ILOG OPL Development Studio Language Reference Manual

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The discontinuous piecewise linear function sign()Then this modeldvar float x;dvar float signx;dvar float y;dvar float signy;maximize x;subject to {x == 2;signx == piecewise{0->0; 2->0; 0}(1,1) x;y == -2;signy == piecewise{0->0; 2->0; 0}(1,1) y;}gives the following output:Final solution with objective 2.0000:x = 2.0000;signx = 1.0000;y = -2.0000;signy = -1.0000;98I L O G O P L D E V E L O P M E N T S T U D I O L A N G U A G ER E F E R E N C E M A N U A L
Figure The discontinuous piecewise linear function sign() shows that the value of the signfunction at the breakpoint is either -1 (on the left-hand slope) or 1 (on the right-hand slope).For example, this model takes this into account and sets the constraint x==y; on both values.dvar float x;dvar float signx;dvar float y;dvar float signy;maximize signx-signy;subject to {x == y;signx == piecewise{0->0; 2->0; 0}(1,1) x;signy == piecewise{0->0; 2->0; 0}(1,1) y;}This model solves with the following output:Final solution with objective 2:signx = 1;signy = -1;x = 0;y = 0;Example 2: discontinuous costThe following piecewise functionpiecewise{0->10; 5->10; 0->20; 5->20; 0} (0,10) unit;represents a discontinuous cost.This function is illustrated in Figure Discontinuous costs for the values summarized in TableA discontinuous cost function.A discontinuous cost functionValues of Unit20Cost0101520I L O G O P L D E V E L O P M E N T S T U D I O L A N G U A G ER E F E R E N C E M A N U A L99
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CopyrightCOPYRIGHT NOTICECopyright
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C O N T E N T STable of contentsLan
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Language Reference ManualThis manua
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OPL, the modeling languagePresents
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ModelsDescribes the overall structu
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}ctMaxTotal:Gas + Chloride
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Data typesDescribes basic data type
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Basic data typesDescribes integers,
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FloatsShows how to declare floats i
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Data structuresDescribes how the ba
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The range float declarationA range
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{Edge} Edges = {, , };int a[Edges]
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TuplesData structures in OPL can al
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In Declaring a tuple using a set of
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SetsDefinitionSets are non-indexed
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Sorted and ordered setsBy default,
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The data shows that the team includ
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Data sourcesDescribes data and data
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Data initializationDefines internal
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{Ship} shipData = ...;and assume th
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* .dat file */a = #[“Monday”: 1
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}}the same can be expressed with th
Page 47 and 48: Initializing tuplesYou initialize t
Page 49 and 50: Initializing setsYou can initialize
Page 51 and 52: As generic setsOPL supports generic
Page 53 and 54: Initialization and memory allocatio
Page 55 and 56: Database initializationDescribes ho
Page 57 and 58: Supported databasesSupported databa
Page 59 and 60: Reading from a databaseIn OPL, data
Page 61 and 62: DBconnection db("oracle9", connecti
Page 63 and 64: Note: OPL supports the same element
Page 65 and 66: Spreadsheet Input/OutputDescribes h
Page 67 and 68: Connection to a spreadsheetThe spre
Page 69 and 70: ♦Sets of tuples: The data has to
Page 71 and 72: Data consistencyDefines the purpose
Page 73 and 74: Data membership consistencyThe keyw
Page 75 and 76: AssertionsOPL provides assertions t
Page 77 and 78: execute{writeln(s2);s1.add(3);write
Page 79 and 80: Decision typesVariables in an OPL a
Page 81 and 82: tuple Route {City orig;City dest;}{
Page 83 and 84: Dynamic collection of elements into
Page 85 and 86: The all syntaxThen, the all syntax
Page 87 and 88: Appending arraysYou can also concat
Page 89 and 90: ExpressionsDescribes data and decis
Page 91 and 92: Data and decision variable identifi
Page 93 and 94: (condition)?thenExpr : elseExprwher
Page 95 and 96: Piecewise-linear functionsPiecewise
Page 97: eakpoint[k-1] < ship[o][d] 0; 0}(1,
Page 101 and 102: x == y;signx == piecewise{0->0; 2->
Page 103 and 104: Functions over setsFunction Descrip
Page 105 and 106: ConstraintsSpecifies the constraint
Page 107 and 108: Using constraintsExplains how to ap
Page 109 and 110: Conditional constraintsIf-then-else
Page 111 and 112: Constraint labelsExplains why label
Page 113 and 114: Labeling constraintsTo label a cons
Page 115 and 116: subject to {forall( p in Products ,
Page 117 and 118: Limitations to constraint labelingN
Page 119 and 120: Compatibility between constraint na
Page 121 and 122: Types of constraintsDescribes const
Page 123 and 124: Discrete constraintsDiscrete constr
Page 125 and 126: Implicit constraintsImplicit constr
Page 127 and 128: Symbol=>!===MeaningImplyDifferent f
Page 129 and 130: Constraints available in constraint
Page 131 and 132: ♦Interval grouping constraint: al
Page 133 and 134: Formal parametersDescribes basic fo
Page 135 and 136: {forall(i in 1..8)forall(j in 1..8:
Page 137 and 138: Tuples of parametersOPL allows tupl
Page 139 and 140: int array[i in set1] = ((sum(j in s
