1 ilog modeling examples

8/14/2019 1 ILOG Modeling Examples

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2011 IBM Corporation

Modeling Optimization Problems with IBMILOG Cplex Optimization Studio

IBM Advanced Analytics Summit April 2011


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Agenda

Optimization Development

Sample Application

CPLEX Studio

Projects

Run Configurations

OPL Language

Primitive Types

Tuples

Sets

Arrays

Application to Mathematical Programming

Application to Detailed Scheduling Using Constraint Programming


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Optimization Development

Mathematical Model

Development

Optimization Expert

Traditional Application

Development

Software Developer

IBM ILOG CPLEX Studio reduces the time to

market for optimization applications


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Simple Application

Mathematical Model

Engine

Database

Spreadsheet

Input Data

Database

Spreadsheet

Output Data

GUI

Database FormsSpreadsheet

User Interface

Database

SpreadsheetGUI

Reporting

IBM ILOG OPL

IBM ILOG CPLEX

RawD

ata

Reposito

ry

Solve

IBM ILOG CP

Optimizer


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Key Features

OPL: Optimization Programming LanguageA compact language to represent optimization problems

Advanced types for data organization

Supports solving mathematical programming models with CPLEX and applying

constraint programming including scheduling with CP Optimizer

Connects to relational databases and Excel spreadsheets ILOG Script for data processing and iterative solving


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Key Features

Integrated Development Environment Graphical editor for OPL models and data files

File and project organization

Review data and solutions as tables

Menus/buttons to debug optimization

Online help for OPL syntaxAccess to engine features

Infeasibility Analysis

Solution Pools

Engine Parameters



Run Configuration

Run Configuration

Run Configuration

OPL Project

Anatomy of an OPL Project

Data Structure Definitions

Pre-Processing

Decision Variables

Objective FunctionConstraints

Post-Processing

Model File (.mod)

Excel Connections

Database Connections

Data Structure

Initializations

Data File (.dat)

CPLEX Settings

CPO SettingsLanguage Settings

Settings File (.ops)



Anatomy of an OPL Project

Model Files

You can share multiple model files between different run configurations: Good for

running the same model on many different data instances

You can have multiple model files in the same run configuration: Good for separating

data structure definitions from model definitions

Data Files

You can share multiple data files between different run configurations: Good for testingdifferent models on the same data instance

You can have multiple data files in the same run configuration: Good for separating

different data initializations



The Optimization Programming Language(OPL)


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OPL Language: Tuples

OPL allows you to create structured data types, called tuplestuplepair

{

int v;

string s;

};

You can define sets of tuplessetof(pair) S = { , , };


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OPL Language: Arrays

OPL allows you to define arrays of fundamental types

int a[1..4] = [10, 20, 30, 40];

and arrays indexed on sets of tuplestuple Edges

{

int orig;

int dest;}

{Edge} Edges = {, , };

int a[Edges] = [10,20,30];


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OPL Language: Decision variables and expressions

Decision variable - dvar

Can be defined as: int, float, boolean

Indexed on ranges or sets

dvar int nWorkers[1..nShifts];

dvar float+production[p in products][timePeriods];

dvar boolean assign[workers][tasks];

Decision expression - dexpr

For readability and to separate parts of the objective function

dexpr float tasksWorked = sum(w inworkers, t in tasks)assign[w][t];

minimize tasksWorked;


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Conditional loops

Standard Loopforall (i in 1..10) {

Conditional (filtered) Loopforall (i in 1..10 : mydata[i]


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Data driven relaxations

Use data to conditionally state a collection of constraints

Data declarationsint includeBundleConstraint = ...;

Conditional constraintsif (includeBundleConstraint == 1) {

forall (i in S1) {

sum (j in S2) x[j]


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Examples of logical and nonlinear expressions

Semi-continuous order quantity:(x == 0) || (x >= 100);

Logical indicators(x == 0) => (y == 0);

Zeros == sum (i in Index) (x[i] == 0);

Maximum deviation from a target valuedeviation ==

max (i in Index) abs(x[i]-target);

Benefits Model is easier to develop and maintain

Can eliminate some big-M bounds


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Examples and Demo


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A Production Planning Example

A manufacturer wants to sell a product

The product can be made either

Inside the factory

Scarce resources are required to build the product

There is a cost per unit to manufacture the product

Outside the factory

There is a cost per unit to purchase the product

All demand must be satisfied

The objective is to minimize cost


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A Production Planning Example: Data Declarations

Sets of products and resources

setof(string) Products = ...;setof(string) Resources = ...;

Number of units of each resource needed to produce one unit of each

product

float consumption[Products][Resources] = ...;

