Ideas_Download.txt

IDEA FOR DOWNLOAD WINDOW FITTING CONSTRAINT :
Decision variable treated = StartDownTime(a1)

forall(a1 in StoredAcquisitions, dw in DownloadWindows : EndTime(dw) > EndAckTime(a1)+DonwloadDur(a1) ){
	StartDownTime(a1) > StartTime(dw);
	StartDownTime(a1) < EndTime(dw) - DonwloadDur(a1);
}

# PROBLEM! When I use "for all dw", it means that this constraint is valid for every window! Which is not necessarily true...

NEXT IDEAS :

--> Use a matrix [StoredAcquisitions][DownloadWindows] := {1 if the StoredAck will be downloaded in that window ; 0 if not} 

# PROBLEM = Too many decision variables! And this one has no interest, because downloads don't depend on a specific choice of download window.

MAYBE IT IS A GOOD IDEA?

STATING PROBLEM LOGIC

If (donwload candidate k is assigned to window j) then StartTime[k] > StartTime[j] and StartTime[k] + DownloadDur[k] < EndTime[j].
Else 	OR StartTime[k] < StartTime[j] 			(I)
	OR StartTime[k] > EndTime[j]			(II)
	OR StartTime[k] + DownloadDur[k] > EndTime[j] 	(III)
	OR StartTime[k] + DownloadDur[k] < StartTime[j]	(IV)

The assignment means the adding of another decision variable, that is, the "StoredAck by Window matrix" (AllocationMatrix). So it might as well be useful.
In this case, we would have:

forall(a1 in StoredAcquisitions, dw in DownloadWindows){
	if (AllocationMatrix[a1][dw] == 1) then {
		StartTime[a1] > StartTime[dw];
		StartTime[a1] + DownloadDur[a1] < EndTime[dw];
	}
}

In BIG-M we should get:

forall(a1 in StoredAcquisitions, dw in DownloadWindows){
	StartTime[a1] > (1-AllocationMatrix[a1][dw])*(EndTime[dw]-DownloadDur[a1]-StartTime[dw]) + StartTime[dw];
	StartTime[a1] < (1-AllocationMatrix[a1][dw])*(StartTime[dw]-EndTime[dw] + DownloadDur[a1]) + EndTime[dw] - DownloadDur[a1];
}

This formulation is the same as:

If (a1 is allocated to dw) then 
	StartTime[a1] > StartTime[dw]; 
	StartTime[a1] + DownloadDur[a1] < EndTime[dw];

else 
	StartTime[a1] + DownloadDur[a1] > EndTime[dw];	(II = Union of II and III)
	StartTime[a1] < StartTime[dw];			(I = Union of I and IV)

This formulation solves the problem of window fitting. On the other hand, it does not use this constraint to select acquisitions...
Maybe, the acquisition selection should be only and totally linked with the "next" matrix.

Now, the question is : Could I use only this matrix (without the next matrix) for the download non-intersection constraint? 

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IDEAS FOR DOWNLOAD NON-INTERSECTION CONSTRAINT :

Decision variables used = dnext(a1,a2), StartTime(a1)


forall(a1,a2 in StoredAcquisitions){
	StartTime[a2] >= (dnext[a1][a2]-1)*(StartTime[a1] + DownloadDur[a1]) + StartTime[a1] + DownloadDur[a1]
}


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"NEXT" VARIABLE SEQUENCING CONSTRAINT (definition of next) :


forall(a1 in StoredAcquisitions){
	sum(a2 in StoredAcquisitionsExt : a2 != a1) dnext[a1][a2] == selectDwl[a1];
	sum(a2 in StoredAcquisitionsExt : a2 != a1) dnext[a2][a1] == selectDwl[a1];
	dnext[a1][a1] == 0;
}

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"SELECT" VARIABLE DEFINITION CONSTRAINTS :

- The one up here too /\

selectDwl[0] = 1;

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DEFINE ranges and dvars:

StoredAcquisitions = 1..NSelectedAcks;
StoredAcquisitionsExt = 0..NSelectedAcks;

float+ LastWindowTime = ...; 	//Supremum of window
dvar int selectDwl[StoredAcquisitionsExt] in 0..1;
dvar int dnext[StoredAcquisitionsExt][StoredAcquisitionsExt] in 0..1;
dvar float+ StartTime[a in StoredAcquisitions] in EndAckTime[a]..LastWindowTime;
// We also need another "StartTime" vector - The one with the window start times. 
// This other one would not be a dvar, but a data variable. When writing the code --> REDEFINE StartTime variable NAMES!!!