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

Information SystemsInformation SystemsDr Heng-Soon GANDr Heng-Soon 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 copyright This 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 Heng-Soon GanCopyright© 2005 by Heng-Soon Gan

Optimisation = Efficiency + SavingsOptimisation = Efficiency + Savings• Kellogg’sKellogg’s

– 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 in Utilised integer programming and network optimization worked in

concert with Geographical Information System (GIS) to re-engineering concert with Geographical Information System (GIS) to re-engineering product 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 optimization Robust 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

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

Decision SupportDecision Support

Decision Support Tool

Interface

Information Systems

A Team EffortA Team Effort

Interface

Information Systems

Users

Comp SciOps Res Decision Support Tool

Info SysBiz Analyst

Staff RosteringStaff Rostering

Allocating Staff to Work ShiftsAllocating Staff to Work Shifts

A significant role for the “Team”A significant role for the “Team”

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 operating The childcare centre is operating 5 days/week5 days/week..– There are There are 10 staff members10 staff members..– Each staff member is paid at an agreed Each 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 into Skills 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)

……other informationother information• CONSTRAINTS:CONSTRAINTS:

– Skill Demand Skill Demand • The daily skill demand is met.The daily skill demand is met.

– Equitability (breaks,salaries)Equitability (breaks,salaries)• Each staff member must Each staff member must at least work 2 days/weekat least work 2 days/week and and

can can at most work 4 days/weekat most work 4 days/week..

– Workplace RegulationWorkplace Regulation• On any day, there must be On any day, there must be at least 4 staff membersat least 4 staff members

working.working.

• OBJECTIVE: OBJECTIVE: – Minimise Total Employment Cost/WeekMinimise Total Employment Cost/Week

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

Mathematical Programming

CPLEX

XpressMP

LINGO

Excel with VBA

Childcare Centre Manager

The Mathematical ProblemThe Mathematical Problem

• Modelled as an Modelled as an Integer LPInteger LP

– Decision variables are integers, i.e. variables can Decision variables are integers, i.e. variables can only 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.

– A A 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.

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

DkEix

Dkx

Eix

DkSjdxats

xcMinimise

ik

iik

kik

jki

ikij

i kiki

,,1,0

,4

,42

,,..

10

1

5

1

10

1

10

1

7

1

otherwise,0

day on works staff if,1 kixik

otherwise,0

skill possesses staff if,1 jiaij

ici stafffor daily wage

kjd jk day on skillfor tsrequiremen

Skill Demand

Equitability

Workplace Regulation

XpressXpressMPMP

• Large-scale optimisation software developed Large-scale optimisation software developed by Dash (by Dash (http://www.http://www.dashoptimizationdashoptimization.com.com))

• XpressXpress-IVE-IVE ( (IInteractive nteractive VVisual isual EEnvironment)nvironment)

Decision Support Software Decision 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 disseminate Information system installed to disseminate information (shift preference, roster etc.) effectively information (shift preference, roster etc.) effectively throughout the organisationthroughout the organisation

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/fortnight limit 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)

Other Industry Requiring Staff Other 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) staff MORe is currently involved in several (long-term) staff rostering projects for Australia-based companies in rostering projects for Australia-based companies in at least one of the industries mentioned above.at least one of the industries mentioned above.

Force OptimisationForce OptimisationA collaborative project betweenA collaborative project between

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

Defence Science and Defence Science and Technology Organisation (DSTO),Technology Organisation (DSTO),

Department of Defence,Department of Defence,Australian GovernmentAustralian Government

Project BackgroundProject Background• DSTO LOD working with Melbourne Operations Research DSTO 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 their Project aim: support the Army (Force Design Group) with their capability 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 its Project started in mid-2004 and successfully completed its modelling, interface design and testing phases in the modelling, interface design and testing phases in the beginning of year 2005beginning of year 2005

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

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

Force configuration

The Mathematical ModelThe Mathematical Model• An integer LP-based prototype decision An integer LP-based prototype decision

support tool has been developed.support tool has been developed.

• The support tool, The support tool, ForceOpForceOp, has an Excel , has an Excel interface, written with VBA and optimised interface, written with VBA and optimised using using XpressXpressMPMP..

• Future directionsFuture directions– database managementdatabase management– integrated military systems – Military Information integrated military systems – Military Information

SystemSystem

The The ForceOpForceOp Tool Tool • Before this tool,Before this tool,

– force design was carried out manually force 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 of difficult to assess effectiveness or compare quality of

solutionssolutions

• 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 period many sets of objectives can be tested within a short period

of time.of time.– many different force configurations can be tested against a many different force configurations can be tested against a

given set of objectives.given set of objectives.

Facility Location DecisionsFacility Location Decisions

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

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 as using 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 problem With OR techniques, solutions for the facility location problem can be obtained fast, and hence, we are able to perform a can be obtained fast, and hence, we are able to perform a large range of “what-if” scenarios.large range of “what-if” scenarios.

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 same Warehouses have the same O/H costO/H cost

• Warehouse has very large Warehouse has very large capacitycapacity

Problem modelled as an Problem modelled as an integer linear program, and integer linear program, and solved using Xpresssolved using XpressMPMP..

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

36km

The Mathematical ModelThe Mathematical Model

egerintisy

,x

dj,Dy

ni,xCy

.t.s

yWxfMinimise

ij

i

j

n

iij

ii

d

jij

n

i

d

jijij

n

iii

10

1

1

1

1

1 11

jj ijy

iix

Scenario 1Scenario 1• Scenario 1: Scenario 1:

Warehouse O/H Warehouse O/H cost is cost is very smallvery small as as compared to compared to transportation 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 the operate the

warehouse closest warehouse closest to each customerto each customer

W-4

AAFF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

Scenario 2Scenario 2• Scenario 2: Warehouse Scenario 2: Warehouse

O/H cost is O/H cost is very largevery large as compared to as compared to transportation costtransportation cost– Warehouse O/H:Warehouse O/H:

$1 800 000 000$1 800 000 000

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

– too expensive to too expensive to operate a warehouseoperate a warehouse

– hence, the most hence, the most centralised warehouse centralised warehouse selected (based on selected (based on demand & distance) demand & distance)

W-4

AAFF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

Scenario 3Scenario 3• Scenario 3: Both Scenario 3: Both

warehouse O/H and warehouse O/H and transportation costs transportation costs are competing are 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 not solution is not

obvious; too many obvious; too many possibilitiespossibilities

W-4

AAFF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

Scenario 4Scenario 4• Scenario 4: Both Scenario 4: Both

warehouse O/H and warehouse O/H and transportation costs transportation costs are competing AND are competing AND warehouse capacity warehouse capacity limited limited – Warehouse O/H:Warehouse O/H:

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

$20/km/unit$20/km/unit– Warehouse Warehouse

capacity: 150 000 capacity: 150 000 unitsunits

W-4

AAFF

DDCC

W-1

W-2

W-3

W-5

W-6

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

10 000

70 000

10 00030 000

110 000

150 000

150 000

70 000

10 000

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

Other OR ApplicationsOther OR Applications• Other areas where OR techniques have been proven Other areas where OR techniques have been proven

to 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.