Page 141 and 142: SchedulingDescribes how to model sc
Page 143 and 144: IntroductionILOG OPL Development St
Page 145 and 146: Piecewise linear and stepwise funct
Page 147 and 148: I L O G O P L D E V E L O P M E N T
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e equal to 1. For a fixed interval
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ExamplesFor examples of using inter
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Precedence constraints between inte
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A logical constraint between interv
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Important:The piecewise linear func
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♦prev(p, a, b) states that if bot
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Cumulative functionsIn scheduling p
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Constraints on cumul function expre
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Syntax and examplesFor the syntax a
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♦That everywhere over a given fix
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in state s. If algn e is true, it m
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NotationsThe main notations used th
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ILOG Script for OPLDescribes the st
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Language structurePresents the stru
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SyntaxWhat composes a scripting sta
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Compound statementsA compound state
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IdentifiersIdentifiers are used to
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Expressions in ILOG ScriptExpressio
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LiteralsLiterals can represent the
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Syntax of different types of expres
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Property accessThere are two ways o
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Function callsSyntactic shorthandSy
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Special operatorsSpecial operator s
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Other operatorsOther operators are
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StatementsA statement can be a cond
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SyntaxEffectfor (var i=0; i < a.len
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Outside a function definitionAt the
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Default valuesDefault value syntaxS
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Built-in values and functionsPresen
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NumbersNumber representations and f
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IntroductionNumbers can be expresse
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Hexadecimal numbersA hexadecimal nu
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Special numbersThere are three spec
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Number methodsThere is only one num
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Numeric constantsThe following nume
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Syntax~ xx > yx >>> yEffectBitwise
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ILOG Script stringsString represent
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Examples of string literals using e
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String propertiesThere is a single,
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Syntaxstring.toUpperCase()EffectExa
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String operatorsString operatorsSyn
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ILOG Script BooleansBoolean represe
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Automatic conversion to BooleanWhen
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Logical operatorsThe following Bool
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ILOG Script arraysArray representat
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Array constructorThe array construc
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Array methodsArray methodsSyntaxarr
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ObjectsObject representation and fu
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Defining methodsSince a method is r
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Object constructorObject constructo
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Built-in methodsThere is only one o
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DatesDate representation and functi
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Date constructorThe date constructo
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Date methodsDate methodsSyntaxdate.
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Date functionsDate functionsSyntaxD
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The null valueThe null value is a s
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ILOG Script functionsIn ILOG Script
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I N D E XIndexABabs, OPL function 9
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limitations in tuples 29ranges 22se
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GHIgeneric sets 51, 137groundbreakp
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NOfor the null value 259for the und
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sparsityand multidimensional arrays
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ILOG OPL Development Studio Language Reference Manual

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