Constructs the grade blending constraint matrix
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Updated May 27, 2009
Date: Aug 06, 2008, ver01
% By: Hooman Askari
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Inputs
Blocks:
a struct containing Blocks(numBlocks) elements with the field
correspoiding to the input file format.
numBlocks:
a 1*1 vector containing the total number of blocks
numOfPeriods:
a 1*1 vector containing the number of periods
numOfElements:
a 1*1 vector containing the number of Elements
varargin: variable number of input arguments
holding the min and max average grade allowed for each
element.
in this case: oreGradeMin, oreGradeMax, sGradeMin, sGradeMax,
pGradeMin, pGradeMax:
a 1*1 vector containing the min and max grade for each element
that are allowed to be sent to the processing plant
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outputs
construct an A_grade matrix using
A_grade = [sparse(m, numCuts * numOfPeriods )...
A_grade...
sparse(m, numCuts * numOfPeriods)];
b_Ugrade = grade boundary conditions
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--------------------------------------------------------------------------0001 % Constructs the grade blending constraint matrix 0002 %-------------------------------------------------------------------------- 0003 % Updated May 27, 2009 0004 % Date: Aug 06, 2008, ver01 0005 % % By: Hooman Askari 0006 %-------------------------------------------------------------------------- 0007 %Inputs 0008 % Blocks: 0009 % a struct containing Blocks(numBlocks) elements with the field 0010 % correspoiding to the input file format. 0011 % numBlocks: 0012 % a 1*1 vector containing the total number of blocks 0013 % numOfPeriods: 0014 % a 1*1 vector containing the number of periods 0015 % numOfElements: 0016 % a 1*1 vector containing the number of Elements 0017 % varargin: variable number of input arguments 0018 % holding the min and max average grade allowed for each 0019 % element. 0020 % in this case: oreGradeMin, oreGradeMax, sGradeMin, sGradeMax, 0021 % pGradeMin, pGradeMax: 0022 % a 1*1 vector containing the min and max grade for each element 0023 % that are allowed to be sent to the processing plant 0024 %-------------------------------------------------------------------------- 0025 % 0026 %-------------------------------------------------------------------------- 0027 % outputs 0028 % construct an A_grade matrix using 0029 % A_grade = [sparse(m, numCuts * numOfPeriods )... 0030 % A_grade... 0031 % sparse(m, numCuts * numOfPeriods)]; 0032 % 0033 % b_Ugrade = grade boundary conditions 0034 %-------------------------------------------------------------------------- 0035 % 0036 %-------------------------------------------------------------------------- 0037 0038 function [A_grade b_Ugrade] = grade_blending_constraints(Blocks,... 0039 numBlocks,... 0040 numCuts,... 0041 numOfPeriods,... 0042 numOfElements,... 0043 varargin) 0044 0045 % varargin is a cell array, a special kind of MATLAB array that consists of 0046 % cells instead of array elements 0047 0048 % unpacking varargin 0049 % unpacks the minimum and maximum element grades into two arrays 0050 % elementsMin (1, 1:numberOfElements) = element's minimum grade 0051 % elementsMax (1, 1:numberOfElements) = element's maximum grade 0052 % the matrix column index corrosponds to the element index 0053 % example: second element maximum is in elementsMax(1,2) 0054 iMin = 1; 0055 iMax = 1; 0056 for k = 1:length(varargin); 0057 % check to see if the index of varargin is odd 0058 % add the variable to the elementsMin 0059 % other wise add it to the elementsMax 0060 if rem(k,2)~= 0 0061 if isempty(varargin{1,k}) 0062 elementsMin(1, iMin) = NaN; 0063 else 0064 elementsMin(1, iMin) = varargin{1,k}; 0065 end 0066 iMin = iMin + 1; 0067 else 0068 if isempty(varargin{1,k}) 0069 elementsMax(1, iMax) = NaN; 0070 else 0071 elementsMax(1, iMax) = varargin{1,k}; 0072 end 0073 iMax = iMax + 1; 0074 end 0075 end 0076 0077 % vectors containing the relevant elements 0078 oreTonnage = [Blocks.OreTonnes]'; 0079 sTonnage = [Blocks.S]'/100; 0080 pTonnage = [Blocks.P]'/100; 0081 0082 % elementsTonnage(numberOfElments, numBlocks) 0083 elementsTonnage = [oreTonnage'; sTonnage'; pTonnage']; 0084 0085 % new version make sure you change to this after fixing the problem 0086 oreGrade = [Blocks.gradeMWT]'; 0087 sGrade = [Blocks.gradeS]'; 0088 pGrade = [Blocks.gradeP]'; 0089 0090 elementsGrade = [oreGrade'; sGrade'; pGrade']; 0091 0092 % initialize the A_grade vector 0093 A_grade =[]; 0094 0095 for iElements = 1 : numOfElements 0096 0097 %unequality constraints for elements number iElements minimum 0098 if ~isnan (elementsMin(iElements)) 0099 % .* = an element by element multiplication 0100 0101 % minMWTVector =(oreGradeVector-oreGradeMinValue).* ... 0102 % oreTonnageVector.*-1; 0103 minVector =... 0104 (elementsGrade(iElements,:)- elementsMin(iElements))... 0105 .* elementsTonnage(iElements,:).*-1; 0106 0107 A_grade = update_constraints(A_grade,... 0108 numBlocks,... 0109 numOfPeriods,... 0110 minVector); 0111 end 0112 0113 %unequality constraints for elements number iElements maximum 0114 if ~isnan (elementsMax(iElements)) 0115 0116 % maxMWTVector =(oreGradeVector-oreGradeMaxValue).*... 0117 % oreTonnageVector; 0118 maxVector =... 0119 (elementsGrade(iElements,:)- elementsMax(iElements))... 0120 .* elementsTonnage(iElements,:); 0121 0122 A_grade = update_constraints(A_grade,... 0123 numBlocks,... 0124 numOfPeriods,... 0125 maxVector); 0126 end 0127 0128 end % for iElements 0129 0130 [m n] = size(A_grade); 0131 b_Ugrade = zeros(m,1); 0132 0133 % convert to a sparse matrix 0134 A_grade = sparse(A_grade); 0135 b_Ugrade = sparse(b_Ugrade); 0136 0137 % the mulitplier vector in the constraints matrix have different sizes 0138 % and units. (some are tonnage some are grade....). It is necessary to 0139 % transform the constraints matrix in a way that it unit less to be 0140 % solved by the MIP code. 0141 0142 % divide each row vector by its norm [A(i,:)* A(i,:)']^1/2 0143 % A_gradeNormVector(m,1) is vertical vector holding the respective norm 0144 % of each row of the A_grade matrix 0145 0146 % try to vectorize this section 0147 0148 for i = 1:m 0149 A_gradeNormVector(i,1) = norm(A_grade(i,:)); 0150 end 0151 0152 for i = 1:m 0153 normA = A_gradeNormVector(i,1); 0154 A_grade(i,:) = A_grade(i,:)/normA; 0155 end 0156 0157 % b_Ugrade is all zero so doesn't need normalizing in cases where b_U 0158 % and b_L have values greater than zero they need to be normailized as 0159 % well. 0160 0161 % construct an A_grade matrix using 0162 A_grade = [sparse(m, numCuts * numOfPeriods )... 0163 A_grade... 0164 sparse(m, numCuts * numOfPeriods)]; 0165 0166 end 0167 0168 0169 0170 0171 0172