WINSEM2012-13_CP1147_02-Jan-2013_RM01_ORandInfoSys

7/29/2019 WINSEM2012-13_CP1147_02-Jan-2013_RM01_ORandInfoSys

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Operations Research:Operations Research:


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Optimisation = Efficiency + SavingsOptimisation = Efficiency + Savings

KelloggsKelloggs The largest cereal producer in the world.The largest cereal producer in the world.

LP-based operational planning (production, inventory, distribution)LP-based operational planning (production, inventory, distribution)system saved $4.5 million in 1995.system saved $4.5 million in 1995.

Procter and GambleProcter and Gamble

A large worldwide consumer goods company.A large worldwide consumer goods company. Utilised integer programming and network optimization worked inUtilised integer programming and network optimization worked in

concert with Geographical Information System (GIS) to re-engineeringconcert with Geographical Information System (GIS) to re-engineeringproduct sourcing and distribution system for North America.product sourcing and distribution system for North America.

Saved over $200 million in cost per year.Saved over $200 million in cost per year.

Hewlett-PackardHewlett-Packard Robust supply chain design based on advanced inventory optimizationRobust supply chain design based on advanced inventory optimizationtechniques.techniques.

Realized savings of over $130 million in 2004Realized savings of over $130 million in 2004

Source: InterfacesSource: Interfaces


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Mathematics in OperationMathematics in Operation

Mathematical Solution Method (Algorithm)

Real Practical Problem

Mathematical (Optimization) Problem

x2

Computer Algorithm

Human Decision-Maker

Decision Support Software System


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Decision SupportDecision Support

Decision Support Tool

Interface

Information Systems


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A Team EffortA Team Effort

Interface

Information Systems

Users

Comp SciOps Res Decision Support Tool

Info SysBiz Analyst


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Staff RosteringStaff RosteringAllocating Staff to Work ShiftsAllocating Staff to Work Shifts

A significant role for the TeamA significant role for the Team


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The Staff Rostering ProblemThe Staff Rostering Problem

What is the optimal staff allocation?What is the optimal staff allocation? Consider a Childcare Centre:Consider a Childcare Centre:

The childcare centre is operatingThe childcare centre is operating 5 days/week5 days/week..

There areThere are 10 staff members10 staff members..

Each staff member is paid at an agreedEach staff member is paid at an agreed daily ratedaily rate,,according to the skills they possess.according to the skills they possess.

One shift per dayOne shift per day

Skills can be categorised intoSkills can be categorised into 5 types5 types.. (Singing,Dancing)(Singing,Dancing)

(Arts)(Arts)

(Sports)(Sports)

(Reading,Writing)(Reading,Writing)

(Moral Studies,Hygiene)(Moral Studies,Hygiene)


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other informationother information

CONSTRAINTS:CONSTRAINTS: Skill DemandSkill Demand

The daily skill demand is met.The daily skill demand is met.

Equitability (breaks,salaries)Equitability (breaks,salaries)

Each staff member mustEach staff member must at least work 2 days/weekat least work 2 days/week andandcancan at most work 4 days/weekat most work 4 days/week..

Workplace RegulationWorkplace Regulation

On any day, there must beOn any day, there must be at least 4 staff membersat least 4 staff membersworking.working.

OBJECTIVE:OBJECTIVE:

Minimise Total Employment Cost/WeekMinimise Total Employment Cost/Week


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Problem Solving StagesProblem Solving Stages

Mathematical Solution Method (Algorithm)

Real Practical Problem

Mathematical (Optimization) Problem

Computer Algorithm

Human Decision-Maker

Decision Support Software System

Staff Rostering at

Childcare Centre

MathematicalProgramming

CPLEX

XpressMP

LINGO

Excel with VBA

Childcare CentreManager


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The Mathematical ProblemThe Mathematical Problem

Modelled as anModelled as an Integer LPInteger LP

Decision variables are integers, i.e. variables canDecision variables are integers, i.e. variables canonly take 0,1,2, not 0.2, 1.1, 2.4 etc.only take 0,1,2, not 0.2, 1.1, 2.4 etc.

AA binary variablebinary variable: a decision variable that can only: a decision variable that can only

take 0 or 1 as a solution.take 0 or 1 as a solution.


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Integer LP (just for show)Integer LP (just for show)

{ } DkEix

Dkx

Eix

DkSjdxats

xcMinimise

ik

i

ik

k

ik

jk

i

ikij

i k

iki

=

=

=

= =

,,1,0

,4

,42

,,..

10

1

5

1

10

1

10

1

7

1=

otherwise,0

dayonworksstaffif,1 kixik

=

otherwise,0

skillpossessesstaffif,1 jiaij

ici stafffordaily wage=

kjdjk dayonskillfortsrequiremen=

Skill Demand

Equitability

Workplace Regulation


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XpressXpressMPMP

Large-scale optimisation software developedLarge-scale optimisation software developed

by Dash (by Dash (http://http://www.dashoptimization.comwww.dashoptimization.com))

XpressXpress-IVE-IVE ((IInteractiventeractive VVisualisual EEnvironment)nvironment)
http://www.dashoptimization.com/http://www.dashoptimization.com/http://www.dashoptimization.com/http://www.dashoptimization.com/http://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/StaffRoster.moshttp://www.dashoptimization.com/http://www.dashoptimization.com/


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Decision Support SoftwareDecision Support Software

SystemSystem Excel InterfaceExcel Interface

Database Management:Database Management:

Staff Profile (Name, Category)Staff Profile (Name, Category) Annual leaveAnnual leave Shift preferencesShift preferences Reserve staffReserve staff

RosterRoster

etc.etc.

