what is more? a consulting group based at the department of mathematics and statistics university of...
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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.
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• 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?
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MORe PeopleMORe People
Olivia Smith
Dr Heng-Soon Gan
Prof. Peter Taylor
Prof. Bob Johnston
Prof Natashia BolandUniversity of Newcastle
Prof Mark WallaceMonash University
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• 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
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Mathematical Solution Method (Algorithm)
Real Practical Problem
Mathematical (Optimization) Problem
x2
Computer Algorithm
Human Decision-Maker
Decision Support System
Mathematics in OperationMathematics in Operation
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MORe ExperiencesMORe Experiences
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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
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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
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Forces “wishlist”
$ $ $ $Choose forces(STRATEGIC)
Constraints: Budget
Objectives
Deploy forces(TACTICAL)
e e e e ee e max effectiveness
Decision:Force configuration
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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
??
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AAAA BBBB CCCC DDDD EEEE FFFFBus empty?Bus empty?Bus empty?Bus empty?
Dropoff Dropoff Location 3Location 3
Dropoff Dropoff Location 3Location 3
Pickup Pickup LocationLocationPickup Pickup
LocationLocation
YesYes
NoNo
Car Car ParkPark
Airport terminalsAirport terminals
Dropoff Dropoff Location 2Location 2
Dropoff Dropoff Location 2Location 2
Dropoff Dropoff Location 1Location 1
Dropoff Dropoff Location 1Location 1
PickupPickup
PickupPickup
DropoffDropoff
DropoffDropoff
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Micro-SimulationMicro-SimulationPlanimate® Simulation ModelPlanimate® Simulation Model
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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
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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
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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
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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
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• 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
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• Decisions are interlinked.
• Need wholistic solution techniques that make all decisions simultaneously, and account for interactions.
• Linear (integer) programming is the key.
SolutionSolution
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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.
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• 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…
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CarLO ScreenshotsCarLO Screenshots
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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
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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.
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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
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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
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Facility LocationFacility Location
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
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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
Facility LocationFacility Location
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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
Facility LocationFacility Location
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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
Facility LocationFacility Location
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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
Facility LocationFacility Location
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Visit Us Online…Visit Us Online…
www.more.ms.unimelb.edu.auwww.more.ms.unimelb.edu.au
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