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Operations Research:Operations Research:Making More Out ofMaking More Out of

Information SystemsInformation SystemsDr HengDr Heng--Soon GANSoon GANDepartment of Mathematics and StatisticsDepartment of Mathematics and Statistics

The University of MelbourneThe University of Melbourne

This presentation has been made in accordance with the provisions of Part VB of the copyrightThis presentation has been made in accordance with the provisions of Part VB of the copyright

act for the teaching purposes of the University.act for the teaching purposes of the University.

Copyright 2005 by HengCopyright 2005 by Heng--Soon GanSoon Gan


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Optimisation = Efficiency + SavingsOptimisation = Efficiency + Savings

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

LPLP--based operational planning (production, inventory, distribution)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 reconcert with Geographical Information System (GIS) to re--engineeringengineeringproduct 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.

HewlettHewlett--PackardPackard Robust supply chain design based on advanced inventory optimizationRobust supply chain design based on advanced inventory optimization

techniques.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) Problemx2

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 andand

cancan 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 atChildcare 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 onlytake 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)

_ a DkEix

Dkx

Eix

DkSjdxats

xcMinimise

ik

i

ik

k

ik

jk

i

ikij

i k

iki

u

ee

u

!

!

!

! !

,,1,0

,4

,42

,,..

10

1

5

1

10

1

10

1

7

1

!otherwise,0

dayonworksstaffif,1 kix

ik

!otherwise,0

skillpossessesstaffif,1 jiaij

ici stafffordaily wage!

kjdjk d ynqu m n!

Skill Demand

Equitability

Workplace Regulation


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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 disseminateinformation (shift preference, roster etc.) effectivelyinformation (shift preference, roster etc.) effectively

throughout the organisationthroughout the organisation


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Other Issues and ChallengesOther Issues and Challenges

BreaksBreaks scheduled breaksscheduled breaks

annual leaveannual leave

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

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 (longMORe is currently involved in several (long--term) staffterm) staffrostering projects for Australiarostering projects for Australia--based companies inbased companies inat 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 betweenMelbourne 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 midProject started in mid--2004 and successfully completed its2004 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 for

Operations Research 2005 Conference (26Operations Research 2005 Conference (26--2828thth September)September)


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General Aim of ProjectGeneral Aim of Project

Forces wishlist

$ $ $ $

Choose forces(STRATEGIC) e 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 LPAn integer LP--based prototype decisionbased prototype decisionsupport tool has been developed.support tool has been developed.

The support tool,The support tool,F

orceOpF

orceOp, 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 systemsintegrated military systems Military InformationMilitary InformationSystemSystem


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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 intuitivea 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 a

given set of objectives.given set of objectives.


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Facility Location DecisionsFacility Location DecisionsLP as a WhatLP as a What--If ToolIf Tool


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The Facility Location ProblemThe Facility Location Problem

LPLP--based techniques can be used to locatebased 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 a

large range of whatlarge range of what--if scenarios.if scenarios.


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36km

W-4

Problem StatementProblem Statement

AF

DC

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..

10000 units

180000

10000180000

220000

10000

B E

36km


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Scenario 1Scenario 1

Scenario 1:Scenario 1:Warehouse O/HWarehouse O/Hcost iscost is very smallvery smallas compared toas compared 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

A

F

DC

W-1

W-2

W-3

W-5

W-6

10000 units

180000

10000 180000

220000

10000

B E


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Scenario 2: WarehouseScenario 2: WarehouseO/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 tooperate a warehouseoperate a warehouse

hence, the mosthence, the most

centralised warehousecentralised warehouseselected (based onselected (based ondemand & distance)demand & distance)

W-4

A

F

DC

W-1

W-2

W-3

W-5

W-6

10000 units

180000

10

000

180000

220000

10000

B E


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Scenario 3: BothScenario 3: Bothwarehouse O/H andwarehouse O/H andtransportation coststransportation costsare competingare competing Warehouse O/H:Warehouse O/H:

$60 000 000$60 000 000


solution is notsolution is notobvious; too manyobvious; too manypossibilitiespossibilities

W-4

A

F

DC

W-1

W-2

W-3

W-5

W-6

10000 units

180000

10

000

180000

220000

10000

B E


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Scenario 4: BothScenario 4: Bothwarehouse O/H andwarehouse O/H andtransportation coststransportation costsare competing ANDare competing ANDwarehouse capacitywarehouse capacity

limitedlimited Warehouse O/H:Warehouse O/H:

$60 000 000$60 000 000

Transportation cost:Transportation cost:

$20/km/unit$20/km/unit WarehouseWarehousecapacity: 150 000capacity: 150 000unitsunits

W-4

A

F

DC

W-1

W-2

W-3

W-5

W-6

10000 units

180000

10

000

180000

220000

10000

B E

10000

70000

1000030000

110000

150000

150000

70000

10000


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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

warehousewarehouse--customer distance constraintcustomer 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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