## ams_version=1.0
Model Main_Transport {
Comment: {
"This AIMMS project illustrates how to formulate and solve a mathematical
program in AIMMS. It contains the declarations and procedures necessary
to formulate and solve a simple transportation model. The objective of
the model is to find an optimal distribution of transports from a given
set of depots to a given set of customers, such that:
- The demand of every customer is met.
- The amount supplied from each depot does not exceed the total amount
available for supply.
- The total cost associated with the totality of transports is minimal.
For illustration this demo uses a dataset containing Dutch cities.
Keywords:
Linear Programming, Network Object, Database Communication."
}
Section Basic_Section {
DeclarationSection Input_Data {
Comment: {
"This section contains all the declarations which together represent
the input data of the transport model."
}
Set Locations {
Text: "The set of all depots and customer locations";
Index: l;
Parameter: Location;
Definition: Depots + Customers;
}
Set Depots {
SubsetOf: Locations;
Text: "The set of depots from which transports can emanate ";
Index: d;
Parameter: Depot;
OrderBy: d;
}
Set Customers {
SubsetOf: Locations;
Text: "The set of customers to which transport should take place";
Index: c;
Parameter: Customer;
OrderBy: c;
}
Parameter XCoordinate {
IndexDomain: l;
Text: "The (geographical) X coordinate of location l";
}
Parameter YCoordinate {
IndexDomain: l;
Text: "The (geographical) Y coordinate of location l";
}
Parameter Supply {
IndexDomain: d;
Text: "The total amount ready for supply from depot d";
}
Parameter Demand {
IndexDomain: c;
Text: "The total demand of customer c";
}
Parameter UnitTransportCost {
IndexDomain: (d,c);
Text: "The transport cost per unit transported from depot d to customer c";
}
}
DeclarationSection Model_Formulation {
Comment: {
"This section contains all the declarations necessary to formulate
the optimization model for the transport problem."
}
Variable Transport {
IndexDomain: (d,c);
Text: "The actual amount transported from depot d to customer c";
Range: nonnegative;
Comment: "Without specifying a nonnegative range, the optimization model becomes unbounded";
}
Constraint SatisfySupply {
IndexDomain: d;
Text: "The amount supplied by depot d cannot exceed its supply amount";
Definition: sum(c, Transport(d,c)) <= Supply(d);
}
Constraint MeetDemand {
IndexDomain: c;
Text: "The amount transported to customer c should meet its demand";
Definition: sum(d, Transport(d,c)) >= Demand(c);
}
Variable TotalCost {
Text: "The total cost associated with a particular distribution of transports";
Definition: sum((d,c), UnitTransportCost(d,c)*Transport(d,c));
}
MathematicalProgram TransportModel {
Objective: TotalCost;
Direction: minimize;
Constraints: AllConstraints;
Variables: AllVariables;
Text: "The optimizing transportation model";
Type: LP;
Comment: {
"The mathematical program contains all variables and all constraints
declared in the model. To specify this, you can make use of the predefined
set AllVariables and AllConstraints, which, at any time, contain the names
of all variables and constraints in your model, respectively. If you want a
mathematical program to be defined over a subset of the variables or
constraints, you should declare subsets of these sets in your model, and
specify these in the VARIABLES and CONSTRAINTS attributes."
}
}
}
DeclarationSection Additional_Interface_Identifiers {
StringParameter ProblemDescriptionFile {
Definition: "Description.txt";
}
Parameter DepotNameLong;
StringParameter DepotName {
IndexDomain: d;
Definition: {
if DepotNameLong then
FormatString("%e",d)
else
substring(FormatString("%e",d),1,2)
endif
}
}
Parameter CustomerNameLong;
StringParameter CustomerName {
IndexDomain: c;
Definition: {
if CustomerNameLong then
FormatString("%e",c)
else
substring(FormatString("%e",c),1,2)
endif
}
}
Set NetworkBounds {
Index: nb;
Definition: data { Left, Right, Top, Bottom };
}
Parameter ActiveBounds {
IndexDomain: nb;
}
StringParameter BasicInfo {
Definition: "network.txt";
}
Parameter BitmapBounds {
IndexDomain: nb;
}
ElementParameter ACase {
Range: AllCases;
}
}
Procedure BasicMainInitialization {
Body: {
read from file ":netherlands.txt";
Customer := first(c);
Depot := first(d);
Location := first(l);
DetermineDefaultNetworkBounds;
update DepotName, CustomerName;
}
Comment: {
"In this simple model, we obtain all input data from a single ASCII data file called \"netherlands.txt\".
