School&of&Public&Policy

George&Mason&University

Report'On'Peak'Load'Cost'

Modeling)

Robert'Cohen

Charles(McBride

John%Panzar

John%Waller

October(7,(2011
2

Table&of&Contents

1.## Summary#and#Principal#Findings..................................................................................... 4

2.## Introduction................................................................................................................... 5

3.## Approach ....................................................................................................................... 6

4.## Impact#on#Study#of#Postal#Service’s#Announcement#of#Plans#to#Modify#Operations#and#

Service#Standards ................................................................................................................... 8

5. What#are#Peak#Load#Costs? .............................................................................................. 9

6. Modeling#Approach ....................................................................................................... 10

6.1 Mail&Processing.................................................................................................................. 10

6.2 Delivery .............................................................................................................................. 12

6.3 Transportation .................................................................................................................. 16

7. Data#Requirements........................................................................................................ 18

7.1 Mail&Processing&Models .................................................................................................... 18

7.2 Delivery&Models................................................................................................................. 20

7.3 Transportation&Models ..................................................................................................... 21

Appendices........................................................................................................................... 22

Appendix#A:##Analytic#Models#for#Peak#Load#Costs................................................................ 22

1.##Introduction#and#Summary .............................................................................................. 22

2.##A#General#Statement#of#the#Problem................................................................................ 23

2.1&Methodologies&based&upon&the&optimization&hypothesis................................................. 24

2.1.1&Linear&Programming......................................................................................................... 26

2.1.2!Econometric!estimation......................................................................................................... 26

3.##Peak#Load#Costs#in#Mail#Processing .................................................................................. 28

3.1&What&determines&Peak&Load&Costs? .................................................................................... 32

3.1.1!The!cost!of!service!standards. ............................................................................................... 32

3.1.2!!Cost!savings!from!smoothing!the!peak ................................................................................ 34

3.2#Excess#Capacity#Considerations....................................................................................... 34

3.2.1!Peak!Load!Costs!under!excess!capacity ................................................................................ 35

4.##A#very%simple#model#of#peak#load#considerations#in#delivery............................................ 36

4.1&Peak&Load&Costs&in&the&delivery&model............................................................................... 37

5.##Peak#Load#Costs#in#Ground#Transportation:#Relaxing#Service#Standards ........................... 38

6.#Towards#empirical#analysis. .............................................................................................. 39

6.1&Examples&of&data&required&for&an&empirical&analysis ....................................................... 40

6.1.1!Mail!Processing ........................................................................................................................ 40

6.1.2!Delivery................................................................................................................................... 40

6.1.3!Highway!Transportation ....................................................................................................... 40

Appendix#B:##Linear#Programming#Models#of#Peak#Load#Costs............................................... 41

1.##Introduction..................................................................................................................... 41
3

2. Discussion#of#Proposed#Methodologies#for#Analyzing#Postal#Peak#Load#Costs ................... 45

2.1.###Introduction .......................................................................................................................... 45

2.2.#Linear#Programming#Approach ................................................................................................ 47

2.2.1!Overview!of!Linear!Programming ............................................................................................ 47

2.2.2!Mail!Processing!Example.......................................................................................................... 47

2.2.3!Delivery!Example...................................................................................................................... 49

2.2.4!Transportation!Example........................................................................................................... 51

3.##The#Effect#of#New#Labor Rules,#Service#Standards,#and#Network#Size#on#Peak#Load#Costs.......... 52

3.1!Mail!Processing ........................................................................................................................... 53

3.2!Delivery ....................................................................................................................................... 55

3.3!Transportation ............................................................................................................................ 55

Appendix#C:##Linear#Programming#Numerical#Examples......................................................... 57

Appendix#D Slides#from#Panzar’s#September#30#Commission#Briefing............................... 62
4

Report On#Peak#Load#Cost#Modeling

1.&& Summary&and&Principal&Findings

Working!under!a!competitively!awarded!contract,!the!George!Mason!University!(GMU)!

technical!team!has conducted!a!study!of!peak!load!cost!methods!and!issues.!!The!principal!

findings!are:

• Extensive!literature!is!available!on!peak!load!pricing but!virtually!none!exists!on!

peak!load!costs

• Peak!load!costs!can!be!analyzed!as!the!difference!in!optimized!operations!with!and!

without!real!world!constraints!on!the!use!of!labor!and!capital!inputs!in!operations!

under!conditions!of!uneven!demand!for!these!inputs!because!of!mail!arrival!

patterns,!service!requirements!and!labor!agreements.

• Service!standards!and!mail!arrival!patterns!are!also!constraints!whose!costs!can be!

analyzed!in!a!similar!fashion

• Costs!with!and!without!constraints!can!be!calculated!with!further!development!of!

the!analytical!and!linear!programming!models!developed!for!and!presented!in!this

report!for a!sample!of!cases.

• Much!of!the!data!for!these!linear!programming!models!can!be!obtained!from!current!

data!available!to!the!Postal!Service.

• Other!analytic!techniques!can!be!identified,!such!as!econometric!analysis,!but!the!

data!requirements! may!be!more!burdensome!that!the!linear!programming!

approach.

• The!models!can!also!be!used!to!estimate!cost!savings!from!the!significant!changes!in!

service!standards!and!network!consolidations!that!the!Postal!Service!has!

announced.
5

This!report!presents!the!models!in!an!analytical form!and!as! (numerical)!linear!programs

in!Excel!with examples!of!their!use!for!mail!processing,!delivery!and!transportation!cases.

2.&& Introduction

The!work!was!performed!in!the!four!tasks!identified!in!the!RFP!and!used!to!organize!the!

team’s!technical!approach!in!the!winning!proposal.!!

1. Discuss!Peak!Load!Issues!with!Commission!Staff!(7!days!after!contract!award)!

2. Describe!Peak!Load!Cost!Methodology!(within!20!days!of!contract!award)

3. Describe!the!Data!Necessary!to!Execute!any!Peak!Load!Cost!Modeling!Strategies!

(within!20!days!of!contract!award)

4. Report!on!all!Known!and!Proposed!New Methodologies!for!Calculating!Peak!Load!

Costs!(within!20!days!of!contract!award)

Task!1!involved!a!meeting!with!Commission!staff!that!occurred!on!September!9 in!which!

the!Commission!staff!clarified!the!objectives!of! the!study.!!Tasks!2!and!3 are!the!subject!of!

this!report.!It!characterizes!peak!load!costs!and!describes!the!linear!programming!

modeling!techniques!adopted!and!identifies!an!alternative!econometric approach. !!The!

authors!gratefully acknowledge!the!assistance!from!Professor!Frank!Wolak!in!reviewing!an!

earlier!draft of!an!econometric analysis!approach section!and!augmenting!it!with!text!

contained!in!Appendix!A,!Section!2.1.2.!!Task 4!was!fulfilled,!with a!briefing!to!the!

Commission!on!September!30.!!A!copy!of!the!Task!4!briefing!is!attached!in!Appendix!D.!

Appendix!A!contains!a!mathematical!analysis!the Peak!Load!Cost!issue. Appendix!B!presents!a!

numerical!approach!using!linear!programming!techniques. Appendices!A!and!B!have!

independent characterizations!of!the!peak!load!cost!issue. While!this!creates!some!

redundancies,!it!also!permits!each!appendix!to!standPalone. Appendix!C!describes!the!Excel!
6

worksheets!used!to!demonstrate!the!feasibility!of!producing!numerical!estimates!of!peak!load!

costs!using!linear!programming.!

3.&& Approach

Our!approach!was!to!first!draw!on!the project’s!staff’s extensive!experience!with!Postal!

Service!operations!and!costs!to!develop!a!preliminary!definition!of!peak!load!costs.!!At!the!

same!time!we!conducted!a!literature!search!to!identify!previous!modeling!work!that!could!

be!applicable!to!the!Commission’s!request.!!It!was!concluded!that!postal!peak!load!issues!

are!fundamentally!different!from!peak!loads!in!other!contexts!such!as!electricity!demand.!

A!Google!Scholar!search!of!the!postal!literature!yielded!301 papers!with peak(load(pricing in!

the!title,!but!only!one paper!with!peak(load(costs in!the!title:!!

Ofelia Betancor,& Juan&Luis Jiménez,&and&M. Pilar&Socorro, “The!costs!of!peak^

load!demand:!An!application!to!Gran!Canaria!airport,”!Journal(of(Air(Transport(

Management,!Volume!16,!Issue!2,!March!2010,!Pages!59^64

For!a!potential!peak!load!cost!modeling approach,!the following!was!found!applicable

Michael&A.&Crew,&Paul&R.&Kleindorfer&and&Marc&A.&Smith,&“PeakWLoad&Pricing&in&

the&Postal&Services,”&Economic&Journal,&100,&(September&1990),&793W807.&

We!also!met!with!postal!officials on!two!occasions!(at!District!offices!and!at!USPS!

headquarters) to!review USPS!modeling!efforts!and!available!data!on!operations.!!The!

discussions identified!several!proprietary!workload!assignment!models!that!might!have!

some!applicability!in!mail!processing,!delivery!and!transportation!scheduling.!!Publicly!

available!details!concerning these!models!were!not!identified!but!knowledgeable contacts!

have!been!identified!should!further!development!work!be!pursued!under!Task!5.!!

We!reviewed!recent!documentation!on!Peak!Load!cost!issues,!including:
7

“Advisory!Opinion!on!Elimination!of!Saturday!Delivery”!in!Docket!N2010^1,!

especially!Chapter!VII!Peak!Load!Issues.!!Issued!March!24,!2011!and!available!at!

prc.gov.

“Cost!of!Service!Standards”!report!issued!by!the!U.S.!Postal!Service!Office!of!

Inspector!General,!Report!number!RARC^WP^11^008.!!Of!special!interest!is!Chapter!

2,The!“Peak!Load”!Issue!and!Volume!and!Workhour!Profiles!for!the!Postal!Service,!

in!an!attached!analysis by!Christensen!Associates.!Both the!report!and!supporting!

analysis!are!available!at!uspsoig.gov.

Much!of!this!background!research!helped!formulate!the!discussion!with!Commission!staff!

required!in!Task!1.!!The!first!discussion!occurred!in!a!meeting!on!September!9!at!the!

Commission.!!Subsequent!telephone!conservations!and!email!exchanges!occurred!

throughout!September.! A meeting!at!the!Commission!was!held!on!September!23,!and!a!

briefing!of!Commissioners!and!staff!took!place on!September!30!to!summarize our!findings.!!!

John!Panzar!developed the!analytical models!for!this!report!and!Charles!McBride!

developed!the!linear!programming!models.!!The!model development!effort!helped!the!team!

to!identify!specific data!requirements!and!methods!for!addressing!the!questions!that!the!

Commission!has!raised.!!!

Shortly!after!this!study!was!initiated!the!Postal!Service!announced!plans!to!significantly!

shrink!the!mail!processing!network!and!modify delivery!service!standards.!!Since!many!

peak!load!issues!occur!because!of!existing!service!standards,!the!planned!elimination!of!

overnight!service!is!likely!to!mitigate!some!peak!load!costs!and!create!costs!savings.!!The!

proposed!models!can!be!tailored!to assist!the!Commission!in!the!analysis!of!these!Postal!

Service!plans!as!part!of!the!expected!filing!of!a!request!for!an!advisory!opinion
8

4.&& Impact&on&Study&of&Postal&Service’s&Announcement&of&Plans&to&

Modify&Operations&and&Service&Standards

The!essential!feature!of!the!new!plan!is!to!change!the!current!1!to!3!day!service!standard!to!

2!to!3!days!(i.e.!eliminate!the!overnight!delivery!standard!for!preferential!mail.)1!!This!in!

turn!will!allow!the!processing!of!originating!and!incoming!mail!on!the!day!shift!of!the!next!

day!and!a reduction o!the!number!of!processing!plants!by!more!than!half.2!!Without!the!

overnight!commitment,!there should!not!be!a!significant hourly!peak!in!mail!processing!

which!occurs!now.!Currently, the!Postal!Service!must!!process!all!!mail!originating!in!a!

plant’s!service!area!in!time!to!meet!the!critical!dispatches!for!mail!with!an!overnight!

service!standard!during!the!latter!half!of!tour!3!so!it!can!be!delivered!the!next!day.!There!is!

a!short!window!beginning!about!4!to!5!PM!and!ending a!few!hours!later!to!finish!the!

outward!processing!of!mail!so!that!the!portion!with!an!overnight!service!standard!can!be!

put!into!containers!and!transported!to the!destinating!plants!or!set!aside!for!sequencing!on!

tour!1.!The!destinating!plants!do!inward!processing!on!that!mail!and!dispatch!it!to!carrier!

stations!for!delivery!the!next!morning!in!time!to!be!delivered!that!day.

The!overnight!standard!creates!the!hourly!peak!on!tour!3!in!the!originating!plant.!There is!

a!related!peak!in!both!the!originating!and!destinating!plants!on!tour!1!when!all!incoming!

and!originating!overnight!mail!must!be!sequenced!starting!around!midnight!and!finishing!

about!4!AM!to!be!ready!for!transport!to!delivery!units.!.

The!proposed!plan!would!store!mail!originating!on!day!zero (the!day!it!enters!the!plant)!

and process!it!the!next!day!!(day!one)!during!the!period!when!there!is!no!night!time!

differential!(between!6!AM!and!6!PM.)3 The!plan!envisions!outward!processing!to!begin!on!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 It is not clear at the time of this report whether time value periodicals will still be able to be dropped at plants for 

overnight delivery. However, this is a small portion of total volume. 

2 The overnight service standard requires a reasonably close proximity between plants in an overnight service area 

so that mail can be dispatched and arrive at the incoming plant in time for processing and next day delivery. 

Consequently, the service area of plants can be expanded when the overnight standard is eliminated and this in turn 

allows for a reduction in the number of plants.

3 Very little processing occurs during this period in the current operating plan. For example, the recent Christiansen 

Associates report shows that only one of the eight hours on tour 2 has more than 100,000 dollar weighted clerk 

IOCS tallies. The rest of the hours in that tour have about 50, 000 tallies. In contrast, all the hours in tours 1 and 3 
9

tour!2!at!about!8!AM!and!sequencing!for!carriers!to begin!about!noon!and!continue!till!

about!2!AM4.!This!means!that!originating!mail!on!day!zero!would!be!processed!on!day!one!

and!delivered!on!day!two.!Mail!that!has!a!current!overnight!standard!from!other!plants!

could!arrive!later!(on!day!one)!because!it!would!be!held!for!tour!two!processing!at!the!

originating!plant.!That!mail!would!be!delivered!on!day!2.!The!proposed!plan!would!be!

compatible!with!the!current!two!and!three!day!standard.!Most!of!that!mail!is!not!shipped!

from!the!originating!plant!until!the!next!day!currently,!so!there!would!be!little!change.!

5. What&are&Peak&Load&Costs?&

Peak!load!costs!occur!because!of!constraints!placed!on!the!ability!of!the!Postal!Service!to!

handle!the!flow!of!mail!into!and!through!the!postal!operations!in!the!most!efficient!manner.!!

The!difference!in!costs!between!the!constrained!situation!and!the!unconstrained,!or!less!

constrained!situation,!becomes!the!peak!load!costs!due!to!the!constraints!being!examined.!!

Conversely,!it!is!the!cost!savings!from!removing!or!mitigating!the!constraints.!!For!example,!

without!overnight!service!standards,!mail!could!be!stored!and!processed!without!the!cost!

impact!of!night!differentials!or!expanded!processing!capability.

With!this!definition,!the!cost!of!the!constraints!is!the!difference!between!the!cost!of!the!

optimal!operating!cost with!and!without!the!constraints.!!To!perform!the!calculation,!one!

needs!a!cost!function!to!be!minimized!with!associated!constraint!equations.!!If!the!cost!

function!and!associated!constraints!can!be!expressed!as linear!relationships, then!linear!

programming!techniques!can!be!used!to!find!optimal!solutions!for!the!cost!function!with!

and!without!the!constraints.

Fortunately,!linear!relationships!can!be!used!for!mail!processing,!delivery!and!

transportation!operations.!!To!demonstrate!the!feasibility!and!value!of!this!approach, the!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

have at least 150,000 and 11 of the 16 hours have more than 250,000 tallies. They range as high as 400,000 tallies. 

(See page 22.)

4 Machine utilization would increase under the new plan. Currently, sorting machines run from about 5 PM to about 

4 AM or about 11 hours a day. Under the new operating plan they would run about 18 hours.
10

study!team!has!developed!both!analytical and!empirical models!for!these!postal!operations!

that!are!presented!here!and!in!the!Excel!worksheets submitted!along!with!this!report.

