Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
103 lines
3.8 KiB
MiniZinc
103 lines
3.8 KiB
MiniZinc
/** @group globals.scheduling
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Requires that a set of tasks given by start times \a s, durations \a d, and
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resource requirements \a r, never require more than a global resource bound
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\a b at any one time.
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Assumptions:
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- forall \p i, \a d[\p i] >= 0 and \a r[\p i] >= 0
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Linear version.
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*/
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predicate fzn_cumulative(array[int] of var int: s,
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array[int] of var int: d,
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array[int] of var int: r, var int: b) =
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if mzn_in_redundant_constraint() /\ fMZN__IgnoreRedundantCumulative then
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true
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else
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let {
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set of int: tasks =
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{i | i in index_set(s) where ub(r[i]) > 0 /\ ub(d[i]) > 0 },
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set of int: times = dom_array( [ s[i] | i in tasks ] )
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} in
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if 0==card(tasks) then /*true*/ 0==card(index_set(s)) \/ b>=0
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elseif MZN__Cumulative_Fixed_d_r /\
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is_fixed(d) /\ is_fixed(r) /\ is_fixed(b) then
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fzn_cumulative_fixed_d_r(s, fix(d), fix(r), fix(b))
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elseif nMZN__UnarySizeMax_cumul>=card(times)*card(tasks) then
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cumulative_time_decomp(s, d, r, b, times)
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else
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cumulative_task_decomp(s, d, r, b)
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endif
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endif;
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%% Can be called with a given set of times:
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predicate cumulative_set_times(array[int] of var int: s,
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array[int] of var int: d,
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array[int] of var int: r,
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var int: b,
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set of int: TIMES01) =
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assert(index_set(s) == index_set(d) /\ index_set(s) == index_set(r),
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"cumulative: the 3 array arguments must have identical index sets",
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assert(lb_array(d) >= 0 /\ lb_array(r) >= 0,
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"cumulative: durations and resource usages must be non-negative",
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let {
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set of int: tasks =
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{i | i in index_set(s) where ub(r[i]) > 0 /\ ub(d[i]) > 0 },
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set of int: times = dom_array( [ s[i] | i in tasks ] )
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intersect TIMES01
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} in
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if false then
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cumulative_time_decomp(s, d, r, b, times)
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else
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cumulative_task_decomp(s, d, r, b)
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endif ));
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predicate cumulative_time_decomp(array[int] of var int: s,
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array[int] of var int: d,
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array[int] of var int: r,
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var int: b,
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set of int: TIMES01) =
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let {
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set of int: tasks =
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{i | i in index_set(s) where ub(r[i]) > 0 /\ ub(d[i]) > 0 },
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set of int: times =
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{ i | i in min([ lb(s[i]) | i in tasks ]) ..
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max([ ub(s[i]) + ub(d[i]) | i in tasks ]) where i in TIMES01 }
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}
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in
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forall( t in times ) (
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b >= sum( i in tasks ) (
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if is_fixed(d[i]) then
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bool2int( s[i] in t-fix(d[i])+1..t )
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else
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bool2int( s[i] <= t /\ t < s[i] + d[i] )
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endif
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* r[i]
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)
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);
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predicate cumulative_task_decomp(array[int] of var int: s,
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array[int] of var int: d,
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array[int] of var int: r,
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var int: b) =
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let {
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set of int: tasks =
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{i | i in index_set(s) where ub(r[i]) > 0 /\ ub(d[i]) > 0 }
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}
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in
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forall( j in tasks) (
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b-r[j] >= sum( i in tasks where i != j
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/\ lb(s[i])<=ub(s[j]) /\ lb(s[j])<ub(s[i]+d[i]) %% -- seems slower on mspsp ???
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) (
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r[i] * %% r[i] * !
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bool2int( s[i] <= s[j] /\ s[j] < s[i]+d[i] )) )
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;
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%% A global cumulative with SCIP: fixed d and r
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predicate fzn_cumulative_fixed_d_r(array[int] of var int: s,
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array[int] of int: d,
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array[int] of int: r, int: b);
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