'cumulative' and 'disjunctive' constraints for scheduling and planning problems
Description
- cumulative.mos: using the 'cumulative' constraint to formulate a
scheduling problem with resource constraints (renewable resource with discrete capacity)
- disjunctive.mos: using the 'disjunctive' constraint for implementing a sequencing problem (single-maching scheduling minimizing the total weighted tardiness.
- resource_capacity.mos: using 'task' and
'resource' objects to model a cumulative resource relation (renewable resource with different capacity levels over time).
- resource_coupled_setup_times.mos: specifying setup times between pairs of tasks assigned to the same resource.
Further explanation of this example:
'Xpress Kalis Mosel Reference Manual'
Source Files
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disjunctive.mos
(!****************************************************************
CP example problems
===================
file disjunctive.mos
````````````````````
Scheduling disjunctive tasks.
(c) 2008 Artelys S.A. and Fair Isaac Corporation
Creation: 2005, rev. 2007, rev. Mar. 2013
*****************************************************************!)
model "Disjunctive scheduling with settle_disjunction"
uses "kalis", "mmsystem"
declarations
NBTASKS = 5
TASKS = 1..NBTASKS ! Set of tasks
DUR: array(TASKS) of integer ! Task durations
DURs: array(set of cpvar) of integer ! Durations
DUE: array(TASKS) of integer ! Due dates
WEIGHT: array(TASKS) of integer ! Weights of tasks
start: array(TASKS) of cpvar ! Start times
tmp: array(TASKS) of cpvar ! Aux. variable
tardiness: array(TASKS) of cpvar ! Tardiness
twt: cpvar ! Objective variable
zeroVar: cpvar ! 0-valued variable
Strategy: array(range) of cpbranching ! Branching strategy
Disj: set of cpctr ! Disjunctions
end-declarations
DUR :: [21,53,95,55,34]
DUE :: [66,101,232,125,150]
WEIGHT :: [1,1,1,1,1]
setname(twt, "Total weighted tardiness")
zeroVar = 0
setname(zeroVar, "zeroVar")
! Setting up the decision variables
forall(t in TASKS) do
start(t) >= 0
setname(start(t), "Start("+t+")")
DURs(start(t)):= DUR(t)
tmp(t) = start(t) + DUR(t) - DUE(t)
setname(tardiness(t), "Tard("+t+")")
tardiness(t) = maximum({tmp(t), zeroVar})
end-do
twt = sum(t in TASKS) (WEIGHT(t) * tardiness(t))
! Create the disjunctive constraints
disjunctive(union(t in TASKS) {start(t)}, DURs, Disj, 1)
! Define the search strategy
Strategy(1):= settle_disjunction
Strategy(2):= split_domain(KALIS_LARGEST_MIN,KALIS_MIN_TO_MAX)
cp_set_branching(Strategy)
setparam("KALIS_DICHOTOMIC_OBJ_SEARCH",true)
if not cp_minimize(twt) then
writeln("Problem is inconsistent")
exit(0)
end-if
forall(t in TASKS)
writeln(formattext("[%3d==>%3d]:\t %2d (%d)", start(t).sol,
start(t).sol + DUR(t), tardiness(t).sol, tmp(t).sol))
writeln("Total weighted tardiness: ", getsol(twt))
end-model
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