What is MORe? A consulting group based at the Department of Mathematics and Statistics University of...

What is MORe?What is MORe?A consulting group based at the A consulting group based at the

Department of Mathematics and StatisticsDepartment of Mathematics and Statistics

University of MelbourneUniversity of Melbourne

providingproviding

Operations Research (OR) Operations Research (OR) ConsultingConsulting

to business, industry, government & to business, industry, government & community organisations.community organisations.

• Strategic decision making– resource requirements and allocations

• e.g. vehicles, machines, operators– location/relocation decisions

• e.g. building new facilities, relocating/closing existing facilities

– system design• e.g. warehouse

• Operational decision making– scheduling– timetabling– sequencing– routing– rostering– production planning– inventory control

What are Operations What are Operations Research Problems?Research Problems?

MORe PeopleMORe People

Olivia Smith

Dr Heng-Soon Gan

Prof. Peter Taylor

Prof. Bob Johnston

Prof Natashia BolandUniversity of Newcastle

Prof Mark WallaceMonash University

• Mathematical modelling and analysis:– Resource planning, including inventory management– Strategic and operational planning– System design and optimisation– Scheduling and timetabling– Yield management

• Optimisation and simulation systems– Linear programming and mixed integer programming – Discrete event and macro simulation– Constraint programming– Queuing theory and risk analysis

Our ExpertiseOur Expertise

Mathematical Solution Method (Algorithm)

Real Practical Problem

Mathematical (Optimization) Problem

x2

Computer Algorithm

Human Decision-Maker

Decision Support System

Mathematics in OperationMathematics in Operation

7

www.more.ms.unimelb.edu.auwww.more.ms.unimelb.edu.au

MORe ExperiencesMORe Experiences

Warehouse Design Maximizing Operational Efficiency Warehouse Design Maximizing Operational Efficiency in collaboration with Agilisticsin collaboration with Agilistics

Incoming Incoming ProductsProducts

Customer Customer Order HistoryOrder History

Operations Research Operations Research TechnologyTechnology

CustomersCustomers

Storage RacksStorage Racks

Where to store Where to store products?products?

……affects order affects order pickingpicking

Storage Storage locationlocation OrdersOrders

Pick Pick orderorder

Savings Savings of 27-of 27-

43% on 43% on order order

picking picking costscosts

Warehouse DesignWarehouse Design

Defence Defence ObjectivesObjectives

What types of forces should be

maintained?

What force strength is required?

Force OptimisationForce OptimisationDefence Science and Technology Organisation (DSTO), Defence Science and Technology Organisation (DSTO),

Department of Defence, Australian GovernmentDepartment of Defence, Australian Government

Forces “wishlist”

$ $ $ $Choose forces(STRATEGIC)

Constraints: Budget

Objectives

Deploy forces(TACTICAL)

e e e e ee e max effectiveness

Decision:Force configuration

SAMPLE

SAMPLE

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Melbourne Airport Melbourne Airport Long-Term Car ParkLong-Term Car Park

How How many many

buses to buses to purchasepurchase

??

Bus Bus scheduleschedule

? ?

Hourly bus Hourly bus requiremenrequiremen

t? t?

Bus driver Bus driver roster? roster?

Asset ManagementAsset Management

Bus Bus SizesSizes

??

AAAA BBBB CCCC DDDD EEEE FFFFBus empty?Bus empty?Bus empty?Bus empty?

Dropoff Dropoff Location 3Location 3


Pickup Pickup LocationLocationPickup Pickup

LocationLocation

YesYes

NoNo

Car Car ParkPark

Airport terminalsAirport terminals





PickupPickup

PickupPickup

DropoffDropoff

DropoffDropoff

Micro-SimulationMicro-SimulationPlanimate® Simulation ModelPlanimate® Simulation Model

Performance measure based on tail Performance measure based on tail probability:probability:– no more than 10% of customers wait no more than 10% of customers wait

more than 5 minutes for a bus, in the car more than 5 minutes for a bus, in the car park and at the Airport Terminals.park and at the Airport Terminals.

Customer Customer Waiting TimeWaiting Time

Probability Probability distribution distribution

functionfunction

5 minute5 minute

1.0

Bus Service ObjectiveBus Service Objective

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A consulting project with

Hi Fert Pty Ltd

Transport and Transport and LogisticsLogistics

Hi FertHi Fert

• Australian importer Australian importer and distributor of and distributor of agricultural materials.agricultural materials.

• Operates 9 coastal Operates 9 coastal distribution facilities distribution facilities across the east coast across the east coast of Australia.of Australia.

• Approx 30% market Approx 30% market share (#2 player).share (#2 player).

