ILOG OPL Development Studio Language Reference Manual

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Expressions on interval variablesInteger and numerical expressions are available to access or evaluate different attributes ofan interval variable.These expressions can be used, for example, to define a term for the cost function or to connectinterval variables to integer and floating point expressions.The integer expressions are startOf, endOf, lengthOf, and sizeOf and they provide access tothe different attributes of an interval variable. Special care must be taken for optional intervals,as an integer value dval must be specified which represents the value of the expression whenthe interval is absent. If this value is omitted, it is supposed to be 0. For the syntax of integerexpressions, see endOf, lengthOf, sizeOf, and startOf in the OPL Language Quick Reference.The numerical expressions are startEval, endEval, lengthEval, and sizeEval, and they allowevaluation of a piecewise linear function on a given bound of an interval. As with integerexpressions, in the case of optional intervals an integer value dval must be specified whichrepresents the value of the expression when the interval is absent. If this value is omitted, itis supposed to be 0. For the syntax and examples of the use of a numerical expression, seeendEval, lengthEval, sizeEval, and startEval in the OPL Language Quick Reference.Let denote a fixed interval variable. The semantics of these expressions is shown in thetable.156I 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
Important:The piecewise linear function F used in ’eval’ expressions must be a semi-convexfunction. A semi-convex function is a function such that, if one draws a horizontalline anywhere in the Cartesian plane corresponding to the graph of the function,the set of x such that F(x) is below the line is empty or forms a single interval.Some examples of semi-convex piecewise linear functions are depicted in thefollowing figure.I 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 L157
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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
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Initializing tuplesYou initialize t
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Initializing setsYou can initialize
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As generic setsOPL supports generic
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Initialization and memory allocatio
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Database initializationDescribes ho
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Supported databasesSupported databa
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Reading from a databaseIn OPL, data
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DBconnection db("oracle9", connecti
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Note: OPL supports the same element
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Spreadsheet Input/OutputDescribes h
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Connection to a spreadsheetThe spre
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♦Sets of tuples: The data has to
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Data consistencyDefines the purpose
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Data membership consistencyThe keyw
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AssertionsOPL provides assertions t
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execute{writeln(s2);s1.add(3);write
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Decision typesVariables in an OPL a
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tuple Route {City orig;City dest;}{
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Dynamic collection of elements into
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The all syntaxThen, the all syntax
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Appending arraysYou can also concat
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ExpressionsDescribes data and decis
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Data and decision variable identifi
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(condition)?thenExpr : elseExprwher
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Piecewise-linear functionsPiecewise
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eakpoint[k-1] < ship[o][d] 0; 0}(1,
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Figure The discontinuous piecewise
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x == y;signx == piecewise{0->0; 2->
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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
Page 149 and 150: e equal to 1. For a fixed interval
Page 151 and 152: ExamplesFor examples of using inter
Page 153 and 154: Precedence constraints between inte
Page 155: A logical constraint between interv
Page 159 and 160: ♦prev(p, a, b) states that if bot
Page 161 and 162: Cumulative functionsIn scheduling p
Page 163 and 164: Constraints on cumul function expre
Page 165 and 166: Syntax and examplesFor the syntax a
Page 167 and 168: ♦That everywhere over a given fix
Page 169 and 170: in state s. If algn e is true, it m
Page 171 and 172: NotationsThe main notations used th
Page 173 and 174: ILOG Script for OPLDescribes the st
Page 175 and 176: Language structurePresents the stru
Page 177 and 178: SyntaxWhat composes a scripting sta
Page 179 and 180: Compound statementsA compound state
Page 181 and 182: IdentifiersIdentifiers are used to
Page 183 and 184: Expressions in ILOG ScriptExpressio
Page 185 and 186: LiteralsLiterals can represent the
Page 187 and 188: Syntax of different types of expres
Page 189 and 190: Property accessThere are two ways o
Page 191 and 192: Function callsSyntactic shorthandSy
Page 193 and 194: Special operatorsSpecial operator s
Page 195 and 196: Other operatorsOther operators are
Page 197 and 198: StatementsA statement can be a cond
Page 199 and 200: SyntaxEffectfor (var i=0; i < a.len
Page 201 and 202: Outside a function definitionAt the
Page 203 and 204: Default valuesDefault value syntaxS
Page 205 and 206: 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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