It contains the data for depots and customers which both are a collection of Dutch cities.
This .txt file is stored as a project user file (see menu Tools - Project User Files);"
}
}
Procedure DetermineDefaultNetworkBounds {
Body: {
ActiveBounds(nb) := BitmapBounds(nb);
}
Comment: "Determines the bounds of the network object such that all locations are visible";
Parameter Tmax {
Text: "Temporary maximum";
}
Parameter Tmin {
Text: "Temporary minimum";
}
}
Procedure BasicMainExecution {
Body: {
solve TransportModel;
}
Comment: {
"A mathematical program can be solved using the SOLVE statement.
It causes AIMMS to generate a matrix based on the current content
of the sets and parameters used in the declaration of the variables
and constraints in a model. This matrix is sent to a solver for
optimization, after which the result is read back in AIMMS."
}
}
}
Section Database_Section {
DeclarationSection Database_Declarations {
StringParameter ExampleDataSource {
Definition: "AIMMS Transport Example Database.dsn";
}
StringParameter DatabaseInfo {
Definition: "Database.txt";
}
DatabaseTable LocationTable {
DataSource: ExampleDataSource;
TableName: "Locations";
Mapping: {
"Location" --> Locations,
"XCoord" --> XCoordinate( l ),
"YCoord" --> YCoordinate( l )
}
}
DatabaseTable DepotTable {
DataSource: ExampleDataSource;
TableName: "Depots";
Mapping: {
"Depot" --> Depots,
"Supply" --> Supply(d)
}
}
DatabaseTable CustomerTable {
DataSource: ExampleDataSource;
TableName: "Customers";
Mapping: {
"Customer" --> Customers,
"Demand" --> Demand( c )
}
}
DatabaseTable TransportTable {
DataSource: ExampleDataSource;
TableName: "Transports";
Mapping: {
"Depot" --> Depots,
"Customer" --> Customers,
"UnitCost" --> UnitTransportCost(d,c),
"Transport" --> Transport
}
}
}
Procedure ReadInputData {
Body: {
if CheckDatabaseLink then
read from table LocationTable;
read from table DepotTable;
read from table CustomerTable;
read UnitTransportCost from table TransportTable filtering d,c;
empty Transport;
endif;
}
Comment: "This procedure simply reads all data from the database tables";
}
Procedure ReadTransport {
Body: {
if CheckDatabaseLink then
read Transport from table TransportTable filtering d,c;
endif;
}
}
Procedure WriteTransport {
Body: {
if CheckDatabaseLink then
write Transport to table TransportTable in replace mode;
endif;
}
Comment: "This procedure write the data for Transport back into the database";
}
Procedure CheckDatabaseLink {
Body: {
if not TestDataSource(ExampleDataSource) then
DialogMessage("Please make sure the DSN file '"+ ExampleDataSource + "' exists and links to the database of this project");
return 0;
endif;
return 1;
}
}
Procedure DatabaseMainInitialization {
Body: {
ReadInputData;
Customer := first(c);
Depot := first(d);
Location := first(l);
DetermineDefaultNetworkBounds;
update DepotName, CustomerName;
}
Comment: {
"In this model, we obtain all input data from the access database transportexample.mdb (via ODBC or OLE DB link).
It contains the relevant data for depots and customers which both are a collection of Dutch cities."
}
}
Procedure DatabaseMainExecution {
Body: {
solve TransportModel;
}
Comment: {
"An mathematical program can be solved using the SOLVE statement.
It causes AIMMS to generate a matrix based on the current content
of the sets and parameters used in the declaration of the variables
and constraints in a model. This matrix is sent to a solver for
optimization, after which the result is read back in AIMMS."
}
}
}
Section Expressions_Section {
StringParameter ExpressionsInfo {
Definition: "expressions.txt";
}
Procedure ExpressionsMainInitialization {
Body: {
BasicMainInitialization;
}
Comment: {
"In this simple model, we obtain all input data from a single ASCII data file called \"netherlands.txt\".