Total number of available resourcesfloat capacity[Resources] = ...;

Number of units in demand for each productfloat demand[Products] = ...;

Cost per unit of inside and outside productionfloat insideCost[Products] = ...;

float outsideCost[Products] = ...;


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A Production Planning Example: Decision Variables

Inside and outside production

dvar float+ inside[Products];

dvar float+ outside[Products];


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A Production Planning Example: Objective Function

Inside and outside production cost

dexpr float InsideCost =

sum(p in Products) insideCost[p] * inside[p];

dexpr float OutsideCost =sum(p in Products) outsideCost[p]* outside[p];

minimize InsideCost + OutsideCost;


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A Production Planning Example: Constraints

Capacity and demand constraints

subject to

{

forall (r in Resources)

ctCapacity:

sum (p in Products)

consumption[p][r]*inside[p] = demand[p];

};


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Products Could be Jewelry

Products and Resources

Products = { rings earrings };Resources = { gold diamonds };

ConsumptionConsumption = [ [3, 1], [2, 2] ];

Capacity (Available units of gold and diamonds)Capacity = [ 130, 180 ];

Demand (Number of rings and earrings)

Demand = [ 100, 150 ];

Costs (per unit for rings and earrings)InsideCost = [ 250, 200 ];

OutsideCost = [ 260, 270 ];


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Products Could be Pasta

Products and Resources

Products = { kluski capellini fettucine };Resources = { flour eggs };

ConsumptionConsumption = [ [0.5, 0.2], [0.4, 0.4], [0.3, 0.6] ];

Capacity (Available units of flour and eggs)Capacity = [20, 40];

Demand (Quantities of kluski, capellini, and fettucine )

Demand = [100, 200, 300];

Costs (per unit for of kluski, capellini, and fettucine )

InsideCost = [0.6, 0.8, 0.3];

OutsideCost = [0.8, 0.9, 0.4];


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Demo of Production Planning Example

Open OPL

Import Project

Show configuration

Show model, data and settings files

Show input data tables

Solve

Show output data tables

Show Solutions, Engine log, Statistics and Profiler tabs

Show Online help


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Scheduling using CP Optimizer - Demo

Building 5 houses with 3 workers and a cash budget.

Tasks are masonry, roofing, painting .

Some tasks must necessarily take place before others.

The building of a house must start after its release date

Each task requires one worker.

30,000 is available at the beginning of the project and 30,000 is added every 60 days.

Each task costs a given amount of cash per day which must be available at the start of

the task.

The objective is to minimize the overall completion date.


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Demo of sched_cumul

Import the sched_cumul project

See model and data file

Solve problem

Display the results in the Console tab and the Solutions tab


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Brief intro to the Scheduling API in OPL

interval variable:

An interval variable represents an interval of time during which an

activity is carried out. Its position in time is an unknown of the scheduling problem.

It is characterized by a start value, an end value and a size.

cumulFunction:

A cumulative function is used to model a quantity that varies over

time. Its value depends on other decision variables of the problem.

An activity usually increases the cumulFunction at the start of the usage of the

cumulative resources, and decreases the function when the resource is released at its

end time (pulse function).


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Brief intro to the Scheduling API in OPL - cont

pulse:

Pulse is a cumulative function expression that is used when an

activity increases the resource usage function at its start

decreases usage when it releases the resource at its end time.

precedence constraint:

Precedence constraints are common scheduling constraints used

to restrict the relative position of interval variables in a solution. Examples: startAtEnd, endAtStart, startAfterEnd, etc.


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CP Example Scheduling

using CP;

intNbWorkers = ...;

intNbHouses = ...;

range Houses = 1..NbHouses;

{string} TaskNames = ...;

int Duration [t in TaskNames] = ...;

tuple Precedence {

stringbefore;

string after;

};

{Precedence} Precedences = ...;

int ReleaseDate[Houses] = ...;


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CP Example - Scheduling

dvar interval itvs[h in Houses][t in TaskNames] inReleaseDate[h]..maxint size Duration[t];

cumulFunctionworkersUsage =

sum(h in Houses, t in TaskNames)pulse(itvs[h][t],1);

cumulFunction cash =

sum (p in 0..5) step(60*p, 30000)

- sum(h in Houses, t in TaskNames) stepAtStart(itvs[h][t],

200*Duration[t]);


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CP-Example Scheduling

minimize max(h in Houses) endOf(itvs[h]["moving"]);subject to {

forall(h in Houses)

forall(p in Precedences)

endBeforeStart(itvs[h][p.before], itvs[h][p.after]);

workersUsage = 0;

}

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