Network Optimization using AIMMS in the Analytics & Visualization Era

Dr. Ovidiu Listes

Senior Consultant

AIMMS Analytics and Optimization

• Analytics, Optimization, Networks

• AIMMS: The Modeling System

• Network Models Building

• Dealing with Complexity and Uncertainty

• From Model to Application

• Network Planning Applications

• More about AIMMS

Analytics

Optimization

Networks

Decision Support/(Web) UI Apps

Solution/Visualization

Modeling

Outline

Analytics, Optimization, Networks

The New Trend: Analytics

Better Decisions based on Data Analysis

Analytics at Work (2010): Smarter Decisions, Better Results

Competing on Analytics (2007): The New Science of Winning

Getting the Optimization Edge

Competitive advantage through Optimization

Why do some companies become industry leaders, while others never rise to the top?

… these companies posses an ability to make complex decisionsfaster, more accurately, and more consistently than their competition

… because they are big users of Optimization!

The Field of Network Flows

Optimization based on the Network concept

Fundamental field in Analytics, Operations Research & Optimization

… solid theory

… rich collection of algorithms

… vast area of applications

… eventually using

Modeling & Optimization!

AIMMS: The Modeling System

AIMMS: integrated & interactive modeling system

• Modeling language

• Extensive development tools

• Seamless solvers links

• Integrated GUI

• Advanced deployment options

• Development of AIMMS Apps

• Win UI and Web UI

The AIMMS System

AIMMS Features (selection)

• Point & Click / Drag & Drop IDE

• Global & local compilation

• Procedural execution & definitions

• Advanced diagnostic & development tools: debugger, profiler, MP Inspector, data pages

• Data management & batch run options

• Modeling of time constructs

• Broad class of commercial and open source solvers

• Broad call of model types (LP, MIP, NLP, MINLP, CP, etc.)

AIMMS Features (selection cont’d)

• Update, call-back, parallel solver options

• Extensive matrix update functionality

• Advanced & interactive GUI objects: Gantt-chart, Pivot table, Network object, etc. (for analyst, developer, and end user)

• GIS connectivity

• Units, Multi-Language & Conventions

• GUI Templates for standard look-and-feel of applications

• Multi-Developer Support

• Advanced Deployment options: AIMMS PRO and Web UI

• Much more…

Network Models Building

Network Flow ModelsNetwork Optimization and Visualization

Network Flow ModelsGeneric Arcs and Nodes

Network Flow ModelsEquivalent Modeling Formulation

Facility Location Models

Network Optimization and Visualization

Facility Location Models

Multi-Commodity Network Flow

Facility Location Models

Supply & Demand Constraints

Facility Location Models

Flow Balance Constraints

Petrochemical Processes Models

Network Optimization and Visualization

Petrochemical Processes Models

Unit Composition and Flow Constraints

Petrochemical Processes ModelsSeparation and Transformation Constraints

Dealing with

Complexity and Uncertainty

Production and Distribution Model

Multi-dimensional Network Data

• Indices– l Locations– f Factories– c Distribution Centers– t Periods– s Scenarios

• Parameters

– Dlts Demand [hl]

• Variables– ylts Stock [hl]– qlt Production [hl]– xfcts Transport [TL]

Demand is uncertain stochastic scenarios

Rolling horizon, (time) decomposition

Production and Distribution Model

Stochastic Scenarios & Rolling Horizon

𝑦𝑙𝑡𝑠 = 𝑦𝑙,𝑡−1,𝑠 + 𝑞𝑙𝑡 + 𝑓 𝑥𝑓𝑙𝑡𝑠 − 𝑐 𝑥𝑙𝑐𝑡𝑠 − 𝐷𝑙𝑡𝑠 ∀(𝑙, 𝑡, 𝑠)

Network Design Model

Problem Description

• Undirected graph (V,E); capacity Ce and cost ce

• Each edge e ∈ E can be used in both directions −> (V,A)

• Set of commodities Q with origin s(q) and destination t(q)

