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