The!three!operational!areas!identified!in!the!RFP!are!used!to!organize!the!discussion!here!

of!peak!loading!issues!and!modeling in!the mail!processing,!delivery!and!transportation

functi

6. Modeling&Approach

After!a!review!of!the!modeling!literature!for!estimating!peak!load!costs,!the!study!team!has!

settled!on!linear!programming!approaches.!A!linear!program!calculates!the!lowest!cost!

solution while!satisfying!the!relevant!constraints.!In!a!sense!it!generates!a!theoretical!or!

normative!(should)!cost!result.!This!result!can!be!compared!to!actual!results!to!get!a!

measure!of!efficiency. It!can!be!used!to!estimate!the!cost!of!labor!constraints!by!running!it!

with!and!without!the!labor!constraints.!It!can!estimate!the!cost!of!peak!loads!by!changing!

the!dispatch!schedules!or!the!arrival!pattern!of!the!mail!and!running!the!model!with!a!

smooth!workflow.! It!can!estimate!the!cost!of!a!change!in!service!standards by!running!it!

with!the!old!and!the!new!service!standard!and!then!comparing!the!results.!!As!discussed!

here!and!in!the!appendices, linear!programming!provides!a!straightforward!approach!to!

describing!decision!variables!and!constraints!involved!in!mail!processing,!delivery!and!

transportation!functions..!!Its!use!is!described!separately!for!each!function!and!with!

examples!of!its!use!given!in!the!appendices.

6.1 Mail&Processing

We!model!peak!load!and!other!mail!processing!issues!by!constructing!a!linear!programming!

model!that!minimizes!staffing!and!equipment!costs!subject!to!perturbations!in!workload.!These!

are!caused!by!the!fluctuations!in!the!arrival!of!mail!coupled!with!service!standards!that!cause!

the!Postal!Service!to!handle!more!mail!at!certain!periods!than!others.!The!linear!programming!

approach (see!Appendices A, B!and C for!more details,!including!preliminary!examples) will use!

actual!union!contract!constraints!and!will!parameterize!the!number!of!machines!available. 5 The!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5 The actual number of machines available would be used if a specific plant were being modeled.
11

user!of!the!model!will!input:!the!total!volume!(if!desired,!by!preferential and!nonPpreferential

and!by!shape),!the!hourly!and!daily!arrival!profiles!for!low!and!high!volume!periods!of!the!year,!

the!labor categories!and!wages,!the!sorting!machine!capacity,!the!labor constraints!to!be!

examined,!and!final!dispatch!times!for!each!category!of!mail.!The!model!then!identifies the!

least!cost!labor!schedule!using!the!different!categories!of!labor!and!the!constraints.

The!figure!shown!below!from!the!Christenson!report!on!changing!service!standards!(Figure!14!

in!the!report)!illustrates!the!fluctuations!in!the!demand!for!clerk!labor!for!the!Postal!Service!as!

a!whole.!It!can!be!seen!for!example,!that!the!Service!uses!approximately!8!times!as!many!clerk!

hours!between!10!PM!and!11!PM!on!a!regular!work!day!as!it!does!between!12!PM!and!1!PM6.

We!can!think!of!the!figure!as!representing!a!typical!plant’s!demand!for!labor!given!the!arrival!

pattern!of!its!mail!and!the!dispatch!schedules!it!is!subject!to.!!The!model!will!calculate!the!

lowest!cost!schedule!of!employees!using!all!the!labor!categories!defined!in!the!clerk!union’s!

contract!with!the!Postal!Service!and!subject!to!the constraints!in!the!contract.!The!labor!

categories!include!regular!clerk,!part!time!clerk,!part!time!flexible!clerk,!regular!overtime,!

penalty!overtime!etc.!The!constraints!include!such!provisions!as!that!each!regular!clerk!must!be!

given!8!hours!work!in!a!9 hour!period!and!must!be!given!two!consecutive!days!off,!etc.!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 6 Of course, the actual levels vary from day to day with the volume of mail. 
12

The!model!can!be!used!to!estimate!the!costs!for!a!day!but!a!typical!application!would!be!for!a!

week!because!some!of!the!constraints!can!only!be!reflected!in!a!week’s!period.!The!volume!for!

each!day!of!the!week!must!be!input.!Seasonality!can!be!represented!by!high,!medium!and!low!

volumes!as!volumes!are!high!in!the!fall!and!in!the!Christmas!season!while!it!is!low!in!the!

summer.!It!should!be!born!in!mind!that!some!of!the!labor!constraints!are!different!in!the!

Christmas!period!than!in!other!times!of!the!year.!

Appendix!A!describes!analytic!models!that!the!study!team!has!constructed!to!demonstrate!

general!modeling!techniques.!!It!contains!examples!of!peak!load!cost!models!that!examine!the!

impact!of!service!standards,!smoothing!of!the!mail!arrival!and!the!existence!of!excess!capacity.!!

Appendices B!and!C!present!specific!linear!programming!examples!involving!two!types!of!

preferential!mail!(originating!and!incoming),!with!overnight!processing!requirements,!and!with!

nighttime!differential!pay.!!Appendix!B!develops!the!linear!programming!model!and!Appendix!C!

describes!the!Excel!worksheets!containing!several!examples!of!the!numerical!calculation!of!

optimal!linear!programming!solutions!for!the!constrained and!unconstrained!situations.!!The!

actual!peak!load!costs!for!these!examples!are!calculated!in!the!Excel!worksheets!described!in!

Appendix!C!and!submitted!as!a!separate!Excel!file, LPExamples.xlsx

6.2 Delivery

There!are!three!major!types!of!delivery!routes:!!city,!rural!and!highway!routes.!!City!

carriers!are!paid!an!hourly!rate!!and!can!receive!overtime!payments.!They are!represented!

by!the!National!Association!of!Letter!Carriers!(NALC).!!Generally!speaking, rural!carriers!

are!paid!a!flat!amount!based!on!periodic!assessments!of!the!volume!of!mail!on!their routes.!

They!do!not!get!paid!overtime!except!in!exceptional!circumstances. They!are!represented!

by the!National!Rural!Letter!Carriers’!Association!(NRLCA).!!Highway!routes!are!procured!

on!a!competitive!bid!basis!and!are!paid!a!fixed!amount.! They!are!represented!by!the!Star!

Route!Association!The!discussion!here!focuses!on!City!Routes!whose!local!supervisors!

make!day^to^day!decisions!on!whether!to!modify!route!operations!in!light!of!changes!in!

volume and!carrier!absence.!They!can!authorize!overtime if!needed.!!
13

City!delivery!operations!are!organized!by!routes!that!operate!out!of!delivery!units!that!

serve!one!or!more!5^digit!ZIP!code!areas.!!!Mail!from!a!local!processing!plant!is!transported!

to!the!delivery!unit!and!then!distributed!to!the!carriers!for!delivery!on!their!assigned!route.!!

Most!of!the!mail!coming!from!the!processing!plant!is!also!organized!by!carrier!and!most!

letters are in!delivery!point!sequence!(DPS)!order.!!Those!delivery!units!served!by!a!

processing!plant!with!Flats!Sequencing!System!(FSS)!sorting!machines!also!receive!flats!in!

DPS!order.!!About!one!third!of!the!routes!now!receive!flats!in!DPS!form.7!!The!DPSed!mail!is!

ready!to!be!taken!to!the!street!for!delivery.!!The!carriers!in!the!delivery!unit!must!sort!non^

DPSed!mail!by!hand.!!

With!the!advent!of!DPSed!mail,!the!carrier!time!in!the!office!has!been!reduced!from!about!

four!hours!to!two!or!less.!!This!has!reduced!the!overall!variability!of!carrier!costs!with!

respect!to!volume,!since!in^office!time!has!nearly!100!percent!variability!while!street^time!

variability!is!about!one!third!of!that.!!A!major!reason!for!the!variability!of!street!time!is!the!

coverage!factor!(the!percent!of!delivery!points!on!the!route!receiving!mail!and!requiring!

deviation!from!the!route!to!the!customer’s!mail!box),!and!another!important!reason!is!

loading!the!mail!into!a!mail!box!which!requires!fingering!the!mail!to!isolate!the!pieces!in!

the!carrier’s!bundle!for!a!specific!address!(called!load!time).!!

Typically, a!carrier!is!assigned!to!a!specific!route.!!During!the!last!few!years,!most!city!

routes!have!been!redesigned!on!an!annual!basis!in!response!to!decreases!in!mail!volume!

that!in!turn!has!reduce!the!number!of!city!routes.!!!Between!periods!of!route!redesign,!

routes!are!fixed.!!However,!each!route!consists!of!well^defined!segments,!such!as!a!distinct!

neighborhood!or!a!certain!set!of!streets.!!On!a!daily!basis,!supervisors!have!the!authority!to!

reassign!segments!to!different!carriers!to!smooth!the!volume!load!or!to!accommodate!

absent!carriers.!!This!process!is!known!as!pivoting!and!is!a!form!of!dynamic!route!

adjustment.!!In!some!postal!districts,!carriers!can!be!reassigned!between!delivery!units!to!

further!assist!in!handling!imbalances!in!the!distribution!of!carriers and!mail.!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 7 The new operating plan envisions sequencing flats for more routes with the same number of machines because of a 

longer sorting window.
14

Unlike!mail!processing!in!which!mail!volumes!show!hourly!peaks,!delivery!volume!

variation!is!solely!by!day!and!season.!!As!shown!in!Table!IV^4!reproduced!from!the!

Commission’s!Advisory!Decision!in!Docket!N^2010^1,!mail!arrival!varies!by!day!of the!week!

with!Monday!being!the!highest!volume!day.!!Saturday’s!average!total!volume!is!lighter!at!

855,548. Total!city!carrier!workhours!are!virtually!constant!on!the!weekdays,!ranging!from!

900,748!to!933,941!per!day.!This!might!support!the!Postal!Service!assertions!that!street!

time!is!virtually!fixed!as!long!as!volume!is!below!the!capacity!of!the!route.!!However,!the!

productivity!in!terms!of!pieces!per!workhour!varies!significantly!from!a!Tuesday!low!of!

354!to!a!Monday!high!of!451.!!

Once!a!set!of!routes!is!established!for!a!year,!the!management!problem!is!one!of!assigning!

carriers!and!other!personnel!to!participate!in!the!in^office!and!street!time!work!so!that!

costs!are!minimized!subject!to!service!and!operational!constraints.!!Issues!that!have!to!be!

addressed!are!the!productivity!of!carriers,!variability!of!carrier!time!with!volume,!use!of!

overtime,!use!of!part^time!and!auxiliary!personnel,!pivoting!segments!of!the!route,!delaying!

some!of!the!mail!to!delivery!on!a!subsequent!day.!!!Table!IV^6!from!the!PRC!Docket!N2010^

1!Advisory!Opinion!shows!the!percent!of!mail!that!is!deferrable!varies!by!day!from!a!

Monday!low!25.6!percent!to!a!Tuesday!high!of!39.1.!!

!"#$%&'(")'(*+,+-,' -'./'-'

'''''''''''''''''''''''''''''''''''''''''''

0%%$)''1234%'56-.'78%8'!95:';2&2'<=">?;%;'?@'=%8<"@8%'&"'AB5C'(")',D'E7%8&?"@'FF+'&"'

#24#742&%'&G%'2>%=2H%';%4?>%=I'<=";7#&?>?&I'288"#?2&%;'0?&G';?JJ%=%@&';2I8'"J'&G%'0%%$'

7@;%='&G%'#7==%@&'8?K-;2I';%4?>%=I'%@>?="@L%@&)'

Table IV-4 

FY 2009 City Delivery Volumes and Carrier Street Hours by Weekday 

A"4)','''''''''''

6"47L%

A"4)'*'''''''''''

B"7=8

M#8)'M%='B=)'

M=";7#&?>?&I''''

NA"4)','O'A"4)'*P

Q"@;2I '''''.*,D+RRDSR/ '''''''''''''TFFDT., .U,

17%8;2I '''''F*/D.R.D,*. '''''''''''''T*,D++/ FU.

V%;@%8;2I F*TD+TUD+F/ ''''' '''''''''''''T,TD+/* FUS

1G7=8;2I '''''FF.D.R*DS,T '''''''''''''T+SDS// F/S

W=?;2I '''''FFUD,*/DR.+ '''''''''''''T++DR.S FR*

:2&7=;2I '''''F**DSFTD+R, '''''''''''''SUUDU.S FRR

1"&24 ''*D+/TD+SUD//U ''''''''''UD.FTD,R, FS+

!2I'XJ&%='B"4?;2I .SRD,T*D+,* ''''' '''''''''''''TU*D+*+ U,*

:"7=#%Y''MCA-ZC-(*+,+-,O*)'

W?H7=%'56-*'8G"08D'&G2&'&G%'=%874&8'"J'2<<4I?@H';?JJ%=%@&'2>%=2H%';2I-"J-&G%-0%%$'

<=";7#&?>?&?%8';?JJ%='L2=$%;4I'J="L'&G%'M"8&24':%=>?#%[8'%8&?L2&%8'"J'8&=%%&';%4?>%=I'G"7=8'

&G2&'0"74;'3%'82>%;'3I'%4?L?@2&?@H':2&7=;2I';%4?>%=I)''VG%@':2&7=;2I'L2?4'?8'2887L%;'

&"'3%';%4?>%=%;'2&'&G%'2>%=2H%'<=";7#&?>?&?%8'288"#?2&%;'0?&G'Q"@;2I8D'&G%'?L<4?%;'G"7=8'

82>%;'2=%'%?HG&'<%=#%@&)''X&'2>%=2H%'<=";7#&?>?&?%8'288"#?2&%;'0?&G';2I8'&G2&'J"44"0'2'

G"4?;2ID'&G%'?L<4?%;'G"7=8'82>%;'2=%',T'<%=#%@&)''X&'2>%=2H%'0%%$4I'<=";7#&?>?&?%8D'&G%'

?L<4?%;'G"7=8'82>%;'2=%'@%H2&?>%'@?@%'<%=#%@&)''1G%'@%H2&?>%'82>?@H8'?@;?#2&%8'&G2&'?J'

&G%'M"8&24':%=>?#%'?8'@"&'234%'&"'?@#=%28%'?&8'<=";7#&?>?&I'3%I"@;'&G%'#7==%@&'0%%$4I'

2>%=2H%D'L">?@H':2&7=;2I'>"47L%'&"'Q"@;2I'#"74;'?@#=%28%'=2&G%='&G2@';%#=%28%'

#"8&8)'

' '
15

The study!team!has!begun!to!demonstrate!the!feasibility!of!building!models!to!calculate!

optimal allocations!of!labor!resources!in!light!of!the!actual!constraints!represented!by!the!

various!operating!conditions.!For!example, the!requirement!that!carriers!work!an!eight^

hour!day!five!days!a!week!with!known!overtime!rates!can!readily!be!built!into!the!model,!

along!with!the!options!to!augment!with!other!types!of!labor,!like!delivery!assistants!or!

routers.!!One!of!Professor!Panzar’s!modeling!examples!deals!with!the!different!types!of!

labor.!!

An!issue!that!will!have!to!be!parametrically!analyzed!is!the!impact!of!variability.!The!

Service!has!basically!claimed!that!street!time!is!fixed!relative!to!volume.!!However,!cost!

analysis!endorsed!by!the!Service!and!the!Commission!indicates!a!street!time!variability!of!

about!33!percent.!!Also,!the!fact!that!volume!decreases!have!forced!the!Service!to!alter!

route!configurations!on!an!annual!basis!further!demonstrates!that!volume!variability!is!an!

important!factor!in!carrier!operations.!!!If Task!5!models!are!developed,!a!means!of!testing!

for!various!variability!levels!should!be!built!into!the!models.

!"#$%&'(")'(*+,+-,' -'.*'-'

Table IV-6 

Percent of FY 2009 City Carrier Average Daily Volume by Mode and Day 

/"01#%2''345-64-(*+,+-,7*)'

89:;%'<=->'?@"A?';91B%'CDEE%1%F#%?'DF'&@%'G%1#%F&9B%?'"E'C%;DH%1%C'!3/'9FC'

C%E%119:;%'I9D;'J?%K0%F#%C'I9D;'9FC'#9?%C'E;9&?L'"F'M"FC9N?'9FC'80%?C9N?)''8@%'C9&9'

?0BB%?&'&@9&'C%;DH%1N'"E'9';91B%'G"1&D"F'"E'?%K0%F#%C'I9D;'D?'C%E%11%C'E1"I'M"FC9N'&"'

80%?C9N'&"'I"C%19&%'&@%'%EE%#&?'"E'&@%'#011%F&'M"FC9N'H";0I%'G%9$)''M"FC9N'#011%F&;N'

@9?'&@%'@DB@%?&'G1"C0#&DHD&N'"E'9FN'C9N'"E'&@%'A%%$'9?'I%9?01%C':N'&"&9;'GD%#%?'

C%;DH%1%C'G%1'@"01)''8@D?'I%9?01%'C"%?'F"&'9##"0F&'E"1'&@%'A"1$'1%K0D1%C'&"'C%;DH%1'

CDEE%1%F&'&NG%?'"E'I9D;)''O"1'%P9IG;%Q'!3/';%&&%1?'91%'&9$%F'CD1%#&;N'&"'&@%'?&1%%&':N'&@%'

#911D%1'1%K0D1DFB'IDFDI9;'"EED#%'9FC'?&1%%&'&DI%)''<F'#"F&19?&Q'#9?%C'E;9&?'1%K0D1%'DF-"EED#%'

#9?DFBQ'9FC'91%'I"1%';9:"1'DF&%F?DH%)''59?%C'E;9&?'1%K0D1%'&A"'&"'E"01'&DI%?'I"1%'#911D%1'

A"1$'&@9F'!3/';%&&%1?)'

