%------------------------------------------------------------------------------%
% singHoist2.mzn
% Peter Stuckey
% September 30 2006
%------------------------------------------------------------------------------%
%------------------------------------------------------------------------------%
% singHoist2.zinc
% Jakob Puchinger <jakobp@cs.mu.oz.au>
% Wed Jun 21
%------------------------------------------------------------------------------%

%------------------------------------------------------------------------------%
% Minizinc model of one-hoist scheduling
%
% Robert Rodosek and Mark Wallace
% A Generic Model and Hybrid Algorithm for Hoist Scheduling Problems
% in Michael J. Maher and Jean-Francois Puget eds.
% Principles and Practice of Constraint Programming - CP98,
% Springer, Lecture Notes in Computer Science, volume 1520, 1998.


%------------------------------------------------------------------------------%
% constants

int:                                             NumTanks;
int:                                             NumJobs;
array [0..NumTanks, 0..NumTanks]     of int:     Empty;
array [0..NumTanks]                  of int:     Full;
array [1..NumTanks]                  of int:     MinTime;
array [1..NumTanks]                  of int:     MaxTime;


%------------------------------------------------------------------------------%
% decision variables

int: PerMax = sum([MaxTime[i] | i in 1..NumTanks]);

array [0..NumTanks] of var 0..(NumJobs * PerMax): Entry;
array [0..NumTanks] of var 0..(NumJobs * PerMax): Removal;
var 0..PerMax                                   : Period;

%------------------------------------------------------------------------------%
% model

solve minimize Period;

constraint
    forall (Tank in 0..NumTanks) (
	 Removal[Tank] + Full[Tank] = Entry[(Tank + 1) mod (NumTanks+1)]
    );

constraint
	forall (Tank in 1..NumTanks) (
		Entry[Tank] + MinTime[Tank] <= Removal[Tank]
	/\	Entry[Tank] + MaxTime[Tank] >= Removal[Tank]
	);

constraint
	Removal[NumTanks] + Full[NumTanks] <= NumJobs * Period;

% disjoint constraint
constraint
	forall (T1 in 0..NumTanks-1, T2 in T1+1..NumTanks, K in 1..NumJobs-1) (
	    Entry[(T1 + 1) mod (NumTanks+1)] + 
	    Empty[(T1+1) mod (NumTanks+1), T2] + K * Period 
	    <= Removal[T2]
	\/  Entry[(T2 + 1) mod (NumTanks+1)] + 
	    Empty[(T2 + 1) mod (NumTanks+1), T1] 
	    <= Removal[T1] + K * Period
	);

constraint
	Removal[0] = 0;

constraint 0 <= Period /\ Period <= sum([MaxTime[i] | i in 1..NumTanks]);

output [
	"singHoist2:\n",
	"Period = ", show(Period), "\n",
	"Entry[] =  ",
	show(Entry), "\n",
	"Removal[] = ", 
	show(Removal), "\n"
];