BRISBANE

NEWCASTLE

ADELAIDE

KADINA

PORT LINCOLN

PORTLANDGEELONG

TOWNSVILLE

MACKAY

Ship Route & TrucksShip Route & Trucks

Red Sea Suppliers

Israel, Egypt

BRISBANE

NEWCASTLEADELAIDE

KADINA

PORTLAND

GEELONG

TOWNSVILLE

MACKAY

25003000

55002500

1500

165001400

3400

10000 10000 10000

7000 7000

Ship Holds

Material A: 29400 TMaterial B: 6900 T

200

80

The company’s “old” process involved iteratively matching a Shipping Schedule to Raw Material Requirements:

– manual and time consuming– predominantly volume-based

constraints considered– no robust assurance that the plan

was ultimately optimal– poor knowledge management– planning 3 months ahead

Existing ERP (SAP) could not cope with the complex maths of the problem.

Sales Forecast

Raw Material Requirements

Shipping Schedule

Sourcing Plan

OPTIMISATION TOOL

Sales Forecast

Raw Material Requirements

Shipping Schedule

Sourcing Plan

The desire was to create an Optimisation Tool with all constraints built in to develop the Sourcing Plan with the lowest overall cost.– 12-15 months planning horizon– centralised information

management– guided feasibility checking– automated generation of reports

The Optimisation ToolThe Optimisation Tool

• How can orders be combined for practical shipment?

• Which orders can come forward, which delayed?

• Should the order in a particular period be from a supplier in a different region in order to facilitate combination shipping? Even if the price is higher?

• How should the order quantities change to facilitate combination in a shipment?

Key QuestionsKey Questions

• Decisions are interlinked.

• Need wholistic solution techniques that make all decisions simultaneously, and account for interactions.

• Linear (integer) programming is the key.

SolutionSolution

Decision Support ToolDecision Support Tool

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Carbon Liability OptimiserCarbon Liability Optimiser

In a carbon constrained environment firms must account for their emissions liability when making strategic planning decisions.

Carbon Liability Optimiser (CarLO) formulates a profit maximising carbon strategy while accounting for a firm’s emissions liability and regulatory constraints.

• Formulates an investment strategy that incorporates both carbon and non-carbon related investments across all areas of business.

• Accounts for the complex interactions between investment activities, the emissions liability, and regulatory requirements.

• Explicitly accounts for the requirements of the Carbon Pollution Reduction Scheme legislation.

• Allows quick and simple ‘what-if’ analysis

CarLO…CarLO…

CarLO ScreenshotsCarLO Screenshots

MORe has been advising a client on stochastic programming approaches for solving a multi-period economic model.

Creative decomposition techniques and solution algorithms have been developed to handle the excessive size of the problem.

Stochastic ProgrammingStochastic Programming

Why Account for Stochasticity?Why Account for Stochasticity?

Deterministic programs provide an optimal solution given fixed parameter values.

This solution will not be optimal when the parameter values change.

Stochastic programming seeks a solution that is optimal over a range of uncertain scenarios.

This provides more robust and realistic outcomes.

This is particularly valuable in strategic planning.

Expandcapacity

Take no action

Highdemand

Highdemand

Lowdemand

Lowdemand

Decision 1

Consider a capacity expansion decision.The return depends upon uncertain demand.A stochastic program will find a complete strategy

of optimal decisions given all demand scenarios.

Uncertain Outcome

Highest return

Low return

Moderatereturn

Expandcapacity

Take no action

Highdemand

Highdemand

Lowdemand

Decision 2

High return

Lowdemand

Uncertain Outcome

An Example…An Example…

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Facility Location DecisionsFacility Location Decisions

Operations Research:Operations Research:A “What-if” ApplicationA “What-if” Application

36km

W-4

Facility LocationFacility Location

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

• Warehouse has very Warehouse has very large capacitylarge capacity

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

10 000 units

180 000

10 000180 000

220 000

10 000

BB EE

36km


ij

i

j

n

iij

ii

d

jij

n

i

d

jijij

n

iii

y

x

djDy

nixCy

ts

yWxfMinimise

1,0

1,

1,

..

1

1

1 11

Scenario 1: Warehouse O/H cost is very small as compared to transportation cost– Warehouse O/H:

$6 000 000– Transportation cost:

$20/km/unit– proximity dominates– operate the

warehouse closest to 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 2: Warehouse O/H cost is very large as compared to transportation cost– Warehouse O/H: $1 800 000 000– Transportation cost:

$20/km/unit– too expensive to

operate a warehouse

– hence, the most centralised warehouse selected (based on 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 3: Both warehouse O/H and transportation costs are competing – Warehouse O/H:

$60 000 000– Transportation

cost: $20/km/unit– solution is not

obvious; too many possibilities

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 4:

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

$60 000 000– Transportation cost:

$20/km/unit– Warehouse

capacity: 150 000 units

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


Visit Us Online…Visit Us Online…


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