5"IG91%C'&"'F"1I9;'80%?C9N?Q'G1"C0#&DHD&N'D?'@DB@%1'"F'80%?C9N?'9E&%1'9'

M"FC9N'@";DC9N)''8@D?'CDEE%1%F#%'D?Q'DF'G91&Q'C1DH%F':N'9'#@9FB%'DF'&@%'IDP'"E'I9D;'&NG%?)''

8@%'I9D;'IDP'"E'80%?C9N?'9E&%1'M"FC9N'@";DC9N?'F%91;N'I9&#@%?'&@%'I9D;'IDP'"E'9'
16

The!above!data!is!for!averages!over!a!year.!!It!is!important!to!note!that!volumes!differ!by!

day!of!the!week,!month!and!season.!!The!linear!programming!delivery!model!that!the!study!

team!has!identified can!take!into!consideration!these!differences!by!using!different!volume!

sets.!!

The!appendices!to!this!report!present!preliminary!models!to!demonstrate!how!models!

would!be!developed!for!the!delivery!function.!!Appendix!A!contains!two!exemplar!analytic!

models!developed!by!John!Panzar.!!The!first!analytic!model!examines!the!peak!load!costs!

where!the!number!of!routes!can!vary!by!delivery!day.!!The!second!analytic!model!examines!

the!peak!load!costs!when!mailers!are!induced!to!smooth!the!flow!of!mail!by!delivery!day.!!

Appendix!B!presents!a!linear!programming!model!that!keeps!the!number!of!routes!the!

same!each!day!but!allows!carriers!with!different!salary!levels!with!constraints!on!the!

number!of!hours!and!days!worked!for!one!of!the!salary!levels.!!

The!examples!in!the!appendices!can!readily!be!expanded!to!include!other!real!world!

constraints!and!opportunities!for!significant!operational!changes!as!proposed!by!the!Postal!

Service.!!Further!development!work!planned!under!Task!5!in!the!original!Commission!RFP,

but!not!included!in!this!contract!work!statement, can!build!on!these!exemplar!prototype!

models.!!

6.3 Transportation

The!Postal!Service’s!highway!transportation!system!is!perhaps!the!most!complex!in!the!world.!!

It!currently!connects!over!500!plants!with!each!other!(using!hub!and!spoke!and!direct!

connection)!and!with!some!30,000!thousand!post!offices. For!the!most!part, the!Service!must!

contract!for!round!trips!(back!haul)!which!frequently!mean!that!capacity!use!is!uneven!as!mail!

flows!are!not!symmetrical.!!In!addition,!the!transportation!system!must!allow!the!Service!to!

meet!its!service!standards!and!this!frequently!requires!trucks!to!be!dispatched!with!less!than!

full!loads.!!We!have!developed!an!exploratory!transportation!model!using linear!programming!

that!efficiently!allocates!trips!to!demand!between!points!subject!to!service!standards and!their!
17

required!final!dispatch!times!in!each!processing!facility.!The!fully!developed!model!could!be!

used,!for!example,!to!estimate!minimum!costs!for!intraPSCF!and!IntraPBMC!transportation!

involving!a!single!point!and!many!delivery!units.!This!would!be!especially!relevant!to!the!

proposed!new!operating!plan!that will!eliminate!the!overnight!standard!for!First!Class.!Other!

ways!the!model!could!be!used!is!to!estimate!the!reduction!in!the minimum!cost for!interPSCF!

and!interPBMC!highway!transportation!under!the!assumption!that!the!number!of!processing!

plants!will!be!cut!in!half!as!has!been!announced by!the!Postal!Service.!!The!model!could!also!be!

used!to!estimate!cost!savings!from!moving!mail!volumes!to!highway!from!air!assuming!that!the!

twoPday!service!standard!would!be!relaxed!between!designated!city!pairs. Finally,!the!models!

could!be!used!to!measure!the!cost!of!peak!loads!by!examining!costs!with!and!without!volume!

peaks.

Generally!the!model!will!examine!daily!scenarios!with!hourly!volume!availability!in!the!staging!!

area. 8 Minimum!costs!for!weekly!schedules!could!be!estimated!using!a!series!of!daily!runs.!!As!

with!mail!processing!and!delivery,!seasonal!effects!could!be!captured!by!running!the!model

with!high,!medium!and!low!volumes.!!Different!size!plants!could!be!accommodated!with!

separate!runs!using!different!representative!volumes.!

The!study!team!has!been!informed!by!Postal!Service!staff!that!virtually!all!the!truck!trailers!that!

it!uses!are!about!42!feet!long!and!that!it!must!contract!for!back!haul!in!most!instances.!Thus!it!

appears!that!scheduling!different!size!trailers!is!not!an!option.!9 The!Postal!Service!now

generally!contracts!for!two!years!at!a!time.! It!has!the!ability!to!call!for!extra!trips!on!a!route!

and!to!cancel!a!trip.!The!study!team!would!need!cost!information!to!incorporate!this!

information!into!the!model10.!

The!model!would!require!volume!data!between!points!including!the!arrival!rates of!mail!into!

the!staging!area.!!It!would!also!need!the!last!dispatch!of!value!information!for!each!route.!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 8 “Staging” refers to the area were mail is stored for dispatch after it has been processed..

9 Moreover, the Postal Service staff informs us that the major cost in trucking is the driver and the using smaller 

trailers would yield little savings. 10 The study team was also informed that these options were seldom used for reasons that were not explained.
18

7. Data&Requirements

Data!requirements!flow!from!the!definition!of!the!variables!and!constraints!in!the!models.!!

Based!on!the!team’s!preliminary!modeling!work,!initial!data!requirements!can be!identified!

to analyze!peak!load!costs!and!savings!from!the!new!operating!plan!recently!announced!by!

the!Postal!Service.!!Data!is!required!for!the!current!operating!plan!and!estimates!for!the!

proposed!operating!plan.

The!number!of!facilities!from!which data!should!be!gathered!will!define!the!number!of!

facilities!that!can!be!modeled.!In!a!world!with!unlimited!recourses,!data!from!all!the!

facilities!would!be!used.!Of!course,!it!is!impractical!to!develop!that!many!models!and!it!

would!be!an!undue!burden!on!the!Postal!Service!to!generate!that!amount!of!data. We!think!

that!data!from!a!small,!medium!and!large!facility!would!be!sufficient!to!generate!usable!

results.!

7.1 Mail&Processing&Models

The!mail!processing!models!require!data!on!the!arrival!of mail!by!the!hour!and!the!dispatch!

schedule!by!the!hour..!!In!addition!we!would!need!to!know!if!these!patterns!are!relatively!

constant!over!time.!Processing!peaks!in!a!given!plant!occur!by!hour!of!a!day,!by!day!of!the!

week,!by!day!of!the!month,!and!by!month!or!season!as!driven!by!arrival!rates!and!dispatch!

schedules.!!!The!volume!flows!and!mail!processing!requirements!differ!by!preferential!or!

non^preferential!status,!by!shape!and!by!form!of!mail!presentations!(single^piece,!pre^sort).!!!!

In!addition!data!is!needed!on!the!number!of!machines!of!various!types!and!the!productivity!

of!the!plant!(pieces!per!man!hour)!productivity.

As!a!starting!point,!the!following!data!should!be!obtained!for!a!typical!plant,!such!as!the!

Merrifield, Virginia!Processing!and!Distribution!Center.
19

Mail!arrival!and!flow!rates!by:

• Hour!of!the!day!for!a!week!in!a!low!volume!week,!like!August,!and!a!high!volume!

week,!like!mid!December,!and!also!a!normal^volume!week.

• Broken!out!by!

o Preferential!or!non^preferential!category!mail

o Shape!and

o Source!(collection,!bulk,!and!managed!mail!from!other!plants)

• Volume!flow!matrix!of!mail!by!shape!from/to!all!MODS!operations!!

Labor!

• Categories!of!labor!and!average!salary

o Clerks

 Full!time

 Part!time

 All!categories!identified!in!the!new!APWU!contract.

o Mail!Handlers

• Productivity – average!pieces!per!man!hour!for!each!MODS!operation

• Physical!Characteristics

o Number!and!type!of!machines

o Throughput!in!terms!of!pieces!fed!and!pieces!successfully!processed!per!hour

Much!of!this!information!is!readily!available!from the!current!records!of!a!plant.!!For!

instance,!mail!arrival!rates!for!bulk!and!managed!mail!should!be!available!from!a!mixture!

of!IMb!data,!Mail!Permit!Statements,!FAST!records,!and!mail!surface!visibility!reports.!

Barcodes!on!containers!are!scanned,!as!the!containers!are!unloaded!from!trucks!to!provide!

arrival!time!and!information!on!contents.!!Some!software!programs!may!need!to!be!

developed!to!integrate!the!data!from!these!sources.!!Some!of!this!data!is!already!in!MODS.!!

Data!on!the!collection!mail,!could!be!approximated!by!a!short!special!study!of!Commission!

staff!visiting!the!selected!plant!to!interview!the!dock!workers!and!possibly!counting!

containers!coming!in!during!the!primary!arrival!time!of!late!afternoon!and!early!evening.!!

The!count!could!be!used!to!corroborating!the!estimates!from!the!dockworkers,!or!making!a!

suitable!adjustment.!It!might!also!be!possible!to!rely!on!informed!estimates!by!

knowledgeable!staff!at!the!facility.
20

Work!hour data!can!come!from!Time!and!Attendance!Data!and!from!databases!of!the!

employee!roster!of!a!plant.!!Physical!characteristics!can!come!from!the!variety!of!databases!

used!to!track!the!existence!and!location!of!equipment.!!Much!of!the!data!may!already!be!

available!in!the!Enterprise!Warehouse!databases.!!The!Commission!should!be!given!access,!

on!a!limited!bases,!to!the!databases!currently!available!to!most!Postal!Service!employees.!!

7.2 Delivery&Models

Variation!in!mail!arrival!rates!for!the!delivery!function!occurs!by!day!of!the!week,!month!

and!year.!!City!carriers!are!paid!on!an!hourly!basis,!work!8^hour!days!5!days!a!week.!!Most!

carriers!are!assigned!to!a!specific!route!for!long!periods.!!One!or!more!carriers!in!a!facility!

rotate!between!routes!to!fill!in!for!carriers!taking!a!day!off!during!the!6^day!delivery!week!

and!may!receive!a!higher!wage!than!other!carriers.!!Overtime!occurs!with!supervisor!

approval.!!!Data!on!the!availability!of!the!different!types!of!carriers!available!to!serve!the!

routes!in!a!delivery!unit!and!their!wage!rates!is!needed!for!the!models.!!As!a starting!point,!

the!following!data!should!be!obtained!for!a!sample!of!delivery!units!for!a!week!in!a!light!

and!heavy!volume!month.

Mail!arrival!rates

• Volume!of!mail!by!shape!by!day!of!the!week

o Deferrable!and!non^deferrable!(not!equivalent!to!preferential!and!non^

preferential!since!delivery!point!sequence!mixes!preferential!and!non^

preferential)

Labor!

• Labor!available!by!different!categories!allowable!in!NALC!contract

• Clerks!available!for!sorting!assistance

• Wage!rates

• Man!hours!used!for!each!labor!category!by!day

This!data!should!be!available!through!the!DOIS!and!TACS!systems.!!The!same!source!the!

Service!used!to!produce!the!data!submitted!in!Docket!N2010^1!and!cited!in!the!figures!in!

the!above!section!on!delivery!models!could!be!utilized.
21

7.3 Transportation&Models

Highway!transportation!is!driven!by!service!standards!and!cubic!foot!capacity!of!vehicles.!

The!following!appear!necessary!to!build!the!linear!program!models!that!we!have!described:

• Mail!arrival!rates!at!staging!for!highway!transportation,!by!destination!and!in!terms!

of!cubic!feet!and!total!volumes!by!destination!in!terms!of!cubic!feet

• Number!used!and!capacity!(cubic!feet)!for!each!available!truck!size

• Last!dispatch!of!value!by!destination

• Plants!that!will!remain!after!consolidation

• Which!plants!will!be!served!by!P&DC’s!and!which!will!have!direct!connection

• Travel!time!matrix!for!the!remaining!plants

• Cost!of!air!vs.!cubic!foot!mile!for!highway!transportation

• Volume!matrix!moving!by!air!between!plants

Potential!sources!for!this!data!are:!!

Highway!Contract!Cost!System!(HCCS). A!record!from!HCCS!contains!annual!cost,!annual!

miles!traveled,!number!of!trucks,!cubic!capacity!of!trucks,!route!length,!highway!cost!

account,!etc.

Transportation!Information!Management!Evaluation!System!(TIMES).!!The!Transportation!

Information!Management!Evaluation!System!is!a!data!collection!system!designed!to!track!

highway!contractor!performance!as!well!as!measure!the!utilization!of!the!truck!

transportation!network.

Surface!Visibility.!!The Surface!Visibility!database!describes!the!integration!of!multiple!

systems!used!to!track!mail!transported!within!the!postal!network.!Surface!Mail!container!

barcodes!are!scanned!as!containers!arrive!or!are!unloaded!at!postal!facilities.!Data!is!also!

integrated!with!the!Facility!Access!and!Shipment!Tracking!(FAST)!system,!which!mailers!

use!to!provide!advance!notification!of!drop!shipment!mailings.!The!Surface!Visibility!scans!

verify!acceptance!and!link!containers!to!the!mailer’s!electronic!manifest.!
22

Appendices

Appendix&A:&&Analytic&Models&for&Peak&Load&Costs

1.&&Introduction&and&Summary&

Our!objective!in!writing!this!report!is!to!develop!a!methodology!for!measuring!the!“peak!

load!costs”!of!various!operations!of!the!Postal!Service.11!!There!is!an!extensive!economics!

literature!on!“peak!load!pricing,”!but!not!on!“peak!load!costs.”12!!Thus,!the!first!order!of!

business!is!to!clearly!delineate!what!is!meant!by!peak!load!costs!for!purposes!of!this!

Report.!!This!is!best!achieved!with!reference!to!the!goals!stated!by!the!Commission!in!its!

RFP:

“These!costs![of!Postal!Service!operations]!should!be!modeled!in!such!a!way!that!the!effect!

on!costs![of]!volume!variation,!of!relaxing!preferential!service!standards,!and!of!relaxing!

staffing!and!scheduling!constraints,!can!be!separately!identified!and!estimated.”

In!response!to!continuing!declines!in!mail!volume,!the!Postal!Service!has!proposed!drastic!

changes!in!its!operating!procedures:!e.g.,!5^day delivery!instead!of!6;!reduction!of!service!

standards!for!preferential!mail,!consolidation!of!mail!processing!operations.!!These!

changes!involve!major!departures!from!the!Postal!Service’s!established!operating!

procedures.!!Insights!regarding!the!cost!effects!of!these!changes!cannot!be!readily!obtained!

directly!from!traditional!USPS!models!and!analyses.!!Therefore,!our!strategy!is!to!develop!

theoretical!models!of!the!changed!nature!of!Postal!Service!operations.

The!basic!approach!is!to!develop!an!optimizing!model!capable!of!calculating!values!of!

“before”!and!“after”!solutions!and!comparing!the!minimized!costs!of!each.!!As!indicated!in!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 11 See PRC RPF 12 A Google Scholar search yielded 301 papers with peak load pricing in the title, but only one paper with peak load 

costs in the title: Ofelia Betancor, Juan Luis Jiménez, and M. Pilar Socorro, “The costs of peak-load demand: 

An application to Gran Canaria airport,” Journal of Air Transport Management, Volume 16, Issue 2, March 2010, 

Pages 59-64. The measure of peak load costs obtained by the authors was calculated by comparing the total 

operating and congestion costs experienced by the airport and its users with their estimate of the costs that would be 

incurred under the counterfactual assumption that airport use was constant over the demand cycle. As we shall see, 

this is consistent with our characterization of one source of peak load costs, below.
23

the!above!quote,!the!term!“Peak!Load!Costs,”!is!best!viewed!as!reflecting!such!a!“before”!

and!“after”!comparison!when!changes!are!made!in!constraints!related!to!short^run!cyclical!

patterns!in!mail!operations:!!e.g.,!changes!in!service!standards,!mail!arrival!profiles,!and!

labor!work!rules.!

The!objective!of!our!stylized!models!of!postal!operations!is!to!formulate!a!nontrivial!

constrained!optimization!problem!facing!the!operations!manager!(e.g.,!minimize!operation!

costs!subject!to!satisfying!various!service!standards!and!work!rules.)!!!!The!next!step!is!to!

solve!the!problem!with!and!without!various!constraints.!!The!reduction!in!the!minimized!

cost!is!the!cost!of!the!constraint!(or!set!of!constraints)!in!question.!!We!have!adopted a!

