Constructs the blending constraint for dyke fines -------------------------------------------------------------------------- Date: July 30, 2010, ver01 By: Eugene Ben-Awuah --------------------------------------------------------------------------
0001 % Constructs the blending constraint for dyke fines 0002 %-------------------------------------------------------------------------- 0003 % Date: July 30, 2010, ver01 0004 % By: Eugene Ben-Awuah 0005 %-------------------------------------------------------------------------- 0006 0007 function [A_finesDykegrade b_finesDykeUgrade] = fines_dyke_blending_constraint1... 0008 (Blocks120, numOfPeriods,... 0009 MaxfinesDyke, MinfinesDyke) 0010 0011 0012 [numBlocks n] = size([Blocks120.EBV]'); 0013 0014 %vectors containing the relevant element and tonnage 0015 finesDykeGrade1 = [Blocks120.finesGradeDyke]; 0016 DykeTonnage = [Blocks120.blockFinesDyke]/100; 0017 0018 %initialize the finesDykeGrade vector by pre-allocating memory to increase speed 0019 finesDykeGrade2=zeros(1,numBlocks); 0020 finesDykeGrade3=zeros(1,numBlocks); 0021 0022 %calculate the maximum and minimum grade constraint vectors based on the formula (refer Yashar's formulation: 0023 %finesDykeGradeMax=((finesDykeGrade1(1,iBlocks)-MaxfinesDyke)*DykeTonnage(1,iBlocks)) 0024 %finesDykeGradeMin=((MinfinesDyke-finesDykeGrade1(1,iBlocks))*DykeTonnage(1,iBlocks)) 0025 for iBlocks=1:numBlocks 0026 finesDykeGrade2(1,iBlocks)=((finesDykeGrade1(1,iBlocks)-MaxfinesDyke).*DykeTonnage(1,iBlocks)); 0027 finesDykeGrade3(1,iBlocks)=((MinfinesDyke-finesDykeGrade1(1,iBlocks)).*DykeTonnage(1,iBlocks)); 0028 end 0029 %The 0.01 added to the minimum fines constraint eqn is to ensure that we 0030 %dont have a zero matrix. May not be needed if data is available for fines 0031 %at all locations. Does not affect NPV because decsion for dyke tonnage has 0032 %already been made. 0033 0034 %pre-allocate memory and create maximum and minimum grade constraint matrix 0035 finesDykeGradeMax = zeros(numOfPeriods,numBlocks*numOfPeriods); 0036 finesDykeGradeMin = zeros(numOfPeriods,numBlocks*numOfPeriods); 0037 for iPeriods = 1:numOfPeriods 0038 finesDykeGradeMax(iPeriods,((numBlocks*(iPeriods-1)+1):iPeriods*numBlocks))... 0039 = finesDykeGrade2(1,:); 0040 0041 finesDykeGradeMin(iPeriods,((numBlocks*(iPeriods-1)+1):iPeriods*numBlocks))... 0042 = finesDykeGrade3(1,:); 0043 end 0044 0045 %create maximum and minimum grade constraint matrix with size (T, N*T) for 0046 %each block-period decision variable and size (T,T) period decision variable 0047 %totalling (T, T*Variables) 0048 [m,n] = size(finesDykeGradeMax); 0049 A_finesDykegradeMax = [zeros(m, numBlocks*numOfPeriods)... 0050 zeros(m, numBlocks*numOfPeriods), finesDykeGradeMax... 0051 zeros(m, numBlocks*numOfPeriods)... 0052 zeros(m,m), zeros(m,m), zeros(m,m), zeros(m,m)]; 0053 0054 A_finesDykegradeMin = [zeros(m, numBlocks*numOfPeriods)... 0055 zeros(m, numBlocks*numOfPeriods), finesDykeGradeMin... 0056 zeros(m, numBlocks*numOfPeriods)... 0057 zeros(m,m), zeros(m,m), zeros(m,m), zeros(m,m)]; 0058 0059 A_finesDykegrade = [A_finesDykegradeMax; A_finesDykegradeMin]; 0060 0061 %create the target for the grade constraint matrix which is a (2T,1) matrix 0062 [m,n] = size(A_finesDykegrade); 0063 b_finesDykeUgrade = zeros(m,1); 0064 0065 %convert to a sparse matrix 0066 A_finesDykegrade = sparse(A_finesDykegrade); 0067 b_finesDykeUgrade = sparse(b_finesDykeUgrade); 0068 0069 % the mulitplier vector in the constraint matrix have different sizes 0070 % and units. (some are tonnage some are grade....). It is necessary to 0071 % transform the constraints matrix in a way that it unit less to be 0072 % solved by the MIP code. 0073 0074 % divide each row vector by its norm [A(i,:)* A(i,:)']^1/2 0075 % A_miningNormVector(m,1) is vertical vector holding the respective 0076 % norm of each row of the A_mining matrix 0077 0078 %b_Ugrade is all zero so doesn't need normalizing in cases where b_U 0079 %and b_L have values greater than zero they need to be normailized as 0080 %well. 0081 0082 for i = 1:m %NB: This should be for i=1:m; the vector to be used to calculate 0083 %the norm should be the A_finesDykegrade but because the minimum side 0084 %is all zeros, finding the norm gives zero, hence normalizing with this 0085 %value results in NaN errors. This may be as a result of the model. 0086 %Correct this when actual oil sand model is used to be consistent with 0087 %the other normalization calculations.This has been fixed for now by adding 0088 % 0.01 to all the fines grade for the minimum fines constraint to avoid 0089 % zeros. Does not affect NPV since the decision for dyke material has 0090 %already been made. 0091 A_gradeNormVector(i,1) = norm(A_finesDykegrade(i,:)); 0092 end 0093 0094 for i = 1:m 0095 normA = A_gradeNormVector(i,1); 0096 A_finesDykegrade(i,:) = A_finesDykegrade(i,:)/normA; 0097 end 0098 0099 A_finesDykegrade; 0100 0101 end