Information system installed to disseminateInformation system installed to disseminate

information (shift preference, roster etc.) effectivelyinformation (shift preference, roster etc.) effectivelythroughout the organisationthroughout the organisation
http://var/www/apps/conversion/tmp/scratch_1/Rostering/Rostering-Xpress.xlshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/Rostering-Xpress.xlshttp://var/www/apps/conversion/tmp/scratch_1/Rostering/Rostering-Xpress.xls


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Other Issues and ChallengesOther Issues and Challenges

BreaksBreaks scheduled breaksscheduled breaks annual leaveannual leave

festive breaks (under-staffing issues)festive breaks (under-staffing issues)

FatigueFatigue limit to number of working hours per day/week/fortnightlimit to number of working hours per day/week/fortnight(Union Requirements)(Union Requirements)

Equitable rosterEquitable roster

equitable weekend/night shiftsequitable weekend/night shifts MotivationMotivation

skill utilisation (avoid monotonous job routine)skill utilisation (avoid monotonous job routine)

TrainingTraining

training and development (scheduled)training and development (scheduled)


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Other Industry Requiring StaffOther Industry Requiring Staff

RosteringRostering

Airline (air crew and ground staff)Airline (air crew and ground staff)

Health (nurses and doctors)Health (nurses and doctors)

Manufacturing (operators)Manufacturing (operators) Transport (truck drivers)Transport (truck drivers)

Entertainment and gamingEntertainment and gaming

Education (teachers, lecturers)Education (teachers, lecturers)

MORe is currently involved in several (long-term) staffMORe is currently involved in several (long-term) staffrostering projects for Australia-based companies inrostering projects for Australia-based companies in

at least one of the industries mentioned above.at least one of the industries mentioned above.


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Force OptimisationForce OptimisationA collaborative project betweenA collaborative project between

Melbourne Operations Research (MORe)Melbourne Operations Research (MORe)

&&

Defence Science andDefence Science and

Technology Organisation (DSTO),Technology Organisation (DSTO),

Department of Defence,Department of Defence,

Australian GovernmentAustralian Government


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Project BackgroundProject Background DSTO LOD working with Melbourne Operations ResearchDSTO LOD working with Melbourne Operations Research

(MORe), The University of Melbourne(MORe), The University of Melbourne

Project aim: support the Army (Force Design Group) with theirProject aim: support the Army (Force Design Group) with theircapability options development and analysis, seekingcapability options development and analysis, seeking

What types of forces should be maintained?What types of forces should be maintained? What force strength is required?What force strength is required?

to ensure forces are effective in achieving defence objectivesto ensure forces are effective in achieving defence objectives

Project started in mid-2004 and successfully completed itsProject started in mid-2004 and successfully completed itsmodelling, interface design and testing phases in themodelling, interface design and testing phases in thebeginning of year 2005beginning of year 2005

The model will be presented at the Australian Society forThe model will be presented at the Australian Society forOperations Research 2005 Conference (26-28Operations Research 2005 Conference (26-28thth September)September)


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General Aim of ProjectGeneral Aim of Project

Forces wishlist

$ $ $ $

Choose forces(STRATEGIC) budget

Objectives

Deploy forces

(TACTICAL)

e e e e ee e max effectiveness

Forceconfiguration


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The Mathematical ModelThe Mathematical Model

An integer LP-based prototype decisionAn integer LP-based prototype decisionsupport tool has been developed.support tool has been developed.

The support tool,The support tool, ForceOpForceOp, has an Excel, has an Excelinterface, written with VBA and optimisedinterface, written with VBA and optimisedusingusing XpressXpressMPMP..

Future directionsFuture directions database managementdatabase management

integrated military systems Military Informationintegrated military systems Military Information

SystemSystem
http://var/www/apps/conversion/tmp/scratch_1/DSTO/DSTO-FOI-12April05.xlshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/DSTO-FOI-12April05.xlshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/ForceOP_V7-3.moshttp://var/www/apps/conversion/tmp/scratch_1/DSTO/DSTO-FOI-12April05.xls


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TheThe ForceOpForceOp ToolTool

Before this tool,Before this tool, force design was carried out manuallyforce design was carried out manually

a lengthy and laborious process, based on intuitive-a lengthy and laborious process, based on intuitive-reasoning (no quantitative basis).reasoning (no quantitative basis).

difficult to assess effectiveness or compare quality ofdifficult to assess effectiveness or compare quality ofsolutionssolutions

With this tool,With this tool,

solutions can be obtained fast.solutions can be obtained fast. quality of solutions can be quantified.quality of solutions can be quantified.

many sets of objectives can be tested within a short periodmany sets of objectives can be tested within a short periodof time.of time.

many different force configurations can be tested against amany different force configurations can be tested against agiven set of objectives.given set of objectives.