• Demand value dq for every q ∈ Q

• Goal: find cheapest capacities on each e ∈ E so that the

resulting network can satisfy each demand

1,1

3,1

1,3

3,1

1,1

1,2

D

EC

3,2

2

2

A

B

Network Design Model

MIP Formulation

Minimize

∑e∈E ceye

Subject to

∑q∈Q (xqij + xq

ji) ≤ Ceye e=(i,j) ∈ E

∑j∈V:(j,i) ∈A xqji – ∑j∈V:(i,j) ∈A xq

ij = dq i ∈ V, q ∈ Q

x ≥ 0

y ≥ 0 and integer

Network Design Model

Automatic Benders Decomposition in AIMMS

Using GMP Benders Decomposition system module:

myGMP := GMP::Instance::Generate(NetworkDesignMP);

GMPBenders::DoBendersDecomposition(

/* GMP */ myGMP,

/* MasterVariables */ AllIntegerVariables,

/* BendersMode */ ‘Classic’ );

Flexibility in Manufacturing Networks

Principles and Benefits of Flexibility

Flexibility in Manufacturing Networks

Automatic RO counterpart generation in AIMMS

Flexibility in Manufacturing Networks

Demand Uncertainty & Robust Optimization

Deterministic Robust Optimization

From Model to Application

Applying Optimization with AIMMS

Iterative & Interactive

Visualize the results and interact with your modelusing the GUI builder

Deploy to end-users• AIMMS GUI• Custom GUI• Excel add-in • Web• Local or remote

Use powerful solversor construct your ownsolution approach

Import data fromdifferent sources

Create and modifylarge models in a clearand concise way

CPLEX …

ODBCOLE DB

AIMMS PRO is ideally suited for company wide

Optimization:

• Allows easy deployment, flexible and fast development

• One platform for all optimization apps required

• Accessable, anywhere and anytime

AIMMS PRO & Enterprise App Stores

Company-wide Optimization

AIMMS PRO & Web UI

Optimization in Everyone’s Browser

Network Planning Applications

Supply Chain Optimization

Network Optimization and Visualization

Supply Chain Optimization

Network Structure and Rolling Horizon

Optimized Supply Chain Design

Network Optimization and Visualization

Optimized Supply Chain Design

Bubble and Service Maps

Demand & Supply Data AnalyticsBusiness Analytics POC Application

Existing Plant

New Plant

Zip Code

Capacitated location - allocation model with options for expansion of

existing capacity and additional side constraints

Demand & Supply Data Analytics

Underlying network structure

Allow easy selection for several model options:

• Consider/Don’t consider specific existing plants

• Allow/Don’t allow location of new plants

• Select specific location choices allowing for new plants

• Tune in the acuracy of the solution process

Allow for group interaction with the model:

• Visualize allocation results

• Compute Key Performance Indicators (KPIs)

• Establish relationships between investment levels

AIMMS apps can easily accommodate all this kind of requirements !

Demand & Supply Data Analytics

“Boardroom” Analysis Requirements

More about AIMMS…

More about AIMMS Use Options

AIMMS, integrated & interactive modeling system

• Modeling language, integrated GUI, direct access to solvers, advanced deployment options, and extensive development tools

• Development of AIMMS Apps

AIMMS PRO & Web UI

• Collaboration and deployment platform

for AIMMS Apps

• Central optimization and management

• Quick delivery of value to end users

Supports the complete optimization chain

• from rapid prototyping to large-scale deployment

• from development to operational use

• from single use to multi use

• from desktop to published (Web UI) application

SOURCE: MIT SLOAN Management Review

THANK YOU !

Questions ?

Dr. Ovidiu Listeso.listes@aimms.com

Next AIMMS Webinar

The next webinar in this series:

“The AIMMS Presolver” will be presented by Marcel Hunting,

AIMMS Optimization Specialist

Join us on July 15, 2015 at

5 PM CET / 8 AM PDT / 11 AM EDT