Linear!Programming!approach!to!conduct!this!“before!and!after”!analysis!of!peak!load!

costs.!!This!has!the!advantage!of!being!implementable!using!readily!available!software!

(Microsoft!Excel).!!The!data!requirements!are!likely!to!be!less!demanding!than!other!

modeling!methodologies.!

2.& A&General&Statement&of&the&Problem

It!is!quite!straightforward!to!describe!the!operations!of!the!Postal!Service,!or!any!other!

decision^making!entity!(DM)!in!quite!general,!abstract!terms.!!The!DM!is!called!upon!to!

choose!the!values!of!n(decision!variables,!i.e.,!specify!a!vector!of!real!numbers!(x1,!x2,!...,!xn)!

=!x∈R!.!!Usually,!the!choices!of!the!DM!are!constrained by!technology,!custom,!politics!

and/or!the!laws!of!physics!to!be!feasible.!!That!is,!they!must!be!chosen!such!that!x∈F⊆R!.!!

The!feasible(set,!F(=({x∈R!|!x&is!a!feasible!choice!for!the!DM},!describes!the!range!of!values!

of!the!decision!variables!that!the!DM!is!actually!able!to!implement.!!The!feasible!set!often!

depends!on!the!value!of!various!exogenous!parameters,!(y1,!y2,!...,!yk)!=!y∈R!,that!affect!the!

DM’s!operating!environment:!!e.g.,!mail!volumes,!service!standards,!etc.!!This!dependence!is!

expressed!by!writing!F(=(F(y).

The!choices!of!the!DM!have!implications!and!may!determine!the!values!of!many!types!of!

outcomes.!!For!example,!the!Postal!Service’s!decisions!on!how!many!hours!of!labor!to!

employ!and!trucks!to!operate!will,!in!part,!determine!the!level!of!operating!costs!it!incurs,!
24

the!number!of!electric!bills!that!are!paid,!the!amount!of!congestion on!the!nation’s!

highways,!and!the!“carbon!footprint”!of!the!Postal!Service.!!In!general,!these!outcomes will!

also!depend!upon!the!levels!of!other!exogenous!parameters,!(w1,w2,!...,!ws)!=!wR!;!e.g.,!

wage!rates,!fuel!costs,!etc.13!!That!is,!depending!on!the!application,!the!analyst!can!specify!

various!outcome(functions,!Oj(x,w),!that!map!the!DM’s!decisions!to!real!numbers!of!

particular!interest.14

We!are!now!in!a!position!to!characterize!the!general!problem!faced!by!the!analyst.!!The!

environment!facing!the!DM!has!is!about!to!change,!and!the!analyst!is!asked!to!determine!

what!change!can!be!expected!to!occur!in!the!values!of!one!or!more!outcomes!of!interest.!!In!

terms!of!our!notation,!the!values!of!the!exogenous!parameters!are!changing!from!(y0,w0)!to!

(y1,w1)!and!the!analyst’s!task!is!to!determine!the!value!of!ΔOj =!Oj(x1,w1)!^ Oj(x0,w0).!!

Assume,!for!simplicity,!that!the!analyst!is!fully!informed!about!the!past!and!future!values!of!

the!exogenous!parameters,!(y0,w0)!and!(y1,w1).15!!There!are!clearly!two!challenges!involved!

in!this!task.!!First,!the!analyst!must,!somehow,!identify the!outcome!functions!of!interest.!!

That!is,!he!must!specify,!by!assumption!or!empirical!measurement,!the!exact!nature of!the!

relationships!that!are!summarized!by!the!outcome!functions!in!question!as!well!as!the!

feasible!set.!!Second,!he!must!be!able!to!accurately!predict the!values!of!the!decision!

variables!that!the!DM!will!select!in!the!situation!characterized!by!(y1,w1).

2.1&Methodologies&based&upon&the&optimization&hypothesis

In!principle,!the!analyst!could!simply!ask!the!DM!to!report!his!planned!(feasible)!response!

to!the!change!in!his!operating!environment.!!This!would!seem!to!obviate!the!need!to!

predict!x1.!!The!analyst!could!then!merely!plug!in!the!reported!value!into!the!outcome!

function!of!interest!and!directly!calculate!ΔOj =!Oj(x1,w1)!^ Oj(x0,w0).!!However,!it!is!quite!

likely!that!the!DM!may!be!unable!or!unwilling!to!provide!an!accurate!statement!of!his!

planned!choice!of!x1.!!It!simply!may!not!be!in!his!interest!to!do!so.!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 13 The vectors y and w may have elements in common. That is, both the feasible set and various outcome functions 

may depend upon the same exogenous parameters; e.g., the ambient temperature.

14 That is, !!: R!×R! → R for ! = 1, ... , !. 15 In the absence of this knowledge, another part of the task would be to predict, or forecast, the future values of the 

exogenous variables, (y1,w1).
25

By!far!the!most!common!approach!to!the!prediction!aspect!of!the!task!is!to!assume that!the!

DM!makes!his!choices!with!the!goal!of!optimizing!one of!the!outcome!functions!discussed!

above.!!For!ease!of!notation,!let!the!“first”!of!many!possible!outcome!functions!denote!the!

firm’s!total!expenditure!on!productive!inputs:!!i.e.,!O1(x1,w1)!=!E(x1,w1).!!Then,!the!analysis!

proceeds!under!the!hypothesis!that!the!choices!of!decision!variables!that!will!pertain!under!

parameter!values!(y1,w1)!are!given!by

!! ∈ !∗(!!, !!) = argmin! ! !, !! : ! ∈ !(!!)

The!optimization!hypothesis!can!then!be!used!to!define!a!value(function associated!with!the!

outcome!function!of!interest.!!The!value!function!associated!with!the!DM’s!expense!

outcome!function,!E(x,w1),!and!feasible!set,!F(y1),!is!its!minimum!cost!function:

! !!, !! = min!{! !!, !! : !! ∈ !(!!) }

At!this!point,!the!analyst’s!task!is!straightforward.!!Once!the function!C has!been!specified,!

all!that!is!required!is!to!evaluate!it!at!two!different!points!and!calculate!the!difference:!i.e.,!

Δ! = ! !!, !! − ! !!, !! .

There!exist!a!wide!variety!of!analytical!specifications!and!software!implementations!

designed!to!solve!such!optimization!problems.16!!!!The!literature!on!applied!optimization!

analysis!is!immense.17!!There!are!both!sophisticated,!general!purpose!software!

optimization!packages!(e.g.,!Mathematica,!MATLAB)!as!well!as!custom!built!packages!

designed!to!solve!particular!problems.!!Given!this!wide!universe!of!possible!analytical!and!

numerical!approaches!to!the!general!constrained!optimization!problem,!why!have!we!

chosen!the!tried!and!true!Linear!Programming!approach!to!the!problem?

The!answer!is!quite!simple.!!Our!task!is!not to!derive!optimal!decisions!for!the!Postal!

Service.!!Rather,!our!goal!is!to!develop!an!analytical!tool!to!provide!the!Commission!with!

insights!into!the!likely!cost!savings!that!would!emerge!from!a!system!wide!change!in!Postal!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 16 Obviously, if a technique can solve the optimization problem for original parameter values (w0

,y0), it can likely 

solve it for (w1,y1) as well. The difference is exactlyΔE, completing the analysis. 17 For a recent thorough introduction to the subject, see Wilhelm Forst and Dieter Hoffmann, Optimization—Theory 

and Practice, Springer 2010
26

Service!operating!procedures.!!If,!for!example,!our!goal!were!to!design!work!schedules!for!

mail!processing!employees!at!a!particular!center!for!a!particular!time!period,!we!would!

seek!to!obtain!(or!have!designed)!the!most!directly!applicable!software!optimization!

package.18!!We!would!then!run!that!package!for!various!relevant!parameter!values,!thereby!

obtaining!the!desired!“before!and!after”!measure!of!the!cost!savings!for!that!particular!

facility.

However,!in!order!for!an!analytical!tool!be!useful!for!evaluating!system!wide!changes,!it!

must!be!recognized!at!the!outset!that!the!analysis!is,!at!best,!an!approximation!of!the!real!

world!operating!environment.!!The!flexibility!and!versatility!of!the!Linear!Programming!

methodology!makes!it!especially!useful!for!this!task.

The!next!subsection!describes!the!Linear!Programming!formulation!we!propose!to!use!for!

a!“before!and!after”!analysis!of!Postal!Service!policy!changes.!!The!following!subsection!

briefly!outlines!the!characteristics!of!an!econometric!analysis!of!postal!operations.!!We!

believe!that!such!an!analysis!would!complement!ours.!

2.1.1&Linear&Programming

The!methodological!approach!we!adopt!to!perform!the!above!calculation!is!Linear!

Programming.!!Linear!Programming!is!designed!to!deal!with!a!particular!subclass!of!the!

general!Mathematical!Programming!problem!described!above.!!It!assumes!that!the!

objective!function!is!a!linear!function!of!the!decision!variables,!w.x,!and!the!feasible!set!is!

characterized!by!the!set!of!linear!inequalities!given!by!the!matrix!equation!Ax < b.

19

2.1.2&Econometric&estimation

An!alternative,!often!complementary,!approach!is!to!specify!an!econometric!model!that!allows!

the!analyst!to!identify!and!estimate!a!behavioral!cost!function,!C(w,y).!!This!function!is!called!a!

behavioral!cost!function!because!it!does!not!require!the!analyst!to!assume!a!specific!objective!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 18 We have asked Postal Service operations managers to identify such packages, but have not, as yet, received a 

response.

19 In terms of the general model described above, the elements of the matrix A and vector b are made up of the 

elements of the parameter vector y.
27

function!on!the!part!of!the!decisionPmaker!in!choosing!the!elements!of!x.!!!The!only!assumption!

required!is!that!the!rules!and!procedures!the!decisionPmaker!uses!choose!the!elements!of!x,!are!

the!same!over!time.!!Under!this!weak!assumption,!the!behavioral!cost!function,!C(w,y),

recovers!the!actual!relationship!between!the!decisionPmaker’s!actual!cost!of!production!and!

input!prices,!w,!and!the!output!vector,!y.!!Using!this!econometrically!estimated!behavioral!cost!

function,,!the!analyst!can!compute!fitted,or!predicted,values!of!C at!the!parameters!of!interest!

and!compute!their!difference,!just!as!above.20!!

An!econometric!study!requires!data!on!costs,!input!prices!(wit)!and!the!vector!(yit).!!!Estimating!

a!cost!function!for!daily!mail!processing!is!possible!using!MODS!operations!data!because!it!is!

collected!at!the!operating!tour!level!each!day!at!more!than!300!mail!processing!facilities.!!!The!

relative!homogeneity!in!mail!processing facilities!across!the!country!makes!it!feasible!to!pool!

data!MODS!data!across!facilities!and!over!time!in!order!to!estimate!of!behavioral!cost!function.!!!

Specifying!a!flexible!functional!form!in!y,!will!allow!an!assessment!of!the!extent!to!which!

production!cost!increases!at!an!increasing!rate!when!daily!mails!volume!are!high,!which!would!

be!indicative!of!the!existence!of!peakPperiod!costs.!

The!behavioral!cost!function!model!could!also!be!estimated!at!different!levels!of!time!

aggregation!to!assess!the!extent!to!which!peakPperiod!costs!occur!on!a!daily!versus!weekly!or!

monthly!basis.!!!For!example,!a!daily!analysis!could!look!at!the!impact!of!dropping!to!5Pday!

delivery!on!the!Monday!mail!processing!peak.!!!Alternatively,!the!weekly!or!monthly!analysis!

could!look!at!the!impact!of!5Pday!delivery!on!the!cost!of!processing!the!Christmas!time!mail!

peak.!!!Certain!elements!of!x!could!be!assumed!to!be!fixed!in!the!daily!analysis,!but!this!

assumption!could!be!relaxed!in!the!weekly!or!monthly!analysis!to!reflect!the fact!that!more!

inputs!are!flexible!over!longer!time!horizons.!!!The!daily!or!even!tourPlevel!analysis!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 20 Empirical work on regulated and government-owned firms finds statistically and economically significant 

deviations from least-cost production, so that most econometrically estimated cost functions are behavioral cost 

functions that requiring only the existence of stable decision rules for their validity.
28

Other!areas,!besides!mail!processing.!could!be!studied!for!the!existence!of!increasing!costs!with!

mail!volume!increases,!as!long!as!there!is!available!data!on!the!costs!of!the!activity,!C,!the!input!

prices,!w,!and!the!vector!of!output!and!other!service!measures,!y.!!For!example,!using!a!dataset!

on!daily!carrier!route!delivery!times,!an!econometric!model!of!the!cost!mail!delivery!could!be!

estimated!and!a!counterfactor!analysis!of!the!impact!of!5Pday!delivery!on!delivery!costs!in!the!

remaining!days!could!be!computed.!!!Another!example!is!the!cost!of!longPhaul!transportation.!!!

Using!a!dataset!on!USPS!contracts!for!longPhaul!transportation!an!econometric!model!of!the!

cost!of!longPhaul!mail!transportation!could!be!estimated!to!perform!a!counterfactual!analysis!of!

the!changes!in!mail!volumes!across!days!of!the!week,!weeks!of!the!year,!or!months!of!the!year!

on!postal!costs.

If!the!Postal!Regulatory!Commission!is able!to!gain!access!to!updated!USPS!datasets!that!were!

formerly!used!in!Postal!Rate!Commission!ratePsetting!proceedings,!these!dataset!can!provide!a!

rich!source!of!information!to!estimate!econometric!models!of!how!postal!costs!are!actually!

incurred!and!thereby!provide!a!method!for!estimating!the!cost!changes!associated!with!

significant!changes!in!the!level!and!distribution!of!postal!mail!volumes!across!days!of!the!year

3.&&Peak&Load&Costs&in&Mail&Processing

This!section!develops!the!model!introduced!by!two decades!ago!by!Crew,!Kleindorfer!and!

Smith!(CKS)21.!!It!highlights!the!peak!load!issues!caused!by!the!service!standard!

requirements!on!preferential!mail!as!well!as!their!partial!mitigation!from!the!ability!to!

defer!non!preferential!mail.!!We!analyze!a!simple!two!period,!two!input,!two!product!

version!of!their!model.!!This!enables!us!to!develop!simple!algebraic!solutions!for!the!

optimal!policies,!with!and!without!constraints.!!Then,!we!derive!simple!formulas!for!the!

difference!between!the!minimized!costs!with!and!without!service!standards,!which!allows!

us!the!measure.!!We!also!employ!the!model!to!derive!a!simple!formula!for!calculating!the!

costs!savings!that!results!from!shifting!a!unit!of!preferential!mail!from!the!high!cost!period!

to!the!low!cost!period.!!The!model!presented!here!is!quite!simple,!in!order!to!highlight!the!

underlying!intuition.!!However,!the!most!general!version!of!the!CKS!model!is!also!a!Linear!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 21 Michael A. Crew, Paul R. Kleindorfer and Marc A. Smith, “Peak-Load Pricing in Postal Services,” Economic 

Journal, 100, (September 1990), 793-807.
29

Program.!!Thus!it!is!straightforward!to!add!additional!variables!(classes!of!mail,!time!

periods)!and!constraints!(lengths!of!shifts,!hours!per!week)!for!a!more!detailed!

quantitative!analysis.

Following!CKS,!we!assume!that!the!day!is!divided!into!two!time!periods!or!Tours!(t(=(1,2)!

and!there!are!two!classes!of!mail,!preferential!mail!and!non!preferential!whose!volumes!in!

period!t are!given!by!Pt and!Nt, respectively.!!(Let!P=P1+P2 and!N=N1+N2,!respectively,!

denote!the!total!volumes!of!preferential!and!non!preferential!mail!and!let!V=P+N denote!

the!total!volume!of!mail!over!the!demand!cycle.) We!assume!that!most!preferential!mail!

arrives!on!Tour!1,!so!P1 >!P2.!!(Let!Δ =!P1 – P2 denote!the!size!of!the!peak!in!preferential!

mail.)!!In!view!of!recent!trends!in!mail!volumes,!we!also!assume!that!N >!P.

22((

Non!preferential!mail!can!be!deferred!one!period!without!processing,!but!preferential!mail!

must!be!processed!during!the!period!in!which!it!arrives.!!(Let!Yt denote!the!volume!of!non!

preferential!mail!processed!during!period!t.)!!It!is!assumed!that!labor!can!be!adjusted!over!

the!day,!but!processing!capacity!cannot.!!(Let!Lt denote!the!amount!of!labor!employed!in!

period!t.)((Each!unit!of!mail!processed!requires!on!unit!of!labor!and!one!unit!of!machine!

processing!capacity!(M).!!The!price!of!a!unit!of!machine!capacity,!which!is!available!for!use!

on!both!Tours,!is!denoted!by!m.!!The!basic!wage!rate,!paid!to!labor!on!Tour!2!is!denoted!by!

w1 =!w.!!Tour!1!labor!is!paid!a!wage!premium!of!100ρ per!cent,!so!that!w1 =!(1+ρ)w.!!Table!1!

summarizes!the!notation!used!in!our!mail!processing!example.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 22 See, for example, U.S. Postal Service Office of Inspector General, Risk Analysis Research Center, Report 

Number: RARC-WP-11-008. As noted above, the model can be analyzed with many patterns of volume over 

service category and arrival times. In this 2×2×2 model, this realistic assumption serves to reduce the number of 

analytical cases that need be presented.
30

Table&1:&&Notation&used&in&the&Mail&Processing&ExamplePt =!volume!of!

preferential!mail!in!period!t=1,!2.

