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2.3. More Complex Examples 29

2.3 More Complex Examples

2.3.1 A Scheduling Problem

Here, we consider the problem of scheduling tasks that require resources to complete,

and have to fulﬁll precedence constraints

. Figure 2.1 shows a precedence graph for

six tasks which are labelled as tX

, where X stands for the identiﬁer of a task t, Y

for its time to complete (duration), and Z for the identiﬁer of a machine m (a resource

needed for performing task tX).

Figure 2.1: Precedence Graph.

The following program (included in the distribution in the directory Examples in the

ﬁle scheduling.toy) models the posed scheduling problem. Observe in the syntax that

function arguments are not enclosed in parentheses to allow higher order applications.

Also, syntactic sugar is provided for expressing Boolean functions `a la Prolog. The

rules that deﬁne a function follow its type declaration. The type declaration consists

of the types for each argument and for the result separated by ->. Lists adhere to the

syntax as Prolog lists and int is a predeﬁned type for the integers. Note also functional

applications in arguments, such as (End-D) in the second rule deﬁning horizon. (Logic)

Variables start with uppercase, whereas the remaining symbols start with lowercase.

include "cflpfd.toy"

include "misc.toy"

data taskName = t1 | t2 | t3 | t4 | t5 | t6

data resourceName = m1 | m2

type durationType = int

type startType = int

type precedencesType = [taskName]

type resourcesType = [resourceName]

type task = (taskName, durationType, precedencesType, resourcesType, startType)

start :: task -> int

start (Name, Duration, Precedences, Resources, Start) = Start

duration :: task -> int

duration (Name, Duration, Precedences, Resources, Start) = Duration

Adapted from Marriot and Stuckey, 1998.

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Ascend FD-23R Manual de usuario Pagina 41