Staff Scheduling at USPS Mail Processing & Distribution Centers A Case Study Using Integer...
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Transcript of Staff Scheduling at USPS Mail Processing & Distribution Centers A Case Study Using Integer...
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
DU
DU
DU
DU
DU
DU
DU
DU
P&DC
DDC
P&DC: Processing & Distribution Center
DDC: District Distribution Center
DU: Deliverey Unit
Processing & Distribution Center
OUTGOING
INCOMING/TURNAROUND
Manual arrivals210-030
Barcoded arrivals210-891
Stamped arrivals210-015
Metered arrivals210-891
Incoming arrivalsManual
Incoming mixed210-893
Incoming arrivalsSort to 3 digit
210-895
Incoming arrivalsSort to 5 digit
210-918
AFCSCancelingStamps
015
MLOCRPrimary
881
DBCSPrimary
891
DBCSSecondary
892
RECDBCSOSS
Primary271
Primary Manual 030
SecondaryManual 040
Section CenterManual 044
DBCSManaged
893
DBCSSection
894
DBCSPrimary
895
DBCSSecdonaryBox, 897
DBCS1st Pass
918
DBCS2nd Pass
919
to otherP&DCs
to DU
MLOCRPrimary
885
Section CenterManual 150
Carrier Route Manual 160
to DU
Incoming arrivaslIncompele barcode
USPS Scheduling Problem
Equipmentscheduler
Staff scheduler
facility configuration
Mail arrivalprofiles &
volume Workerdemand
Union rules &local policies
Flow patterns &
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
Categories Full-Time Regulars, Part-Time Regulars Part-Time Flexibles
Goal : Minimize labor costs
Skills (15 Categories) Input Data Labor Requirements (1/2 hour increments) Labor Costs by Worker Type
Model Components for Long-TermStaff Scheduling
Operations analysis
(simulation)
optimal amount Determine
of equipment
• Daily mail arrivals • Mail flow configuration • Machine parameters
• Work rules • Labor ratio
Days offShifts
Equipmentcounts
Equipment schedules
Tours
Personnelscheduling
(optimization)
Computational Flow
Input data Optimization
engine Initial output Post-processing Weekly schedules
Microsoft Excel
SpreadsheetsCPLEX
Days-off scheduling
(Visual Basic)
FT, PT(Visual Basic)
OPL Studio(ILOG)
Staff levels and shifts (FT, PT)
Breaks (OPL Studio)
Modelinglanguage
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 ∑∑==
+=PF n
pppf
n
ff vcwcz
11
(1a)
dtdt
n
ppdpt
n
ffdft DyPxG
PF
≥−+∑∑==
β11
, d = 1,…,7; t = 1,…,48 (1b)
∑∑==
≥PF n
pp
n
ff vw
11
ρ (1c)
∑=
≥7
151
dfdf xw , f = 1,…,nF (1d)
fdf xw ≥ , f = 1,…,nF; d = 1,…,7 (1e)
01
=−+ ∑∑∑=∈=
q
ktdt
Tppd
n
ffd yx
F
β , d = 1,…,7 (1f)
0, 0, 0, 0, 0, , , , and all variables integer (1g)f p dt fd pdw v x y t k p dβ≥ ≥ ≥ ≥ ≥ ∀
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
HeadquartersHeadquarters – Implementation in 9 months system-wide Contracting OfficerContracting Officer – Statement of Work is just a starting point (don’t expect any more money, though, for additional work)
Plant ManagerPlant Manager – More modeling features
IT ManagerIT 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
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
Computational Results
Parametric Analysis
90000
92000
94000
96000
98000
100000
102000
104000
106000
baseline ratio 3:1 ratio 5:1 2-days ina row
6-hrworkers
variablestart time
part-timeflexible
Benefits of Flexibility
$370,000
$380,000
$390,000
$400,000
$410,000
$420,000
$430,000
$440,000
0 5 10 15 20 25 30 35 40 45 50
Percent Part-time to Full-time
Total Cost
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.)
Do not Try to Explain Optimization to Anyone Who Does not Have an Advanced Degree
Nobody Reads Manuals so Make Sure the Interfaces are Simple and Clear
However, Don’t Underestimate the Intuition of the Customer
Skill Categories