P(=(P1 +!P2 =!total!volume!of!preferential!mail

Δ =!P1 – P2 >!0!measures!the!variability!of!preferential!mail!across!periods

Nt =!volume!of!non!preferential!mail!in!period!t(=(1, 2.

N(=(N1 +!N2 total!period!volume!of!non!preferential!mail!

V(=(N(+(P =!total!volume!of!mail!

Yt = amount!of!non!preferential!mail!processed!in!period!t(=(1,2.

M(=(machine!processing!capacity.

Lt =!labor!hired!in!period!t =!1,!2.

w(=(w2 =!base!(period!2) wage!rate

ρ =(shift!wage!premium

(1+ρ)w = w1 =!wage!rate!in!period!1.

m(=(unit!cost!of!machine!processing!capacity

Thus,!in!this!example,!the!cost!minimization!problem!facing!the!manager!of!the!mail!

processing!center!is!to:!

min L ,L ,M ,Y ,Y {w(1+ )L1 + wL2 + mM} 1 2 1 2 ρ

This!minimization!is!subject!to!(1)!Technological!constraints!that!each!unit!of!mail!have!

available!the!required!amount!of!labor!and!machine!processing!capacity;!and!(2)!Quality!of!

service!(dispatch)!constraints!that!requires!preferential!mail!to!be!processed!during!the!

period!it!arrives!and!that!all!the!mail!be!processed.!!That!is,

; 1,2 M ≥ Pt +Yt Lt ≥ Pt +Yt Y1 +Y2 ≥ N t =

Clearly,!this!problem!is!a!(very)!simple!Linear!Programming!problem.!!The!objective!

function!is!a!linear!function!of!(three!of)!the!(five)!decision!variables!and!the!feasible!set!is!

determined!by!five!linear!inequality!constraints.

This!illustrative!mail!processing!LP!problem!is!“small”!enough!to!derive!simple,!intuitive!

formulas!for!the!optimal!solutions!in!two!parametric!cases!of!interest.!!The!logic!of!the!
31

analysis!is!as!follows.!!Because!preferential!mail!must!be!processed!during!the!period!in!

which!it!arrives,!it!is!certainly!necessary!that!installed!machine!capacity!must!be!at!least!as!

large!as!Tour!1!preferential!mail!volumes:!i.e.,!M > P1 >!P2.!!Then,!the!operations!manager!

must!decide!how!much!of!the!non!preferential!mail!to!process!in!each!period.!!Here,!there!

is!a!tradeoff!between!efficient!capacity!utilization!and!incurring!shift!premium!costs:!!Either(

additional!machine!capacity!must!be!installed!to!process!all!non!preferential!volumes!in!

period!2,!or some!of!the!non!preferential!mail!must!be!processed!using!higher!priced!

period!1!labor.!!The!solution!depends!quite!intuitively!upon!whether!machine!capacity!is!

“cheap”!or!“expensive”!relative!to!the!size!of!the!Tour!1!wage!premium:!i.e.,!whether!m(<(

wρ or!m(>(wρ.

Case!(i):!!Capacity!is!cheap,!so!that!it!is!optimal!to!install!enough!capacity!so!that!all non!

preferential!mail!can!be!processed!in!period!2,!thereby!minimizing!the!amount!of!shift!

premium!wages!paid.!!The!optimal!solution!requires!M(=(Y2 = P2!+!N,!Y1 =!P1 and!the!

(minimized)!costs!of!providing!mail!processing!services!are!given!by:!!

( , , ; , , ) (1 ) ( )( ) Ci P1 P2 N ρ w m = w + ρ P1 + w+ m P2 + N

The!intuition!behind!these!results!is!as!provided!by!the!following!thought!experiment.! If

sufficient!machine!capacity!were!installed!to!serve!Tour!2!preferential!mail!and!all non!

preferential!mail!there!would!be!enough!capacity!to!serve!Tour!1!preferential!mail!as!well!

as!long!as!total!non!preferential!volumes!are!at!least!as!large!as!preferential!volumes.23!!

Now,!imagine shifting!one!unit!of!non!preferential!mail!to!Tour!1.!!Doing!so!would!allow!

you!to!reduce!machine!capacity!by!one!unit,!saving!an!amount!equal!to!m.!!However,!you!

would!then!incur!the!wage!premium!on!one!additional!unit!processed!during!Tour!1,!at!an!

added!cost!equal!to!wρ.!!When!capacity!is!cheap!(m(<!wρ)!this!does!not!pay.

Case!(ii):!!Capacity!is!expensive,!so!that!it!is!optimal!to!schedule!non!preferential!mail!so!as!

to!fully!utilize!capacity!in!both!periods.!!Then,!the!optimal!solution!requires!M(= Y1 =!Y2 =!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 23 That is, M = P2 + N implies M > P1 whenever N > P = P1 + P2.
32

(P1 +!P2 +!N)/2,!so!that!some!non!preferential!mail!is!processed!in!period!1.!!The!

(minimized)!costs!of!providing!mail!processing!services!are!given!by:

( , , ; , , ) [ (2 ) ]( )/ 2 [ (2 ) ] / 2 Cii P1 P2 N ρ w m = w + ρ + m P1 + P2 + N = w + ρ + m V

Again,!the!intuition!behind!the!results!can!be!obtained!from!a!simple!thought!experiment.!!

When!machine!capacity!is!expensive,!it!makes!sense!to!conserve!it!by!fully!utilizing!

capacity!on!both!Tours:!M(= V/2.!!Now,!imagine,!shifting!one!unit!from!Tour!1!to!Tour!2!in!

order!to!avoid!the!Tour!1!wage!premium.!!The!resulting!wage!savings!are!wρ.((However,!an!

additional!unit!of!machine!capacity!must!be!installed!to!process!this!mail!on!Tour!2,!

increasing!machine!costs!by!the!amount!m.!!When!capacity!is!expensive!(m(> wρ),!this!does!

not!pay.

3.1&What&determines&Peak&Load&Costs?

We!have!derived!simple!formulas!for!total!costs!that!reflect!various!parameter!values!and!

constraints.!!Intuitively!(as!well!as!mathematically),!there!are!three!reasons!to!suspect!that!

the!resulting!level!of!costs!is!higher!than!it!might!be!in!other!circumstances.!!

Consider!first!the!impact!of!the!period!1!wage!premium.!!Clearly,!C1A,!C1B and!C1C are!all!

increasing!functions!of!the!wage!premium,!ρ.!!Thus!it!is!tempting!to!consider!identifying!the!

total!amount!paid!in!shift!premiums as!“peak!load!costs”.!!However,!this!is!not!appropriate.!!

In!a!competitive!labor!market,!the!shift!premium!is!merely!a!cost!of!doing!business.!!

Certainly,!mail!processing!costs!would!be!lower!if!period!1!wage!rates!were!lower.!!

However,!this!has!nothing!to!do!with!the!peaking!structure!of!postal!operations.!!Mail!

processing!costs!would!also!be!lower!if!period!2!wage!rates!and/or!equipment!costs!were!

lower.!!As!we!shall!see,!the!amount!of!appropriately!measured!peak!load!costs!may!depend!

upon!the!value!of!ρ.!!But!they!will!also!depend!upon!the!values!of!w and!m.!!In!terms!of!the!

present!model,!we!are!left!with!two!“peak!load”!sources!of!added!mail!processing!costs:!!

service!standards!and!the!arrival!behavior!of!preferential!mail.

3.1.1&The&cost&of&service&standards.

All!that!is!necessary!to!measure!the!cost!of!the!service!standard!that!requires!preferential!

mail!to!be!processed!in!the!period!in!which!it!arrives!is!to!compare!the!minimized!costs!
33

derived!above!to!the!costs!that!would!be!incurred!if!it!were!possible!to!“roll!the!mail:”!i.e.,!

process!it!whenever!possible!without!regard!to!arrival!time.!!Again,!the!result!differs!

depending!upon!whether!machine!capacity!is!“cheap”!or!“expensive.”!!When!capacity!is!

cheap!and!there!are!no!service!standards,!it!is!optimal!to!install!enough!capacity!so!that!all!

mail!is!process!during!period!2.!!On!the!other!hand,!when!capacity!is!expensive,!the!optimal!

solution!in!the!absence!of!service!standards!involves!dividing!total!volume!equally!across!

the!two!periods.!!The!“roll!the!mail”!cost!functions!for!the!two!cases!are!given!by:!

2

( ) ( , , ; , , ) 1 2w m V Cc P P N w m+

ρ =

2

[ (2 ) ] ( , , ; , , ) 1 2w m V Ce P P N w m+ + = ρ ρ

It!is!now!possible!to!derive!formulae!for!the!cost!of!service!standards!for!the!two!cases:

(i)!Cheap!Capacity:!!In!this!case!service!standard!costs!are!given!by:

SS(i) =!C(i) – Cc =!w(1+ρ)P1 +!(w+m)(P2+N)!– (w+m)V !!!!!!!=!wρP1 – mP1

When!capacity!is!cheap,!“rolling!the!mail”!results!in!an!expansion!of!capacity,!the!costs!of!

which!partially!offset!the!elimination!of!premium!wages.!

(ii)!Expensive!Capacity.!!The!difference!between!minimized!costs!with!and!without!service!

standards!is

SS(ii) =!C(ii) – Ce =!w(1+ρ)P1+w(P2+N)+mV/2!– (2w+wρ+m)V/2!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!=!wV +!wρP1!+!mV/2!– (2w+wρ+m)V/2!=!0

In!this!case,!the!high!cost!of!capacity!makes!it!optimal!to!process!one!half!of!total!mail!

volumes!in!each!period,!both!with!and!without!service!standard!constraints.!!Shift!premium!

costs!of!wρ(V/2)!are!incurred!in!either!situation.!!Since!the!optimal!mail!processing!

configuration!remains!unchanged!after!the!relaxation!of!the!service!standard,!the!

appropriately!measured!service!standard!costs!are!zero.
34

3.1.2&&Cost&savings&from&smoothing&the&peak&

Even!with!service!standards!in!place,!it!may!be!possible!to!induce!some!preferential!

mailers!to!change!their!behavior!so!that!their!volumes!arrive!during!Tour!2.!!If!it!is!

necessary!to!induce!mailers!to!shift!their!deposits!of!mail!by!offering!a!discount,!it!is!

important!to!determine!how!much!is!saved!by!shifting!a!small!amount!(one!unit)!of!

preferential!mail!from!Tour!1!to!Tour!2

The!cost!savings!from!such!smoothing!can!be!analyzed!more!easily!when!costs!are!

rewritten!in!terms!of!total!volumes!and!peak!size,!Δ.

C(i) =!w(1+ρ)(P+Δ)/2!+!(w+m)[(P–Δ)/2+N];

C(ii) =!w(1+ρ)!(P+Δ)/2 + w[(P–Δ)/2+N)] + mV/2!;

When!capacity!is!cheap,!shifting!1/2!unit!from!Tour!1!to!Tour!2!(so!that!Δ increases!by!one!

unit)!necessitates!an!increase!in!capacity,!which!reduces!the!cost!savings:!

dC(i)/dΔ =!(wρ–m)/2

When!capacity!is!expensive,!the!shift!of!1/2!unit!of!preferential!mail!from!Tour!1!to!Tour!2!

has!no!effect!on!optimal!machine!capacity!so!that:

dC(ii)/dΔ =!wρ/2.

3.2&Excess&Capacity&Considerations

The!above!analyses!have!been!carried!out!from!the!economist’s!typical!“timeless”!or!“long^

run”!perspective.!!That!is,!it!is assumed!that!one!is!designing!a!facility!“from!the!ground!up,”!

before!any!resources!are!committed!to!facilities,!machines,!or!labor!contracts.!!Thus,!one!is!

free!to!vary!machine!capacity!from!one!scenario!to!another!in!order!to!achieve!the!least!

cost!feasible!configuration.!!However,!under!current!circumstances,!the!proposals!for!

service!standard!reductions!and!other!cost!saving!initiatives!are!associated!with!significant!

declines!in!mail!volumes.!!Thus,!it!is!also!necessary!to!consider!the!cost!implications!of!
35

service!standard!changes!in!cases!in!which!the!postal!operator!has!a!large!amount!of!

available!machine!processing!capacity!that!cannot!be!reduced!over!the!planning!horizon.

Fortunately,!this!possibility!is!easily!handled!within!the!current!framework.!!Formally,!one!

assumes!that!there!is!an!initial!(“legacy”)!level!of!machine!capacity,!M0,!that!has!already!

been!paid!for!and!is!freely!available!for!use!in!both!periods.!!Then!the!technological!

constraints!on!machine!resources!become!M0 +!M > Pt +(Yt;!t = 1,2.!!For!a!large!enough!level!

of!legacy!capacity!(i.e.,!M0 >!P2+N),!the!machine!capacity!constraints!will!not!be!binding!in!

either!period!for!the!current!volume!levels.!!The!solution!to!the!problem!then!becomes!

even!simpler,!with!the!optimal!values!of!the!decision!variables!given!by:

0; ; ; ; 0. Y1 = Y2 = N L1 = P1 L2 = P2 + N M =

The!minimized!level!of!costs!is!then:

0 0

1 2

0

2

( ) (1 ) ( ) wV mM w P C w P w P N mM + ++ Δ = + + + + = ρ ρ

3.2.1&Peak&Load&Costs&under&excess&capacity

Because!of!the!practical!relevance!of!this!situation,!it!is!worthwhile!to!briefly!summarize!

and!restate!the!results!for!this!case.!!The!cost!of!service!standards!is!just!the!difference!

between!base!costs,!C0,!and!the!cheap!capacity!flow!mail!costs,!Cc:!i.e.,

1 2 1

0 0 SS = C −Cc = w(1+ ρ)P + w(P + N) − wV = wρP

Thus,!in!the!simple!excess!capacity!situation,!the!peak!load!costs!associated!with!service!

standards!are!exactly!equal!to!the!total!amount!of!the!shift!premia!paid!to!process!

preferential!mail!during!Tour!1.

The!analysis!of!peak!shifting!in!the!excess!capacity!case!proceeds!as!before.!!Shifting!one!

half!unit!of!volume!from!Tour!1!to!Tour!2!would!decrease!Δ by!one!unit.!!As!a!result!the!

wage!premium!on!1⁄2!unit!of!volume!would!be!saved.!!Equivalently,!the!cost!savings!from!

shifting!the!marginal!unit!of!volume!to!Tour!2!is!given!by:

2

0 wρ

d

dC = Δ
36

There!is!an!important!caveat!to!keep!in!mind,!both!in!the!context!of!these!simple!models!

and!in!practice.!!The!available!capacity!volume,!M0,!underlying!the!cost!function!C0 was!

presumably!determined!by!capacity!installation!decisions!made!in!the!past,!when!volumes!

were!significantly!larger:!e.g.,!at!P10 >!P1;!P20 >!P2;!and!N0 >!N (and,!of!course,!V0 >!V).!

Suppose!that!those!decisions!were!made!optimally,!i.e.,!to!minimize!costs!to!serve!the!

initial!volumes.!!Obviously,!the!amount!of!capacity!installed!depends!upon!which!case!

pertains!in!the!initial!situation.!!However,!the!largest!possible!value!of!optimally!installed!

initial!capacity!would!be!that!corresponding!to!an!initial!“cheap!capacity”!situation:!i.e,!M0 =!

P20+N0 > V0/2.!!But,!the!optimal!level!of!capacity!that!one!would!need!to!install!to!avoid!

paying!the!Tour!2!wage!premium!under!the!“roll!the!mail”!option!would!be!V.!!Even!if!

volumes!decline!significantly,!it!may!still!be!the!case!that!P20+N0 <!V <!V0.

4.&&A&very%simple&model&of&peak&load&considerations&in&delivery&

Our!basic!approach!can!be!readily!extended!to!analyze!exogenous!changes!pertaining!to!the!

delivery!function.!!Here,!we!present!a!very!simple!example!driven!by!the!variability!of!mail!

over!the!days!of!the!week.!!Mail!volumes!over!the!two!“days”!of!the!week!are!given!by!V1

and!V2,!respectively.!!Again,!total!volume!is!denoted!by!V =!V1!+!V2,!with!the!size!of!peak!

given!by!Δ =!V1 – V2 >!0.!!For!purposes!of!this!example,!no!distinction!is!made!between!

preferential!and!non!preferential!mail.!!The!operations!manager!must!determine!the!

number!of!routes,!R,!established!to!serve!delivery!area!under!study.!!The!per!period!(daily)

wage!cost!of!a!route!is!assumed!to!be!w.!!The!maximum!amount!of!volume!that!can!be!

delivered!on!a!route!each!day!is!assumed!to!be!r.!!For!simplicity,!there!are!assumed!to!no!

costs!that!vary!with!volume!up!to!the!capacity!of!a!route,!but!the!number!of!routes!

operated!is!constant!across!the!week.!

