Constructs the processing capacity constraint matrix
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Updated May 27, 2009
Date: Aug 13, 2008, ver01
By: Hooman Askari
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Inputs
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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 of each processing capacity
in this case: pcMin and pcMax
a 1*1 vector containing the min and max processing capacity
for each processes.
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outputs
A_processing = [zeros(m, numCuts * numOfPeriods )...
A_processing...
zeros(m, numCuts * numOfPeriods)];
b_processing = processing boundary conditions
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Pseudo Code
--------------------------------------------------------------------------0001 % Constructs the processing capacity constraint matrix 0002 %-------------------------------------------------------------------------- 0003 % Updated May 27, 2009 0004 % Date: Aug 13, 2008, ver01 0005 % By: Hooman Askari 0006 %-------------------------------------------------------------------------- 0007 %Inputs 0008 %-------------------------------------------------------------------------- 0009 % Blocks: 0010 % a struct containing Blocks(numBlocks) elements with the field 0011 % correspoiding to the input file format. 0012 % numBlocks: 0013 % a 1*1 vector containing the total number of blocks 0014 % numOfPeriods: 0015 % a 1*1 vector containing the number of periods 0016 % numOfElements: 0017 % a 1*1 vector containing the number of Elements 0018 % varargin: variable number of input arguments 0019 % holding the min and max of each processing capacity 0020 % in this case: pcMin and pcMax 0021 % a 1*1 vector containing the min and max processing capacity 0022 % for each processes. 0023 % 0024 %-------------------------------------------------------------------------- 0025 % outputs 0026 % A_processing = [zeros(m, numCuts * numOfPeriods )... 0027 % A_processing... 0028 % zeros(m, numCuts * numOfPeriods)]; 0029 % 0030 % b_processing = processing boundary conditions 0031 %-------------------------------------------------------------------------- 0032 % 0033 %-------------------------------------------------------------------------- 0034 % Pseudo Code 0035 % 0036 %-------------------------------------------------------------------------- 0037 0038 function [A_processing b_Upc]=... 0039 processing_capacity_constraints(Blocks,... 0040 numBlocks,... 0041 numCuts,... 0042 numOfPeriods,... 0043 elementsProcessed,... 0044 varargin) 0045 % elementsProcessed(1, number of elements processed) 0046 % this array contains the indices from numOfElements 0047 % example [1 3 4]: elements 1 3 and 4 are processed 0048 0049 % unpacking varargin 0050 % unpacks the minimum and maximum processing capacity for each element 0051 % processed into two arrays 0052 % pcElementsMin (1, 1:numOfElementsProcessed) = element's 0053 % minimum processing capacity 0054 % pcElementsMax (1, 1:numOfElementsProcessed) = element's 0055 % maximum processing capacity 0056 % the matrix column index corrosponds to the element index 0057 % example: second element maximum is in elementsMax(1,2) 0058 iMin = 1; 0059 iMax = 1; 0060 for i =1:numOfPeriods 0061 for k = 1:length(varargin); 0062 % check to see if the index of varargin is odd 0063 % add the variable to the elementsMin 0064 % other wise add it to the elementsMax 0065 if rem(k,2)~= 0 0066 if isempty(varargin{1,k}) 0067 pcElementsMin(1,iMin) = NaN; 0068 else 0069 pcElementsMin(1,iMin) = varargin{1,k}(1,i); 0070 end 0071 iMin = iMin + 1; 0072 else 0073 if isempty(varargin{1,k}) 0074 pcElementsMax(1,iMax) = NaN; 0075 else 0076 pcElementsMax(1,iMax) = varargin{1,k}(1,i); 0077 end 0078 iMax = iMax + 1; 0079 end 0080 end 0081 end 0082 % vectors containing the relevant elements 0083 oreTonnage = [Blocks.OreTonnes]'; 0084 sTonnage = [Blocks.S]'/100; 0085 pTonnage = [Blocks.P]'/100; 0086 0087 % elementsTonnage(numberOfElments, numBlocks) 0088 elementsTonnage = [oreTonnage'; sTonnage'; pTonnage']; 0089 0090 totalProcessed = sum(elementsTonnage(1,:)) 0091 processingCapacity = totalProcessed / numOfPeriods 0092 0093 % initialize the A_grade vector 0094 A_processing =[]; 0095 b_Upc =[]; 0096 0097 for i = 1: length(elementsProcessed) 0098 0099 %unequality constraints for elements number iElements minimum 0100 if ~isnan (pcElementsMin(elementsProcessed(i))) 0101 %minPCVector = oreTonnage.*-1; 0102 minPcVector = elementsTonnage((elementsProcessed(i)),:).*-1; 0103 A_processing = update_constraints(A_processing,... 0104 numBlocks,... 0105 numOfPeriods,... 0106 minPcVector); 0107 %updateValue = mcMin*-1; 0108 updateValue = pcElementsMin(elementsProcessed(i))*-1; 0109 b_Upc = update_boundaries(b_Upc, numOfPeriods, updateValue); 0110 end 0111 0112 %unequality constraints for elements number iElements maximum 0113 if ~isnan (pcElementsMax(elementsProcessed(i))) 0114 % maxMWTVector =(oreGrade-oreGradeMax).* oreTonnage; 0115 maxPcVector = elementsTonnage((elementsProcessed(i)),:); 0116 A_processing = update_constraints(A_processing,... 0117 numBlocks,... 0118 numOfPeriods,... 0119 maxPcVector); 0120 %updateValue = mcMax; 0121 updateValue = pcElementsMax(elementsProcessed(i)); 0122 b_Upc = update_boundaries(b_Upc, numOfPeriods, updateValue); 0123 end 0124 0125 end % i = 1: length(elementsProcessed) 0126 0127 A_processing = sparse(A_processing); 0128 b_Upc = sparse(b_Upc); 0129 0130 [m n] = size(A_processing); 0131 0132 % the mulitplier vector in the constraints matrix have different sizes 0133 % and units. (some are tonnage some are grade....). It is necessary to 0134 % transform the constraints matrix in a way that it unit less to be 0135 % solved by the MIP code. 0136 0137 % divide each row vector by its norm [A(i,:)* A(i,:)']^1/2 0138 % A_processingNormVector(m,1) is vertical vector holding the respective 0139 % norm of each row of the A_processing matrix 0140 0141 for i = 1:m 0142 A_processingNormVector(i,1) = norm(A_processing(i,:)); 0143 end 0144 0145 for i = 1:m 0146 normA = A_processingNormVector(i,1); 0147 A_processing(i,:) = A_processing(i,:)/normA; 0148 0149 % normalizing the upper bound 0150 b_Upc(i)= b_Upc(i)/normA; 0151 end 0152 0153 A_processing = [zeros(m, numCuts * numOfPeriods )... 0154 A_processing... 0155 zeros(m, numCuts * numOfPeriods)]; 0156 end 0157 0158 0159