing & Distribution Center
DDC: District Distribution Center
DU: Deliverey Unit
Processing & Distribution Center
Section Center
Manual 044
to DU
Section Center
Manual 150
Primary
Manual 030
Manual arrivals
210-030
Secondary
Manual 040
DBCS
Primary
891
Barcoded arrivals
210-891
Stamped arrivals
210-015
Carrier Route
Manual 160
AFCS
Canceling
Stamps
015
to other
P&DCs
MLOCR
Primary
881
Metered arrivals
210-891
DBCS
Secondary
892
REC
DBCSOSS
Primary
271
DBCS
Section
894
MLOCR
Primary
885
OUTGOING
Incoming arrivals
Manual
Incoming arrivasl
Incompele barcode
Incoming arrivals
Sort to 3 digit
210-895
Incoming mixed
210-893
DBCS
Primary
895
DBCS
Secdonary
Box, 897
DBCS
Managed
893
Incoming arrivals
Sort to 5 digit
210-918
DBCS
1st Pass
918
INCOMING/
TURNAROUND
DBCS
2nd Pass
919
to DU
USPS Scheduling Problem
Mail arrival
profiles &
volume
Flow patterns &
facility configuration
Union rules &
local policies
Equipment
scheduler
Staff
scheduler
Worker
demand
Weekly staff
assignments
Staff Planning and Scheduling
Long-term planning: Fix size and
composition of permanent workforce
Mid-term scheduling: Determine
days off and shift assignments
Short-term scheduling: Overtime,
individual tasks, requests, part-timers
Real-time control: Emergencies,
absenteeism, and other disruptions
Long-Term Staff Scheduling
Goal : Minimize labor costs
Categories
Full-Time Regulars, Part-Time Regulars
 Part-Time Flexibles

Skills (15 Categories)
Input Data

Labor Requirements (1/2 hour increments)
 Labor Costs by Worker Type

Model Components for Long-Term
Staff Scheduling
• Daily mail arrivals
• Mail flow configuration
• Machine parameters
• Work rules
• Labor ratio
Equipment
schedules
Personnel
scheduling
(optimization)
Shifts
Days off
Tours
Determine
optimal amount
of equipment
Equipment
counts
Operations
analysis
(simulation)
Computational Flow
Input data
Modeling
language
Optimization
engine
Microsoft Excel
Spreadsheets
OPL Studio
(ILOG)
CPLEX
Initial output
Staff levels and
shifts (FT, PT)
Post-processing
Weekly schedules
Days-off
scheduling
(Visual Basic)
FT, PT
(Visual Basic)
Breaks
(OPL Studio)
Shift Optimization Model
Minimize
(Full time costs + Part time costs)
Subject to
1. Cover all time periods during the week
2. Ensure sufficient lunch breaks are assigned
3. Adhere to days off requirements
4. Meet other labor rules and policies
Portion of IP Model
Minimize z 
nF
c
f 1
nF
ft
f 1
w f   c pv p
 vp
f
(1c)
p 1
7
1
5
x
d 1
fd
, f = 1,…,nF
w f  x fd , f = 1,…,nF; d = 1,…,7
nF
f 1
(1b)
p 1
nP
wf 
x
(1a)
p 1
x fd   Ppt y pd   dt  Ddt , d = 1,…,7; t = 1,…,48
nF
f 1
f
nP
G
w
nP
(1d)
(1e)
q
fd
  y pd    dt  0 , d = 1,…,7
pT
(1f)
t k
w f  0, v p  0,  dt  0, x fd  0, y pd  0,  t , k , p, d and all variables integer
(1g)
Size of Typical Staff
Planning Model
Number of Constraints = 1100
Number of Integer Variables = 1500
Number of Logic Variables = 336
Solution Times: seconds  years
Post-Processors
Days-Off Scheduling


Greedy algorithm for assigning days off
Small integer program for 2-days off in a row
Lunch Break Assignments


Transportation problem
Greedy algorithm
Task Assignments


Multi-commodity network flow problem
Tabu search
Modeling Issues
Time to run, # of runs, how often
Users and their skills
GUI sophistication
Training requirements
Version control
Help desk availability
Who Is The Customer ?
USPS Headquarters
Contracting Officer
Facility Managers
Facility Industrial Engineers
Information Technology Manager
Everybody Wants Something More
Headquarters – Implementation in 9 months
system-wide
Contracting Officer – Statement of Work is
just a starting point (don’t expect any more
money, though, for additional work)
Plant Manager – More modeling features
IT Manager – It will take years to provide
the data you want
Model “Creep”
10-hour shifts, 4-day a week schedules
Some schedules 2 days off in row, others
not necessary
Worker assignments during the day
At least “X” workers per shift
No more than 1 shift every “Y” hours
Implementation
Prototype written in OPL Studio to
demonstrate concepts
Web Access – Java
CPLEX is optimization engine
1600 variables (all integers)
 1500 constraints

Two Test Sites – Dallas and Philadelphia
SOS Menu
Workstation Sets
Output Report
Computational Results
Number of
constraints
Number
of
variables
Total
cost
per week
Number
of
full-timers
Number of
part-timers
% 2 days
off in a
row
Baseline
model
1092
888
$96,280
101
25
68.9
Ratio 3:1
1092
888
$95,040
96
32
65.6
Ratio 5:1
1092
888
$97,880
105
21
63.5
Consecutive
off-days
2127
1440
$103,600
108
27
100
6 hr/6 day
workers
1140
936
$95,952
100
25
72.4
Variable
start time
684
837
$95,800
101
25
62.1
Part-time
flexible
1092
1308
$94,976
100
--
67.8
Parametric Analysis
106000
104000
102000
100000
98000
96000
94000
92000
90000
baseline
ratio 3:1
ratio 5:1
2-days in
6-hr
a row
workers
variable part-time
start time flexible
Benefits of Flexibility
$440,000
$430,000
Total Cost
$420,000
$410,000
$400,000
$390,000
$380,000
$370,000
0
5
10
15
20
25
30
35
40
Percent Part-time to Full-time
45
50
Observations and Lessons
The Customer is Not Always Right
Sometimes a Good Product will Sell Itself
but it Pays to Have a Champion
Don’t Expect the Customer to Understand
his Business from Your Point of View
Data are Always a Problem
Observations and Lessons (cont.)
Nobody Reads Manuals so Make Sure the
Interfaces are Simple and Clear
Do not Try to Explain Optimization to Anyone
Who Does not Have an Advanced Degree
However, Don’t Underestimate the Intuition
of the Customer
Skill Categories