Given!these!assumptions,!the!operations!manager’s!problem!is!to!

minR C =!2wR!!!subject!to: R > V1/r!! and!!!R > V2/r

Clearly,!this!is!also!a!(very!simple)!Linear!Programming!problem.!The!objective!function!is!

a!linear!function!of!the!(single)!decision!variable!and!there!are!two!linear!inequality!
37

constraints.!!Obviously,!the!cost!minimizing!solution!is!for!the!operations!manager!to!

choose!a!number!of!routes!that!is!just!adequate!to!serve!the!high!volume!day,!R(=(V1/r,!

recognizing!that!there!will!be!excess!“delivery!capacity”!on!the!off!peak!day.!!!Then,!the!

minimized!level!of!delivery!costs!is!given!by:

C =!2wV1/r(=(w(V+Δ)/r

4.1&Peak&Load&Costs&in&the&delivery&model&

There!are!two!obvious!sources!of!peak!load!costs!in!this!simple!delivery!model.!The!first!is!

the!work(rule constraint!that!the!number!of!routes!must!be!constant!over!the!“week.”!!The!

second!source!of!added!costs!is!the!variability!of!mail!across!days.!!As!in!the!mail!

processing!example,!the!procedure!to!analyze!these!costs!is!derive!the!solutions!to!

counterfactual!“relaxed”!and!“smoothed”!versions of!the!delivery!model!and!subtract!the!

resulting!level!of!minimized!costs!from!the!level!of!minimized!costs!in!the!base!case.!

First!consider!the!case!in!which!work!rules!have!been!relaxed!so!that!the!operations!

manager!no!longer!has!to!operate!the!same!number!of!routes!each!day!of!the!week.!!Now,!

the decision!problem!is!to!

minR1,R2 Cx =!w(R1+R2)!!!subject!to: R1 > V1/r and!R2 > V2/r

The!obvious!solution!to!this!simple!Linear!Programming!problem!is!for!the!operations!

manager!to!choose!exactly!the!required!number!of!routes!for!each!day.!!Thus,!the!optimal!

numbers!of!routes!are!given!by!R1 =(V1/r(and!R2 =!V2/r and!the!level!of!minimized!costs!is!

given!by:

Cx =!w(V1+V2)/r(=(wV/r

Then,!the!peak!load!cost!savings!from!relaxing!delivery!work!rules!is

WRd =(C – Cx =!2wV1/r(– w(V1+V2)/r(=!w(V1–V2)/r =!wΔ/r
38

Next,!let!us!examine!the!cost!savings!that!would!result!if!mailers!could!be!induced!to!shift!

1⁄2!of!a!unit!of!mail!from!day!1!to!day!2.!!Again,!this!would!decrease!Δ by!one!unit.!!

Differentiating!the!minimized!cost!function!with!respect!to!Δ yields

dC/dΔ =!w/r

The!cost!savings!from!shifting!a!unit!of!volume!from!peak!to!off!peak!is!efficient!cost!per!

unit.

5.&&Peak&Load&Costs&in&Ground&Transportation:&Relaxing&Service&

Standards

The!example!we!analyze!involves!two!mail!processing!centers!(A!and!B)!that!transport!mail!

volumes!to!each!other!over!a!two!period!cycle.!!Because!of!service!standards,!each!center!

must!ship!available!volumes!to!the!other!in!each!period.!!In!period!1,!center!A!ships!volume!

A1 to!center!B!and!center!B!ships!volume!B1 to!center!A.!!The!trucks!involved!make!a!

roundtrip!loop,!so!the!same!total!capacity,!T1,!is!always!available!on!trip!AB!as!on!trip!BA.!!

Similarly,!in!period!2,!center!A!ships!volume!A1 to!center!B!and!center!B!ships!volume!B1 to!

center!A!using!T2 units!of!trucking!capacity.!!Let!t denote!the!cost!of!employing!a!unit!of!

roundtrip!trucking!capacity.!!While!many!combinations!of!relative!volumes!are!possible,!we!

analyze!the!case!in!which!A1 >!B1 and!A2!<!B2.

The!transportation!manager’s!scheduling!problem!in!this!example!involves!choosing!the!

level!of!trucking!capacity!to!dispatch!in!each!period.!!That!is,

min ( ) , 1 2 1 2 T T t T +T !!subject!to T1 > A1; T1 > B1; T2 > A2; T2 > B2

Again,!this!is!a!simple!Linear!Programming!problem.!!The!objective!function!and!

constraints!are!linear functions!of!the!decision!variables.!!Many!combinations!of!relative!

volume!levels!are!possible.!!However,!we!analyze!the!case!in!which!A1 >!B1 and!A2!<!B2.!!The!

optimal!solution!is,!obviously,!to!choose!a!level!of!trucking!capacity!equal!to!the!maximum!

directional!demand!in!each!period:!i.e.,!T1 =!A1 and!T2 =!B2.!!Then,!the!minimized!level!

transportation!costs!is!given!by!C0 =!t(A1 +!B2).
39

Now!consider!the!new!problem!facing!the!transportation!manager!after!the!service!

standard!has!been!relaxed,!so!that!he no!longer!has!to!transport!volumes!during!the!period!

in!which!they!become!available.!!His!problem!is!then!to!

minT tT!!subject!to T > A1 +!A2; T > B1!+!B2

The!obvious!solution!to!this!Linear!Programming!problem!is!to!choose!a!level!of!trucking!

capacity!sufficient!to!carry!the!larger!of!the!aggregate!directional!volumes.!!That!is,!T =!

max{ A1+A2, B1+B2}!and!Cx =!t max{ A1+A2, B1+B2}.!!Then!the!cost!savings!from!relaxing!the!

service!standards!are!given!by:

C0 – Cx = t(A1 +!B2)!– t max{ A1+A2, B1+B2}!=!t(min{A1–B1,B2–A2}!>!0.

6.&Towards&empirical&analysis.

As!demonstrated!in!the!Technical!Appendix,!the!approach!we!have!outlined!can!be!readily!

implemented!using!Microsoft!Excel.!!However,!as!yet!we!have!produced!no!“real!numbers:”!

i.e.,!calculations!that!purport!to!approximate!actual!Postal!Service!operations.!!To!

implement!our!approach!quantitatively,!we!would!need!to!“know”!as!much!as!possible!

about!the!parameters!of!the!model;!e.g.,!wage!rates,!labor!rules,!mail!volumes,!the!time!

pattern!of!mail!flows!to!processing!plants!and!delivery!units,!interplant!transport!data,!etc.!!

The!disaggregated!the!data!the!more!useful!it!would!be.!!For!example,!the!analysis!would!

be!more!accurate!using!a!mail!processing!plant’s!hourly mail!arrival!pattern!rather than!its!

daily!totals.!!Similarly,!the!delivery!process!is!better!analyzed!using!data!disaggregated!

down!to!the!level!of!daily!volume!on!each!route!rather!than!aggregate!volume!data!on!a!

delivery!unit!over!a!month.

Not!surprisingly,!this!is!precisely!the kind!of!data!that!an!econometrician!would!seek!into!

order!to!perform!an!empirical!study.!!However,!the!information!requirements!of!our!Linear!

Programming!approach!are!much!more!modest!than!those!of!a!serious!econometric!study.!!

Specifying!and!estimating!an!econometric!model!would!require!an!extensive!panel!data!
40

set24 to!be!deemed!successful.!!In!contrast!our!approach!requires!only!a!point!estimate!or!

“best!guess”!for!each!parameter!of!interest.!!If!a!statistical!estimate!with!a!small!standard!

error25 were!available,!we!would!certainly!make!use!of!it.!!However,!in!the!absence!of!

tightly!estimated!statistical!values,!a!single!value!from!a!“typical”!plant!or!delivery!unit!

would!allow!us!to!implement!the!analysis.

6.1&Examples&of&data&required&for&an&empirical&analysis

This!subsection!provides!a!brief!discussion!of!the!types!of!data!required!for!a!thorough!

empirical/quantitative!analysis!and!likely!Postal!Service!sources.!!Additional!details!are!

provided!in!section!7!of!the!main!report.

6.1.1&Mail&Processing

As!was!illustrated!in!the!mail!processing!example,!mail!arrival!patterns!by!day!and!hour!are!

among!the!most!important!drivers!of!peak!load!costs!in!mail!processing.!!Thus!it!would!be!

useful!to!have!data!on!First!Handled!Pieces!by!plant.!!This!should!be!available!from!MODS.!!

Other!useful!disaggregate!information!on!the!time!pattern!of!mail!arrivals!by!plant!should!

be!obtainable!from!Permit!Mail!Statements!and!IMB!data.!!Disaggregate!data!on!mail!

processing!labor!hours!worked!should!be!available!from!the!TACS!data!set.

6.1.2&Delivery

Weekly!and!seasonal!variability!seems!to!be!the!primary!driver!of!peak!load!costs!for!

delivery!units.!!Mail!volumes!by!day!and!route!should!be!available!from!the!DOIS!data!set.!!

Again,!labor!hours!worked!by!route!should!be!available!from!TACS.!

6.1.3&Highway&Transportation

In!the!highway!transportation!example!discussed!above,!peak!load!costs!were!ultimately!

driven!by!mismatches!in!directional!mail!flows!between!mail!processing!units.26!!Contract!

data!from!the!HCCS!data!set!would!be!required!to!determine!the!Postal!Service!cost!of!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 24 That is, observations on, say, Tour 1 labor hours for each of many mail processing centers, over a time period of 

many months: i.e., a “time series” of “cross-sections.” 25 For example, a sample average taken over a large number of plants. 26 In transportation terminology, relaxing service standards may mitigate the backhaul problem.
41

hiring!truck!capacity.!!Capacity!utilization!levels!by!route!should!aid!in!quantifying!the!

magnitude!of!the!problem.!!This!may!be!available!from!TRACS!data.

Appendix&B: Linear&Programming Models&of&Peak&Load&Costs

1.&&Introduction

Peak!load!costs!for!the!Postal!Service!arise!from!the!combination!of!uneven!mail!arrival!

rates,!service!standards,!and!labor/capacity!constraints.!!Mail!arrival!rates!vary!by!hour!of!

day,!day!of!week,!day!of!month,!and!season!of!year.!!Service!standards!vary!by!type!of!mail,!

but!can!be!approximately!characterized!as!preferential!and!non^preferential.!!Both!

preferential!and!non^preferential!mail!can!be!usefully!further!subdivided!into!two!types!

depending!on!the!origin!and!destination!of!the!mail.!!Originating!mail!(also!called!collection!

and!acceptance!mail)!is!mail!being!handled!in!its!first!plant!and!may!be!destined!for!either!

local!or!non^local!plant!areas.!Incoming!mail!originates!in!a!different!plant’s!service!area!

and!destinates!in!the!given!plant’s!service!area.

Most!originating!mail!arrives!after!5!PM!each!day.!The!preferential!mail!portion!has!service!

standards!that!dictate!that!it!must!be!processed!by!a!final!dispatch!time!(also!called!cut^off!

time!or!dispatch!of!value)!between!10!PM!and!midnight.!!As!a!result,!there!is!an!hourly!

peak!during!Tour!3.!!Non^preferential!originating!mail!generally!has!the!same!final!dispatch!

time,!but!it!can!be!delayed!until!the!next!day!if!necessary.!!Incoming!mail!arrival!patterns!

are!similar!to!those!of!originating!mail!but!overnight!committed!mail!usually!arrives!after!

midnight!and!it!has!a!final!dispatch!time!in!the!early!morning,!so!much!of!it!is!processed!

during!Tour!1!which!has!a!peak!period!prior!to!dispatch!to!delivery!offices!at!about!5!AM.!

Figure!1!below!is!an!illustration!of!the!patterns!of!cumulative!arrival!rates!for!originating!

(collection!and!acceptance),!as!well!as!typical!final!dispatch!times!for!these!two!mail!types.!!

In!this!example,!preferential!and!non^preferential!mail!arrival!rates!are!combined.!!It!can!

be!seen!that!originating!mail!has!the!narrowest!window!for!processing.
42

Figure#1.##Example#of#Cumulative#Hourly#Arrival#Rates#with#Final#Dispatch#Times#for#Originating#and#

Incoming#Mail

Delivery!presents!peak!load!issues!similar!to!mail!processing!except!that!there!are!no!

hourly!peaks.!Work!rules!for!the!two!functions!are!different!also.! Rural!and!city!carriers!

are!compensated!differently!and!so!present!different!issues.!The!former!are!paid!by!the!

route!while!the!latter!are paid!by!the!hour.!Establishing!routes!for!rural!carriers!is!done!at!a!

time!of!year!according!to!the!union!agreement!that!represents!neither!a!peak!nor!slack!

period.!Thus!the!carrier!must!work!longer!hours!during!peak!periods!and!fewer!during!

slack!periods.!From!the!Postal!Service!standpoint!the!cost!of!peak!and!slack!periods!

(especially!seasonal!ones)!is!minimized!provided!that!the!period!when!routes!are!

established!is!one!of!average!volume.!

City!carriers,!however!receive!overtime payments!especially!during!peak!periods.!These!
43

routes!may!be!divided!into!sections!which!can!then!be!handed!off!to!part!time,!

temporary,!or!regular!carriers!and,!of!course,!overtime!can!be!used!to!meet!peaks.!In!

addition,!routers!can!be!used!to!perform!the!in!office!duties!of!city!carriers.!Thus,!the!

Service!has!several!means!to!minimize!the!cost!of!day!of!the!week,!day!of!the!month!and!

seasonal!peak!and!slack!periods.

As!an!example!of!delivery!peak!loads,!Table!1!below!shows!typical!variations!in!delivery!

workload!from!Monday!to Saturday,!as!presented!in!the!Commission’s!Advisory!Opinion!in!

the!recent!5^day!delivery!case!(Docket!No.!N2010^1).!!Since!there!is!an!opportunity!to!delay!

delivery!of!non^preferential!mail!by!at!least!one!day,!the!arrival!rates!at!a!carrier!station!

are!likely!to!be!more!variable!than!the!daily!delivered!volumes.

Table#1.##Delivery#Volume#Variations#by#Day#of#Week27

(Percentage&Difference&between&Daily&Volume&and&Average&Daily&Volume)

Day!of!Week Percentage!Difference!

from!Average

Monday +15%

Tuesday +2%

Wednesday +1%

Thursday ^2%

Friday +8%

Saturday ^8%

There!are!also!significant!differences!in!mail!processing!and!delivery!arrival!rates!over!

longer!time!periods!than!a!week.!!For!example,!volume!is!higher!near!the!first!of!the!month.!!

Also,!volumes!are!significantly!higher!in!the!Christmas!period.

In!spite!of!the!large!variations!in!hourly,!daily,!and!longer!period!mail!arrival!rates,!it!would!

theoretically!be!possible!to!process!and!deliver!mail!efficiently!if!labor!resources!were!only!

paid!when!needed,!as!with!electric!power!consumption.!!However,!this!is!not!the!case!since!

there!is!a!very!complex!set!of!rules!that!the!Postal!Service!must!follow!when!scheduling!

and!using!its!labor!resources.!!These!include!requirements!that!most!employees!be!full^

time!regulars,!with!work!schedules!that!require!primarily!8^hour!shifts!(plus!an!hour!for!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 27 Source: PRC Opinion and Recommended Decision, Docket N2010-1, p. 120.
44

lunch!and!breaks)!and!consecutive!five^day!workweeks.!!There!is!some!flexibility!available!

through!the!limited!use!of!part^time!and!casual!employees,!and!through!limited!use!of!

overtime!for!full^time!employees,!although!the!overtime!rates!(which!do!not!include!

benefits)!are!10^15!percent!higher!than!the!regular!hourly!rates!(including!benefits).!

These!labor!constraints,!together!with!the!uneven!mail!arrival!rates!and!service!standards!

result!in!inefficiencies!in!using!resources.!!If!we!consider!the!completely!flexible!

(unconstrained)!labor!scenario!as!the!minimum!cost!option,!then!we!define!peak!load!costs!

as!the!difference!between!the!costs!with!all!constraints!included!and!the!unconstrained!

case.!!Another!useful!measure!would!be!the!percentage!of!total!costs!that!can!be!considered!

peak!load!costs.

Peak!loads!in!transportation!are!also!caused!by!the!daily,!weekly,!monthly!and!seasonal!

variations!in!volume,!but!they!involve!trucking!and!air!capacity!issues!rather!than!labor!

issues.!Most!of!the!Postal!Service’!air!transportation!is!in!the!hands!of!FedEx!who!has!a!

contract!to!transport!most!of!the!volume!requiring!air!transportation.!An!important!issue!

would!be!to!estimate!the!additional!cost!reflected!in!the!FedEx!contract!caused!by!the!

seasonal!variations!in!mail!volume.!