It contains the data for depots and customers which both are a collection of Dutch cities.
This .txt file is stored as a project user file (see menu Tools - Project User Files);"
}
}
Procedure ExpressionsMainExecution {
Body: {
BasicMainExecution;
}
Comment: {
"An mathematical program can be solved using the SOLVE statement.
It causes AIMMS to generate a matrix based on the current content
of the sets and parameters used in the declaration of the variables
and constraints in a model. This matrix is sent to a solver for
optimization, after which the result is read back in AIMMS."
}
}
}
Section Constraint_Slacks_Section {
ElementParameter LastDepot {
Range: Depots;
}
Parameter NrOfInfeasibilities {
Definition: ConstraintSlacksTransportModel.NumberOfInfeasibilities;
}
Parameter SumOfInfeasibilities {
Definition: ConstraintSlacksTransportModel.SumOfInfeasibilities;
}
Parameter TransportViolationPenalty {
IndexDomain: IndexVariablesConstraints;
}
MathematicalProgram ConstraintSlacksTransportModel {
Objective: TotalCost;
Direction: minimize;
Constraints: AllConstraints;
Variables: AllVariables;
Text: "The optimizing transportation model";
Type: LP;
ViolationPenalty: TransportViolationPenalty;
Comment: {
"The Violation penalty attribute should contain a numerical parameter declared over the set
AllVariablesConstraints, in this case this is TransportViolationPenalty.
Constraints and variables with definition for which TransportViolationPenalty has the value
0 will be handled as in normal optimization.
Constraints and variables with definition for which TransportViolationPenalty has a value
larger than 0 will get a slack variable. If the slack variable has a non-zero value, it
will result in a extra penalty in the objective of the value of the slack variable times
the value of TransportViolationPenalty.
If the TransportViolationPenalty is zero, the constraint or variable with definition will
get a slack variable, but the slack variable will not result in a penalty.
Note that when the value of TransportViolationPenalty is 0 or a positive number for the
objective, the objective will be regarded for the optimization. If this value is zero,
the objective will not be handled for the optimization. This means, only the penalties
from the slack variables will be minimized."
}
}
Set NotSatisfiedDemandNodes {
SubsetOf: Customers;
Index: nsdn;
Definition: {
{ c | MeetDemand.Violation(c) <> 0}
}
}
StringParameter ConstraintSlacksInfo {
Definition: "constraintslacks.txt";
}
Procedure ConstraintSlacksMainInitialization {
Body: {
BasicMainInitialization;
empty MeetDemand.Violation;
TransportViolationPenalty( 'MeetDemand' ) := 100;
LastDepot := last( Depots );
Supply( LastDepot ) := 0;
}
}
Procedure ConstraintSlacksMainExecution {
Body: {
Solve ConstraintSlacksTransportModel;
! for (AllCandV) do
! currentConstraintVariable := AllCandV;
! ConstraintIsViolated := currentConstraintVariable.violation;
! endfor;
}
Comment: {
"For this optimization there will be a slack variable allowed for the MeetDemand
constraint, while the objective, TotalCost, will be handled as normal. The supply
in Zutphen is set to 0 to illustrate what happend if all the demand cannot be
satisfied."
}
ElementParameter currentConstraintVariable {
Range: AllVariablesConstraints;
}
}
}
Procedure MainInitialization {
Body: {
BasicMainInitialization;
}
Comment: {
"In this simple model, we obtain all input data from a single
ASCII data file called \"netherlands.txt\". It contains the data
for depots and customers which both are a collection of Dutch cities."
}
Parameter notNeeded;
Parameter OptionValue {
Range: integer;
}
}
Procedure MainExecution {
Body: {
solve TransportModel;
}
Comment: {
"A mathematical program can be solved using the SOLVE statement.
It causes AIMMS to generate a matrix based on the current content
of the sets and parameters used in the declaration of the variables
and constraints in a model. This matrix is sent to a solver for
optimization, after which the result is read back in AIMMS."
}
}
Procedure MainTermination {
Body: {
return 1;
}
Comment: {
"The return value of 1 indicates that we are not interested in
saving the current data in a case."
}
}
}