ILOG OPL Development Studio Language Reference Manual

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Aggregate operatorsInteger and float expressions can also be constructed using aggregate operators for computingsummations (sum), products (prod), minima (min), and maxima (max) of a collection ofrelated expressions. For instance, the excerptint capacity[Routes] = ...;int minCap = min(r in Routes) capacity[r];uses the aggregate operator min to compute the minimum value in array capacity. Theform of the formal parameters in these aggregate operators is very general and is discussedat length in Formal parameters.For information on operators in general, see Operators in the <strong>Language</strong> Quick <strong>Reference</strong>.94I 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
Piecewise-linear functionsPiecewise-linear functions are important in many applications. They are often specified bygiving a set of slopes, a set of breakpoints at which the slopes change, and the value of thefunctions at a given point. Consider, for instance, a transportation problem in which thetransportation cost between two locations o and d depends on the size of the shipment ship[o][d]. The piecewise-linear expression The piecewise-linear expressionpiecewise{10 -> 100;20 -> 200;40}(0,0) ship[o][d];describes the piecewise-linear function of ship[o,d] depicted in A Piecewise-linear function.The function has slopes 10, 20, and 40, breakpoints 100 and 200, and evaluates to 0 at point0.A Piecewise-linear function.In other words, the piecewise-linear expression is equivalent to the expression:10 * ship[o][d]whenship[o,d]
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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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Page 45 and 46: }}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: (condition)?thenExpr : elseExprwher
Page 97 and 98: eakpoint[k-1] < ship[o][d] 0; 0}(1,
Page 99 and 100: Figure The discontinuous piecewise
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
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Piecewise linear and stepwise funct
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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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