The!Postal!Service!is!responsible!for!securing!its!own!surface!transportation.!It!does!this!by!

purchasing!highway!capacity!over!the!many!routes!that it!transports!mail!on!a!multi^year!

basis!with!the!capacity!sized!to!meet!the!peaks.!This!leaves!overcapacity!much!of!the!time.!

It!may!be!possible!to!buy!reduced!capacity!on!many!routes and!fill!in!from!the!spot!market!

when!required.!Thus,!a!cost!minimization!analysis!could!shed!light!on!the!cost!of!peak!

loads!in!highway!transportation.!Rail!transportation!does!not!present!peak!load!issues!in!

that!it!can!usually!be!purchased!on!the!spot!market!over!all!routes.
45

2. Discussion&of&Proposed&Methodologies&for&Analyzing&Postal&Peak&Load&

Costs

2.1.&&&Introduction

The!RFP!for!this!project!specifies!that!the!Contractor!shall!prepare!a!proposed!

methodology,!or!methodologies,!for!analyzing!peak!load!costs!under!the!constraints!

applicable!to!the!Postal!Service!such!as!labor!union!rules!and!product!specific!service!

standards.!The!methodologies!should!be!able!to!answer!the!following!questions:

1. How!might!delivery!frequency!changes!impact!peak!loads!and!what!are!the!associated!

costs?

2. What!savings!will!be!gained!from!new!flexibilities!in!the!recent!labor!contract!and!when!

will!they!be!achieved?

3. Can!operational!inefficiency!be!quantified?

4. How!do!unit!costs!change with!seasonal!fluctuations!in!volume?

Subsequent!to!the!publication!of!the!RFP!for!this!project,!the!Postal!Service!announced!

plans!for!a!major!overhaul!of!its!entire!operating!system!as!a!means!for!cutting!costs!in!its!

current!declining^volume!environment.!!The!proposed!changes!involve!extending!the!

current!First^Class!delivery!standards!by!one!day,!as!well!as!consolidation!of!the!mail!

processing!network!from!the!current!500+!plants!to!about!250.!!As!a!result,!we!also!

considered!methodologies!that!would!be!useful!in!evaluating!these!major!changes.!!We!

include!this!subject!by!adding!a!fifth!question!to!the!above!list:

5.!!What!additional!savings!will!be!gained!from!relaxing!service!standards!for!First^Class!

mail!and!from!consolidating!the!processing!network?

Question!3!will!be!addressed!by!comparing!our!estimated!minimum!costs!that!reflect!all!

constraints!(hourly,!daily,!and!seasonal)!with!the!actual!costs!for!the!same!time!period.!!

Question!1!will!be!addressed!by!finding!minimum!costs!reflecting!only!hourly!and!day^of^

week!constraints!minus!the!minimum!unconstrained!costs.!!Question!4!will!be!addressed!
46

by!estimating!minimum!costs!that!reflect!all!constraints,!then!subtracting!the!minimum!

costs!from!Question!1.!!Question!2!will!be!answered!by!first!changing!all!constraints!to!

reflect!the!new!labor!agreements,!then!finding!adjusted!minimum!costs!reflecting!all!

constraints,!then!subtracting!the!minimum!unconstrained!cost.!!Question!5!will!be!

addressed!by!first!changing!the!service!standards!and!the!number!of!processing!facilities,!

then!finding!adjusted!minimum!costs!reflecting!all!changes,!then!subtracting!the!minimum!

unconstrained!costs.!

We!considered!several!peak!load!costing!methodologies!for!addressing!the!above!issues.!!

The!first!was!to!use!existing!(commercial)!mail!processing,!delivery!and!transportation!

models!used!by!the!Postal!Service!to!assist!field!managers!with!developing!labor!and/or!

equipment!schedules!for!mail!processing,!delivery,!and!transportation.!!Our!discussions!

with!knowledgeable!USPS!managers!revealed!that!this!approach!would!not!be!viable!

because!these!commercial!models!are!considered!confidential.!!Second,!we!investigated!the!

development!of!an!econometric!approach!to!the!peak!load!cost!problem,!which!is!described!

at!pp!??!below.!!Finally,!we!developed!a!linear^programming!approach!for!estimating!postal!

peak!load!costs.!!Linear!programming!is!a!widely!used!tool!for!solving!cost!minimization!

(or!maximization)!problems!with!many!embedded!constraints.!!

In!Section 2.2,!we!present!an!overview!of!the!linear!programming!(LP)!approach,!along!

with!a!simple!example!of!the!use!of!LP!in!the!mail!processing,!delivery,!and!transportation!

functions.!!In!Part!C,!we!discuss!the!mail!processing,!delivery,!and!transportation!

constraints!in!the!current!environment!in!some!detail,!as!well!as!how!these!constraints!

would!change!in!two!scenarios:!a)!the!current!environment with!the!new!labor!flexibilities!

provided!in!recently^adopted!union!contracts,!and!b)!the!new!environment!with!relaxed!

service!standards!and!fewer!facilities.
47

2.2.&Linear&Programming&Approach&&

2.2.1&Overview&of&Linear&Programming

Linear!programming!is one!of!the!most!common!optimization!techniques!used!in!the!field!

of!Operations!Research.!!It!is!used!to!find!the!minimum!(or!maximum)!value!of!an!objective(

function,!which!consists!of!a!sum!of!terms!involving!a!constant!times!a!decision(variable.!!

One!or!more!constraints are!included!in!the!specification!of!a!problem!which!impose!

limitations!on!the!values!of!the!decision!variables.!!The!linear!programming!solution!

algorithm!finds!the!values!of!all!decision!variables!that!minimize!(or!maximize)!the!value!of

the!objective!function!while!satisfying!all!constraints.

Although!many!linear!programming!software!packages!are!readily!available,!it!is!also!

available!as!a!tool!in!Microsoft!Excel!(Solver!application).!!We!feel!that!Excel!would!be!the!

most!efficient!alternative!because!of!its!widespread!availability,!but!it!may!not!be!feasible!if!

the!number!of!variables!and!constraints!for!the!peak!load!cost!problem!is!too!large.!!To!

illustrate!the!Excel^based!linear!programming!approach,!we!developed!several!detailed!

numerical!examples!of!cost!minimization!problems!in!mail!processing,!using!typical!values!

for!the!required!input!parameters!(including!arrival!rates,!final!dispatch!times,!labor!

constraints,!and!use!of!premium!pay!labor).!!These!examples!are!described!in!Appendix!A.

2.2.2&Mail&Processing&Example

The!following!simple!example!will!be!used!to!illustrate!the!linear!programming!approach!

for!the!mail!processing!function.28!!Assume!we!want!to!find!the!unconstrained!minimum!

total!one^day!cost!of!processing!two!types!of!preferential!mail!^^ originating!and!incoming!^

^ at!a!single!plant.!!Also!assume!that!there!is!only!one!type!of!employee!and!that!no!labor!

constraints!or!premium!costs!are!reflected.!!We!will!also!assume!that!mail!processing!costs!

are!100%!variable!with respect!to!volume,!so!unit!processing!costs!will!not!vary!with!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 28 More complex mail processing examples that incorporate labor constraints and premium pay are presented in 

Appendix C.
48

volume.!!Finally,!we!assume!there!is!adequate!existing!sorting!machine!capacity!to!handle!

the!input!volume.!!So!the!objective!function!for!this!example!can!be!expressed!as:

Minimize!!Σ (h(i,!j)!*!r(i)!*!c !!!!!!!i,j

where! h(i,!j)!=!number!of!employee!hours!(in!all!operations)!assigned!for!mail!type!i

during!hour!j!(the!decision!variables!chosen!by!the!LP!algorithm),!!!!!!!!!!!!!

r(i)!!!=!flow!path!productivity!for!mail!type!i!(first!handling!pieces!per!employee

!!!!!!!!!!!!!!!!!!!!!!!!!!hour),!and

c!!!!!!=!cost!per!employee!hour.

First,!we!need!a!set!of!non^negativity!constraints!for!the!decision!variables:

h(i,!j)!>=!0!for!all!i!and!j.

Next,!we!need!a!set!of!constraints!that!restricts the!total!processed!volume!for!type!i!during!

hours!1!through!k!to!be!no!more!than!the!cumulative!arrivals!of!type!i!mail!at!each!hour!k!

(see!Figure!1):

k

Σ ((h(i!,j)!*!r(i))!!<=!!v(i,!k)!!for!all!i!and!k

j=1

where!v(i,!k)!=!cumulative!hourly!arrivals!for!mail!type!i!at!hour!k.

A!constraint!is!also!needed!to!ensure!that!all!mail!is!processed!during!the!24^hour!day:

Σ ((h(i,!j)!*!r(i))!=!v(i,!di)!for!all!i

j

where!!!di!!!!!!!=!!final!dispatch!time!for!mail!type!i!(see!Figure!1),!and

v(i,!di)!=!!total!daily!arrival!volume!for!mail!type!i.
49

2.2.3&Delivery&Example

The!linear!programming!model!for!minimizing!delivery!cost!is!similar!to!the!mail!

processing!model!described!above,!except!that!hourly!arrival!variations!are!not!an!issue.!!

The!following!example!illustrates!a!simple!delivery!model!for!calculating!minimum!total!

cost!for!two!days!at!a!carrier!station29.!!Assume!that!there!is!only!one!type!of!mail,!and!

there!are!two!types!of!employees,!full^time!(type!1)!and!part^time!(type!2).!!Both!types!of!

employees must!work!eight^hour!days.!!Full^time!employees!have!a!higher!wage!rate!than!

part^time!employees.!!Full^time!employees!must!work!on!both!days.!!Part^time!employees!

can!work!either!no!days!or!one!day.!!All!routes!have!the!same!volume!on!a!given!day.!!Since

the!delivery!function!is!only!about!50%!variable!with!respect!to!volume,!the!daily!

productivity!for!each!route!will!depend!on!the!daily!volume!for!the!route.!!The!objective!

function!for!this!example!would!be:

Minimize!!Σ (d(i,!j)!*!c(i,!v(j)))

!!!!!!!i,j

where!!!d(i,!j)!!!!!=!!number!of!carriers!assigned!for!employee!type!i!on!day!j!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (the!decision variables!chosen!by!the!LP!algorithm),!!!!!!!!!!!!!

!!!!!!!!!!!c(i,!v(j))!!!=!cost!per!type!i!employee!day!on!day!j!with!volume!v(j)

!!!=!cf(i)!+!cv(i)!*!v(j),!

!!!!!!!!!!!!!!v(j)!!!!!!!=!daily!volume!per!route

!!!!!!!!!!!!!cf!(i)!!!!!!=!fixed!cost!per!type!i!employee!day,!and

!!!!!!!!!!!!!cv(i)!!!!!!=!variable!cost!per!piece!for!a!type!i!employee!

Again!we!need!a!set!of!non^negativity!constraints!for!the!decision!variables:

d(i,!j)!>=!0!for!all!i!and!j.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 29 This is a simple approximation of a weekly cost minimization model.
50

We!also!need!constraints!requiring!that!the!number!of!full^time!employees!(i!=!1)!be!the!

same!on!days!1!and!2:

d(1,!1)!=!d(1,!2)!

A!constraint!is!also!needed!to!ensure!that!all!mail!is!delivered!on!each!day:

Σ ((d(i,!j)!*!r(i,!v(j)))!=!v(j)!for!all!j,

i

where!!r(i,!v(j)!=!productivity!for!!employee!type!i!on!day!j!(delivered!pieces/day).
51

2.2.4&Transportation&Example

The!following!example!presents!a!simple!linear!programming!model!for!calculating!

minimum!total!daily!intra^SCF!transportation!cost!under!relaxed!service!standards.!!

Assume!that!the!processing!center!(plant)!in!the!SCF!must!deliver!sorted!mail!to!all!

delivery!units!in!the!SCF!area.!!To!meet!the!current!preferential!mail!service!standards,!

there!are!typically!three!daily!truck!runs!from!the!plant!to!each!delivery!unit.!!The!first!run!

occurs!around!2!am,!and!contains!sorted!non^automated!letters,!flats,!parcels!and!carrier^

route!bundles!for!the!delivery!unit!that!must!be!merged!and!sequenced!manually!by!

carriers!at!the!delivery!unit!during!the!first!or!second!hour!of!their!tour!before!they!deliver!

the!mail.!!The!second!run!is!made!around!dawn!and!takes!the!delivery!point!sequenced!

mail!to!the!delivery!unit.!!There!may!also!be!a!third!run!just!before!the!carriers!go!on!the!

street!that!contains!any!left!over!or!late^arriving!items,!such!as!parcels!and!Priority!mail.

Each!of!the!three!possible!truck!runs!typically!has!excess!capacity,!which!could!be!better!

utilized if!the!preferential!mail!service!standards!were!extended!by!one!day,!as!planned!in!

the!new!USPS!operating!environment.!!In!this!case,!there!would!be!an!opportunity!for!intra^

SCF!transportation!cost!savings!by!reducing!the!number!of!daily!truck!runs!from!the!plant!

to!the!delivery!unit!as!much!as!possible!(conceivably,!one!trip!could!be!adequate).!!!

For!this!example,!assume!that!each!truck!has!the!same!capacity,!and!that!the!maximum!

number!of!truck!runs!to!a!delivery!unit!is!three.!!In!this!situation,!the!objective!function!

would!be:

Minimize!!Σ (f(i,!j)!*!c(i))!

!!!!!!!!!!!!!!!!!!!!i,j

where!!!!f(i,!j)!!!=!!cubic!feet!of!mail!contained!in!the!jth!trip!from!the!plant!to!delivery

!!!!!!!!!!!!!!!!! !!unit!i!!(the!decision variables!chosen!by!the!LP!algorithm),!and

!!c(i)!!!=!!!cost!of!a!truck!run!from!the!plant!to!delivery!unit!i
52

With! this! objective! function,! the! LP!algorithm!will!minimize! the!intra^SCF! transportation!

cost!by!putting!as!many!cubic!feet!as!possible!in!each!truck!run,!so!that!fewer!total!runs!will!

be!needed!(i.e.,!f(i,!j)!will!be!zero!for!j!=!2!and!3!to!the!extent!possible).

Again!we!need!a!set!of!non^negativity!constraints!for!the!decision!variables:

f(i,!j)!>=!0!for!all!i!and!j.

Constraints!are!needed!to!ensure!that!the!cubic!feet!on!each!truck!run!do!not!exceed!the!

truck’s!hauling!capacity:

!!!!!!!!!!!!f(i,!j)!<=!C!for!all!i!and!j,

where!!!C!!!=!!cubic!feet!capacity!of!a!truck.

Finally,!constraints!are!needed!to!ensure!that!all!mail!is!sent!to!each!delivery!unit!on!each!

day:

!!!!!!!!!!!!Σ f(i,!j)!=!F(i)!!!for!all!i,! !!!!!!!!!!!!!!!j

where!!!!!!F(i)!!=!total!cubic!feet!for!delivery!unit!i.

3.&&The&Effect&of&New&Labor&Rules,&Service&Standards,&and&Network&Size&on&Peak&

Load&Costs&&

In!this!section,!we!discuss!the!impact!on!mail!processing,!delivery,!and!transportation!peak!

load!costs!of:

• More!flexible!clerk!scheduling!rules!contained!in!the!new!APWU!contract

• Proposed!relaxation!of!First^Class!mail!service!standards

• Proposed!consolidation!of!the!mail!processing!network!
53

3.1&Mail&Processing

Current(Environment

A!review!of!the!labor!staffing!constraints!described!in!the!former!(2006^2010)!APWU!

National!Agreement,!together!with!discussions!with!field!managers!and!limited!sensitivity!

analysis!resulted!in!the!following!preliminary!conclusions:

• Currently,!a!major!source!of!mail!processing!peak!load!costs!is!the!requirement!that!

most!workers!be!full^time!regulars!with!two!consecutive!days!off.

• Current!preferential!service!standards!require!that!much!of!the!mail!be!processed!

between!6!PM!and!6!AM,!and!so!the!contractually^required!night!differential!(about!

6%)!adds!significant!costs.

• Regular!overtime!is!an!efficient!way!to!provide!capacity!in!peak^volume!periods,!

since!the!overtime!wage!rate!is!only!a!few!percent!higher!than!the!fully^loaded!

straight^time!wage!rate.30

• Penalty!overtime!is!not!an!efficient!way!to!provide!capacity!in!peak^volume!periods,!

but!does!not!have!to!be!paid!during!the!month!of!December.!!Thus,!the!large!holiday!

peak!at!the!end!of!the!year!can!be!handled!more!efficiently!by!using!extra!overtime!

hours.31

• Part^time!employees!are!a!very!efficient!way!to!handle!peak!volume!periods!

because!their!average!wage!is!somewhat!lower!than!full^time!employees!and!

because!they!do!not!have!to!be!paid!for!eight!hours!a!day,!five!days!a!week.!!

However,!there!are!contractual!limits!on!their!use!which!prevent!the!Postal!Service!

from!fully!utilizing!part^time!labor!in!peak!volume!periods.!

