4.2.2.10. Scheduling constraints

In this section: alternative, cumulative, cumulatives, disjunctive, disjunctive_strict, span.

alternative

predicate alternative(var opt int: s0,
                      var int: d0,
                      array [int] of var opt int: s,
                      array [int] of var int: d)

Alternative constraint for optional tasks. The task with start time s0 and duration d0 spans the optional tasks with start times s[i] and durations d[i]), and at most one of those tasks can occur.

cumulative

1.  predicate cumulative(array [$$E] of var int: s,
                         array [$$E] of var int: d,
                         array [$$E] of var int: r,
                         var int: b)

2.  predicate cumulative(array [$$E] of var opt int: s,
                         array [$$E] of var int: d,
                         array [$$E] of var int: r,
                         var int: b)

Requires that a set of tasks given by start times s, durations d, and resource requirements r, never require more than a global resource bound b at any one time.

Assumptions:
- forall i, d[i] >= 0 and r[i] >= 0
Requires that a set of tasks given by start times s, durations d, and resource requirements r, never require more than a global resource bound b at any one time. Start times are optional variables, so that absent tasks do not need to be scheduled.

Assumptions:
- forall i, d[i] >= 0 and r[i] >= 0

cumulatives

1.  predicate cumulatives(array [$$E] of var int: s,
                          array [$$E] of var int: d,
                          array [$$E] of var int: r,
                          array [$$E] of var $$M: m,
                          array [$$M] of var int: b,
                          bool: upper)

2.  predicate cumulatives(array [$$E] of var opt int: s,
                          array [$$E] of var int: d,
                          array [$$E] of var int: r,
                          array [$$E] of var $$M: m,
                          array [$$M] of var int: b,
                          bool: upper)

We have a set of tasks given by start times s, durations d, resource requirements r, and machines m. We also have a set of machines given by resource bounds b. Finally, we have a Boolean flag upper. The constraint requires that forall i, m[i] is in the index set of b and that for each machine j and time instant t, either no task assigned to j executes at t, or the total resource requirement of such tasks is not greater than, if upper is true, or not less than, if upper is false, the given bound b[j]. Resource requirements can be positive (for consumption) or negative (for production).

Assumptions:
- forall i, d[i] >= 0
We have a set of optional tasks given by start times s, durations d, resource requirements r, and machines m. We also have a set of machines given by resource bounds b. Finally, we have a Boolean flag upper. The constraint requires that forall i, m[i] is in the index set of b and that for each machine j and time instant t, either no task assigned to j executes at \t, or the total resource requirement of such tasks is not greater than, if upper is true, or not less than, if upper is false, the given bound b[j]. Resource requirements can be positive (for consumption) or negative (for production).

Assumptions:
- forall i, d[i] >= 0

disjunctive

1.  predicate disjunctive(array [$$T] of var int: s,
                          array [$$T] of var int: d)

2.  predicate disjunctive(array [$$T] of var opt int: s,
                          array [$$T] of var int: d)

Requires that a set of tasks given by start times s and durations d do not overlap in time. Tasks with duration 0 can be scheduled at any time, even in the middle of other tasks.

Assumptions:
- forall i, d[i] >= 0
Requires that a set of tasks given by start times s and durations d do not overlap in time. Tasks with duration 0 can be scheduled at any time, even in the middle of other tasks. Start times are optional variables, so that absent tasks do not need to be scheduled.

Assumptions:
- forall i, d[i] >= 0

disjunctive_strict

1.  predicate disjunctive_strict(array [$$T] of var int: s,
                                 array [$$T] of var int: d)

2.  predicate disjunctive_strict(array [$$T] of var opt int: s,
                                 array [$$T] of var int: d)

Requires that a set of tasks given by start times s and durations d do not overlap in time. Tasks with duration 0 CANNOT be scheduled at any time, but only when no other task is running.

Assumptions:
- forall i, d[i] >= 0
Requires that a set of tasks given by start times s and durations d do not overlap in time. Tasks with duration 0 CANNOT be scheduled at any time, but only when no other task is running. Start times are optional variables, so that absent tasks do not need to be scheduled.

Assumptions:
- forall i, d[i] >= 0

span

predicate span(var opt int: s0,
               var int: d0,
               array [$$E] of var opt int: s,
               array [$$E] of var int: d)

Span constraint for optional tasks. Task (s0,d0) spans the optional tasks (s[i],d[i]) in the array arguments.