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Facility Location DecisionsFacility Location Decisions

LP as a What-If ToolLP as a What-If Tool


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The Facility Location ProblemThe Facility Location Problem LP-based techniques can be used to locateLP-based techniques can be used to locate

manufacturing facilities,manufacturing facilities, distribution centres,distribution centres, warehouse/storage facilities etc.warehouse/storage facilities etc.

taking into consideration factors such astaking into consideration factors such as facility/distribution capacities,facility/distribution capacities,

customer demand,customer demand, budget constraints,budget constraints, quality of service to customers etc.quality of service to customers etc.

using Operations Research techniques such asusing Operations Research techniques such as linear programming,linear programming,

integer linear programming, andinteger linear programming, and stochastic programming.stochastic programming.

With OR techniques, solutions for the facility location problemWith OR techniques, solutions for the facility location problemcan be obtained fast, and hence, we are able to perform acan be obtained fast, and hence, we are able to perform alarge range of what-if scenarios.large range of what-if scenarios.


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36km

W-4

Problem StatementProblem Statement

AAFF

DDCC

W-1

W-2

W-3

W-5

W-6

Customer

Warehouse

(W)

Assume:Assume:

Transportation cost:Transportation cost:

$20/km/unit$20/km/unit

Warehouses have the sameWarehouses have the same

O/H costO/H cost

Warehouse has very largeWarehouse has very largecapacitycapacity

Problem modelled as anProblem modelled as an

integer linear program, andinteger linear program, and

solved using Xpresssolved using XpressMPMP..

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

36km


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The Mathematical ModelThe Mathematical Model

{ }

egerintisy

,x

dj,Dy

ni,xCy

.t.s

yWxfMinimise

ij

i

j

n

i

ij

ii

d

j

ij

n

i

d

j ijij

n

i ii

10

1

1

1

1

1 11

=

=

+

=

=

= ==

jj ijy

i

ix


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Scenario 1Scenario 1 Scenario 1:Scenario 1:

Warehouse O/HWarehouse O/Hcost iscost is very smallvery small asas

compared tocompared totransportation costtransportation cost

Warehouse O/H:Warehouse O/H:$6 000 000$6 000 000

Transportation cost:Transportation cost:$20/km/unit$20/km/unit

proximity dominatesproximity dominates

operate theoperate thewarehouse closestwarehouse closestto each customerto each customer

W-4

AA

FF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000

180 000

220 000

10 000

BB EE


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Scenario 2Scenario 2 Scenario 2: WarehouseScenario 2: Warehouse

O/H cost isO/H cost is very largevery largeas compared toas compared totransportation costtransportation cost

Warehouse O/H:Warehouse O/H:

$1 800 000 000$1 800 000 000


too expensive totoo expensive to

operate a warehouseoperate a warehouse

hence, the mosthence, the most

centralised warehousecentralised warehouseselected (based onselected (based on

demand & distance)demand & distance)

W-4

AA

FF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000

180 000

220 000

10 000

BB EE


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Scenario 3Scenario 3 Scenario 3: BothScenario 3: Both

warehouse O/H andwarehouse O/H andtransportation coststransportation costs

are competingare competing Warehouse O/H:Warehouse O/H:

$60 000 000$60 000 000 Transportation cost:Transportation cost:

$20/km/unit$20/km/unit

solution is notsolution is notobvious; too manyobvious; too many

possibilitiespossibilities

W-4

AA

FF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000

180 000

220 000

10 000

BB EE


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Scenario 4Scenario 4 Scenario 4: BothScenario 4: Both

warehouse O/H andwarehouse O/H andtransportation coststransportation costs

are competing ANDare competing ANDwarehouse capacitywarehouse capacity

limitedlimited Warehouse O/H:Warehouse O/H:

$60 000 000$60 000 000


WarehouseWarehousecapacity: 150 000capacity: 150 000unitsunits

W-4

AA

FF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000

180 000

220 000

10 000

BB EE

10 000

70 000

10 00030 000

110 000

150 000

150 000

70 000

10 000


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Facility LocationFacility Location

Possible variantsPossible variants closure decisionsclosure decisions

acquisition decisionsacquisition decisions

Possible extensionsPossible extensions

limitations to the number of distribution centreslimitations to the number of distribution centres

warehouse-customer distance constraintwarehouse-customer distance constraint complex cost functionscomplex cost functions

uncertain demanduncertain demand


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Other OR ApplicationsOther OR Applications

Other areas where OR techniques have been provenOther areas where OR techniques have been provento be useful includeto be useful include Inventory controlInventory control

Warehouse design, storage and retrieval, order pickingWarehouse design, storage and retrieval, order picking

Vehicle routingVehicle routing Delivery transport mode selectionDelivery transport mode selection

Capacity and manpower planningCapacity and manpower planning

Production schedulingProduction scheduling

and other resource usage and allocation decisions.and other resource usage and allocation decisions.

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WINSEM2012-13_CP1147_02-Jan-2013_RM01_ORandInfoSys

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