As!described!below,!it!appears!that!the!new!APWU!labor!constraints!and!the!relaxation!of!

First^Class!service!standards!are!the!major!changes!as!far!as!the!mail!processing!function.!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 30 For normal work hours (eight per day), regular employees receive straight-time pay plus all benefits, including the 

employer’s contribution to Medicare and Social Security. Up to two additional work hours per day can be scheduled 

and paid at the overtime rate, which is 1.5 times the straight time rate, but only Medicare and Social Security are 

included as benefits. As a result, overtime hours only cost the Postal Service slightly more than normal hours. 

31 Penalty overtime must be paid for work hours in excess of 10 per day. The penalty overtime rate is 2.0 times the 

straight time rate, and also includes Medicare and Social Security. The penalty overtime wage is thus considerably 

higher than the normal wage rate.
54

These!two!changes!should!allow!considerable!cost!reductions!compared!with!the!current!

environment.!!It!is!not!clear!that!consolidation!of!mail!processing!facilities!by!itself!would!

have!a!significant!effect!on!mail!processing!peak!load!costs.

New(APWU(Labor(Constraints

The!new!APWU!National!Agreement!includes!a!Memorandum!of!Understanding!which!

creates!a!new!work!force!– Non^Traditional!Full!Time!(NTFT).!!These!employees!can!have!

much!more!flexible!work!schedules!than!traditional!full^time!employees.!!Their!scheduled!

work!week!can!vary!from!30^48!hours;!their!daily!work!can!vary!between!4^12!hours;!and!

their!number!of!scheduled!days!per!week!can!be!more!or!less!than!five.!!This!could!allow,!

for!example,!schedules!with!four!twelve^hour!days!per!week,!or!six!eight^hour!days!per!

week,!or!six!five^hour!days!per!week.!!The!additional!scheduling!flexibility!and!resulting!

cost!reduction!opportunities!provided!by!NTFTs!can!be!estimated!using!an!LP!approach!

similar!to!that!shown!in!the!Mail!Processing!Example!described!above.

Relaxation(of(FirstWClass(Service(Standards

The!proposed!relaxation!of!current!First^Class!service!standards!should!allow!most!mail!

processing!work!to!take!place!from!6!AM!to!6!PM,!since!late^arriving!mail!can!be!deferred!

to!the!next!day.!!This!change!would!avoid!most!night!differential!pay,!so!mail!processing!

costs!would!be!reduced!considerably.!!These!savings!can!also!be!estimated!using!a!modified

LP!approach!during!the!next!stage!of!this!project.!

As!an!aside,!the!financial!effect!of!any!change!in!service!standards!can!be!estimated!through!

the!LP!approach,!provided!that!the!analyst!can!predict!the!final!dispatch!times!required!to!

meet!the!new!standards.
55

3.2&Delivery

Current(Environment

A!review!of!the!labor!staffing!constraints!described!in!the!(2006^2010)!NALC!National!

Agreement,!together!with!discussions!with!field!managers!showed!that!the!contractual!

rules!for!delivery!staffing!are!very!similar!to!those!for!the!former!APWU!National!

Agreement.!!The!conclusions!for!the!delivery!function!are!thus!the!same!as!listed!above!for!

mail!processing.!!

As!far!as!potential!opportunities!for!reducing!delivery!peak!load!costs,!it!appears!that!only!

the!relaxation!of!First^Class!service!standards!would!have!a!significant!effect.!!At!the!

present!time,!there!is!no!new!NALC!contract,!so!it!is!unclear!whether!any!new!flexibility!in!

scheduling!carriers!will!be!forthcoming.!!As!with!mail!processing,!it!is!not!clear!that!

consolidation!of!the postal!network!would!have!a!significant!effect!on!delivery!peak!load!

costs.

Relaxation(of(Service(Standards

It!is!expected!that!the!extension!of!the!First^Class!service!standards!should!result!in!a!more!

even!flow!of!mail!to!delivery!units!during!the!week,!since!managers!would!have!the!

opportunity!to!level!peaks!by!deferring!delivery!of!some!mail.!!The!resulting!savings!can!be!

estimated!during!the!next!stage!of!the!peak!load!cost!project!using!the!delivery!LP!

approach!described!above.

3.3&Transportation

Current(Environment

A!review!of!the!current!utilization!of!USPS^owned!and!contract!transportation!has!shown!

there!is!considerable!excess!capacity!in!both!local!and!non^local!surface!transportation.!!In!

some!cases,!excess!capacity!may!be!unavoidable,!but!it is!clear!that!in!many!cases!

preferential!service!standards!are!driving!the!need!for!more!frequent!truck!runs!with!less!

efficient!capacity!utilization.
56

It!appears!that!both!the!relaxation!of!First^Class!service!standards!and!consolidation!of!

mail!processing!facilities!would!allow!significant!reductions!of!transportation!peak!load!

costs.!It!is!not!clear!that!any!new!APWU!or!NALC!labor!constraints!would!have!a!significant!

effect!on!transportation!peak!load!costs.

Relaxation(of(Service(Standards

As!described in!the!transportation!LP!example!above,!First^Class!service!standards!drive!

the!need!for!more!frequent!truck!runs!than!would!otherwise!be!necessary.!!More!frequent!

runs!mean!lower!utilization!of!truck!capacity,!both!for!local!and!non^local!surface!

transportation.!!Relaxation!of!First^Class!service!standards!would!result!in!fewer!truck!runs!

and!higher!average!capacity!utilization.!The!resulting!transportation!peak!load!cost!savings!

could!be!estimated!an!LP!approach!similar!to!the!one!described!in!the!transportation!

example!above.

Consolidation(of(the(Mail(Processing(Network

Currently,!there!are!500+!major!mail!processing!facilities!nationwide.!!In!principle,!each!of!

these!network!nodes!must!be!connected!to!every!other!node!by!one!or!more!transportation!

links.!!Each!link!requires!one!or!more!dedicated!trucks,!and!each!truck!contract!has!a!fixed!

cost!component.!!Reducing!the!number!of!nodes!(plants)!to!about!250!would!result!in!

many!fewer!transportation!links,!and!thus!fewer!truck!contracts,!and!thus!less!fixed!costs.!!

These!transportation!peak!load!cost!savings!could!also!be!estimated!an!LP!approach!

similar!to!the!one!described!in!the!transportation!example!above.
57

Appendix&C:&&Linear&Programming&Numerical&Examples

This!Appendix!describes!several!numerical!mail!processing!cost!minimization!examples!

which!use!the!linear!programming!(LP)!approach.!!All!examples!are!contained!in!a Excel!

workbook,!LPExamples.xlsx,!submitted!with!this!report.!The!hourly!and!daily!volume!

profiles!are!presented!on!the!Arrivals!worksheet.!!The!Patterns!worksheet!contains!input!

data!on!the!different!employee!work!schedules!available!to!process!mail!at!each!hour!of!the!

day.!!Each!numerical!LP!example!is!then!presented!in!a!separate!worksheet.!!The!LP!

optimal!solution!for!each!example!was!found!using!the!linear!programming!software!in!the!

Excel!Solver!module.!!It!should!be!noted!that!all!input!data!on!arrival!rates!and!wages!are!

approximate.

1.!Patterns!Sheet

The!Patterns!sheet!shows!the!key!element!to!this!LP!scheduling!approach.!!Each!work!

pattern has!its!own!column,!with!zero!or!one!values.!!A!one!indicates!an!employee!

is scheduled!to!work!during!the!hour!specified!by!the!row. Each!of!the!24!patterns!on!this!

worksheet!identifies!a consecutive!8^hour!shift!with!a!different starting!time. Each!pattern!

can!also!have!a!different!cost!per!hour. Other!patterns!can!be!added!as!necessary!to!

represent!other!work!schedules!and!associated!costs,!e.g.!a!pattern!with!just!one!hour!

representing!overtime,!or!a!pattern!with!3!consecutive!hours!representing!a!part^time!

worker. This!is!what gives!this!approach!the!ability!to!handle!a!wide!variety!of!employee!

schedules!and!wages.

2.!Model1a!Sheet

The!Model1a!sheet!shows!the!optimal!solution!for!scheduling!one!day!of!originating!mail!

processing!with!the!hourly!arrival!rates!shown!on!the!Arrivals!sheet!and!the!24!

employee work!schedules shown!on!the!Pattern!sheet. No!constraints!or!premium!rates!

are!considered!other!than!those!imposed!by!the!midnight!dispatch!of!value!and!the!

consecutive!8^hour!shift!requirement!for!each!employee. For!this!example,!the!following!

parameters!were!used:!!a!total!daily!volume!of!10!million!pieces,!an!hourly!wage!of!$40.00,!
58

and!a!flow!path!productivity!of!200!pieces!per!hour. The!flow!path!productivity!is!the!

weighted!(by operation!unit!cost) average!sum!of handlings!in!all operations!divided!by!

total!first!handling!pieces. This!results!in!a!flow!path!cost!per!piece!of!$0.20,!so!the!

minimum!cost!with!no!constraints!is!$2.0!million. Column!C!shows!the!cumulative!arrivals!

by!hour!assuming!10!million!total!pieces!and!the!hourly!arrival!profile!shown!on!the!

Arrivals!sheet. Row!8!shows!the!cost!per employee!for!each!of!the!24!patterns!(8!hours!

times!$40!per!hour). The!rectangular!area!in!cells!E11:AB34!shows!the!product!of the!

hourly!productivity!and!the!0^1!pattern!matrix!from!the!Pattern!sheet.

The!Excel!Solver!application!was!used!to!find!the!number!of!optimal!(minimum!cost)!

number!of!employees!required!to!start!their!8^hour!shifts!at!each!possible!hour!(see!cells!

E6:AB6).!!It!can!be!seen!that!the!solution!required!600!employees!to!start!their!shifts!at!6!

am!(variable!x7),!400!employees!to!start!at!noon!(variable!x13),!and!so!on. The!resulting!

pieces!processed!by!hour!are!shown!in!Column!B!and!the!cumulative pieces!processed!are!

shown!in!Column!D. The!total!volume!processed!during!the!6!pm!^ 6!am!night!premium!

period!is!shown!at!cell!B40!(5.38!million!pieces).!The!total!cost!with!this!solution!was!$2.0!

million,!which!matches!the!minimum!unconstrained!cost. If!an!arrival!profile!with!a!

narrower!peak!arrival!area!was!used,!some!overtime!hours!would!be!required!(an!example!

using!overtime!will!be!discussed!in!the!Model2a section!below).

3.!Model1b!Sheet

This!example!is!exactly!the!same!as!Model1a,!except!that!the!total volume!was!set!at!13.3!

million!pieces!to!simulate!a!typical!Monday!volume. The!optimal!solution!is!the!same!as!

Model1a!with!the!required!employee!numbers!scaled!up!by!the!ratio!of!the!total!volumes!

(1.33). Again!the!optimal!solution!for!this!model!matches!the!minimum!cost!solution. This!

would!happen!for!any!total!volume,!as!long!as!the!arrival!profile!and!final!dispatch!time!

stayed!the!same.

4.!Model1c!Sheet

This!example!is!the!same!as!Model1a!(10!million!pieces!daily!volume)!except!that!a!10%!

night!premium!for!work!between!6!pm!and!6!am!is!applied!to!each!employee!pattern. An!
59

hourly!night!shift!wage!of!$42.50!was!used!for!this!example. The!costs!for!each!employee!

pattern!in!Row!8!are!calculated!as!a!weighted sum!of!the!scheduled!night!premium!hours

and!day!hours. For!example, Pattern!1 includes!6!hours!of!night!work!and!2!hours!of!day!

work,!so!the!weighted sum!is!(6!x!42.50!+!2!x!40),!or!$335.00.

The!minimum!cost!for!this!case!of!$2.066!million!is!shown!at!cell!A6. This!is!about!2.3%!

higher!than the!minimum!cost!solution. Note!that!the!LP!algorithm!found!a!solution!with!

less!volume!processed!during!the!night!premium!hours!(see!cell!B40)!than!for!Model1a.

5.!Model1d!Sheet

This!example!is!the!same!as!Model1a,!except!that!the!incoming!mail!arrival!profile!and!

final!dispatch!time!is!used!instead!of!the!originating!mail!profile. The!total!volume!is!the!

same!at!10!million!pieces,!but!the!flow!path!productivity!is!assumed!to!be!higher!at!400!

pieces!per!hour. The!optimal!solution,!$1.0!million,!again!matches!the!minimum!cost!

solution.

6.!Model1e!Sheet

This!example!is!the!same!as!Model1d,!except!that!night!premium!costs!are!included!for!

incoming!mail!processing. Total!costs are!$1.044!million,!which!is!4.4%!higher!than!

Model1d. The!incremental!effect!of!the!night!premium!for!incoming mail!is!higher!than!for!

originating!mail,!because!more!night!shift!hours!are!required!for!incoming!mail.

Model1f!Sheet

This!example!is!a!combination!of!Model1a!and!Model1d!in!that!both!originating!and!

incoming!mail!are!included!in!the!same!model. The!solution!shows!that!the!model!solution!

for!both!originating!and!incoming!mail!matches!the!minimum!cost!for!both!mail!types.

7.!Model1g!Sheet

This!example!is!the!same!as!Model1f!except!that!night!premium!costs!are!reflected.
60

8.!Model2a!Sheet

This!example!illustrates!how!multiple!days!of!the!week!as!well!as!hourly!variations!can!be!

included!in!the!optimization!process,!although!only!a!2^day!scenario!is!used!for!this!

case. The!model!is!for!originating!mail only!with!no!night!premium!costs,!but!overtime!is!

reflected!with!an!assumed!wage!5%!higher!than!straight!time!($42.00/hr)!and!penalty!

overtime!at!an!assumed!wage!50%!higher!than!straight!time!($60.00/hr). Rows!8^41!(Day!

1)!reflect!a!typical!Monday!volume level!of!13.3!million!pieces,!while!Rows!44^77!(Day!2)!

reflect!a!typical!average!day!volume!of!10.0!million!pieces. It!is!assumed!that!the!number!

of!full^time!regular!employees!is!the!same!on!both!the!high^ and!low^volume!days. So!the!

optimization!problem!involves!a!tradeoff!between!using!the!lower!number!of!full^time!

employees!required!for!Day!2!volume!together!with!significant!overtime!on!Day!1!versus!

using!the!larger!number!of!full^timers!required!for!Day!1!and!underutilizing!them!on!Day!2.

Columns AC:AZ!have!been!added!to!this!sheet!to! incorporate!24 patterns!for!the!first!hour!

of!overtime;!columns!BA:BX!have!been!added!to!incorporate!24!more!patterns!

representing!a second!hour!of!overtime;!and!columns!CA:CV!have!been!added!for!a!third!

hour!of!(penalty)!overtime.!!For!example,!column AC!(variable!x1a)!contains!only one!non^

zero!value!representing!a!ninth!hour!of!work!for!Pattern!1!employees!with!regular!8^hour!

shifts!starting!at!midnight. Similarly,!column!BA!(variable!x1b)!contains!only!one!non^zero!

value representing!a!tenth!hour!of!work!for!Pattern!1!employees. Finally,!column!CA!

(variable!x1c)!also!contains!only!one!non^zero!value!representing!an!eleventh!hour!of!work!

for!Pattern!1!employees. Constraints!for!these!overtime!variables!are!added!in!the!solution!

process!to!ensure!that!there!can't!be!solutions with!scheduled!overtime!hours!for!employee!

patterns!with no!scheduled full^time!employees,!and!that!there!can't!be!a!second!hour!of!

overtime!scheduled!unless!a!first!hour!has!been!scheduled,!etc.

It can!be!seen!from!cells!B3!and!B45!that!the!unconstrained!minimum!cost!solution!for!the!

two^day!period!is!$4.67!million. The!optimal!LP!solution!shown!at!cell!A8 is!$4.86!million,!

so!the!day^of^week!peak!load!cost!in!this!example!would be!$0.19!million.!!Comparison!of!

the!model solution!for each!day shows!that!there!was!not!enough!regular!overtime!

available!to!handle!all!the!extra!33%!of Day!1!volume,!so 3,394!additional!full^time!
61

employees!(compared!with!the!Day!2!requirements)!were!added!for!both!days!as well as!a!

near^maximum!use!of 3!hours!of!overtime!per!full^time!employee.!!

9.&Delivery!and!Transportation!LP!Models

No!numerical!examples!were!developed!for!the!delivery!and!transportation!functions!due!

to!lack!of!time,!but!the!examples!presented!in!the main!paper!(pp.!48^51)!could!easily!be!

put!into!the!same!LP!matrix!format!used!for!the!mail!processing!examples.

For!the!delivery!example,!the!rows!of!the!matrix!would!correspond!to!the!days!of!the!week,!

and!the!columns!to!employee!types.!!For!the!transportation!example,!the!rows!would!be!the!

delivery!units!and!the!columns!would!be!the!capacity!used!for!each!possible!truck!run.
62

Appendix&D Slides&from&Panzar’s&September&30&Commission&

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