ILOG OPL Development Studio Language Reference Manual

Sequencing of interval variablesAn interval sequence variable is defined on a set of interval variables A. Informally speaking,the value of an interval sequence variable represents a total ordering of the interval variablesof A. Note that any absent interval variables are not considered in the ordering.More formally, an interval sequence variable p on a set interval variables A represents adecision variable whose possible values are all the permutations of the intervals of A. Letbe a set of fixed intervals and n denote the cardinality of .Note that the sequence alone does not enforce any constraint on the relative position of intervalsend-points. For instance, an interval variable a could be sequenced before an interval variableb in a sequence p without any impact on the relative position between the start/end points ofa and b (a could still be fixed to start after the end of b). This is because different semanticscan be used to define how a sequence constrains the positions of intervals. We will see laterhow the noOverlap constraint implements one of these possible semantics.The sequence variable also allows associating a fixed integer type with each interval variablein the sequence. In particular, these integers are used by the noOverlap constraint. T(p, a)denotes the fixed integer type of interval variable a in the sequence variable p.Constraints on sequence variablesThe following constraints are available on sequence variables:♦first(p,a) states that if interval a is present, then it will be the first interval of the sequencep.♦last(p,a) states that if interval a is present, then it will be the last interval of the sequencep.♦before(p, a, b) states that if both intervals a and b are present then a will appear before bin the sequence p.158I 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