Constructs the objective function for the optimization problem -------------------------------------------------------------------------- Date: July 30, 2010, ver01 By: Eugene Ben-Awuah --------------------------------------------------------------------------
0001 % Constructs the objective function for the optimization problem 0002 %-------------------------------------------------------------------------- 0003 % Date: July 30, 2010, ver01 0004 % By: Eugene Ben-Awuah 0005 %-------------------------------------------------------------------------- 0006 0007 function [c normVPQ] = objective_function(Blocks120, numOfPeriods,... 0008 interestRate, C1, C2, C3, P1, P2, P3) 0009 0010 0011 [numBlocks n] = size([Blocks120.EBV]'); 0012 oreValueCutoff = repmat([Blocks120.oreValueCutoff]', 1, numOfPeriods); 0013 dykeCostCutoff = repmat([Blocks120.dykeCostCutoff]', 1, numOfPeriods); 0014 miningCost = repmat([Blocks120.miningCost]', 1, numOfPeriods); 0015 0016 %Preallocate memory for efficiency 0017 v=zeros(numBlocks,numOfPeriods); p=zeros(numBlocks,numOfPeriods); q=zeros(numBlocks,numOfPeriods); 0018 for iPeriods = 1:numOfPeriods 0019 % v is a matrix holding the discounted oreValueCutoff of blocks for all 0020 % periods 0021 v(1:numBlocks, iPeriods)= oreValueCutoff(1:numBlocks,iPeriods)/... 0022 ((1+interestRate)^iPeriods); 0023 0024 % p is a matrix holding the discounted dykeCostCutoff of blocks for all 0025 % periods 0026 p(1:numBlocks, iPeriods)= dykeCostCutoff(1:numBlocks,iPeriods)/... 0027 ((1+interestRate)^iPeriods); 0028 0029 % q is a matrix holding the discounted miningCost of blocks for all 0030 % periods 0031 q(1:numBlocks, iPeriods)= miningCost(1:numBlocks,iPeriods)/... 0032 ((1+interestRate)^iPeriods); 0033 end 0034 0035 % the MIGP function minimizes the function f(x); we multiply by -1 to 0036 % maximize the first part of the function passed to TOMLAB 0037 save Discounted_Values v p q 0038 v = v * (-1); 0039 p = p * (-1); 0040 q = q * (-1); 0041 0042 %create row vector for deviational variables; 1x5 vector for each 0043 %deviational variable (dv). d1=mining target negative dv; d2=processing 0044 %target negative dv; d3=dyke material negative dv; d4=dyke material 0045 %positive dv. 0046 d1 = repmat(1, 1, numOfPeriods); 0047 d2 = repmat(1, 1, numOfPeriods); 0048 d3 = repmat(1, 1, numOfPeriods); 0049 d4 = repmat(1, 1, numOfPeriods); 0050 0051 %the model assumes that there exists a pre-emptive penalty cost for deviating from 0052 %the goals. the most costly goal deviation is mining capacity, C1; then processing 0053 %capacity, C2; and then dyke material requirement, C3. This penalty cost in 0054 %deviating from the target is to convert the deviational tonnes to dollar 0055 %values. NB: cost should be negative; refer your notes. 0056 %C1=-4; C2=-3; C3=-2; %Order of deviational cost using abitrary values. 0057 d1 = C1*d1; 0058 d2 = C2*d2; 0059 d3 = C3*d3; 0060 d4 = C3*d4; 0061 0062 for iPeriods = 1:numOfPeriods 0063 %d1 is a matrix holding the discounted penalty cost from deviating 0064 %negatively from the mining target for all periods 0065 d1(1, iPeriods)= d1(1,iPeriods)/... 0066 ((1+interestRate)^iPeriods); 0067 0068 %d2 is a matrix holding the discounted penalty cost from deviating 0069 %negatively from the processing target for all periods 0070 d2(1, iPeriods)= d2(1,iPeriods)/... 0071 ((1+interestRate)^iPeriods); 0072 0073 %d3 is a matrix holding the discounted penalty cost from deviating 0074 %negatively from the dyke material target for all periods 0075 d3(1, iPeriods)= d3(1,iPeriods)/... 0076 ((1+interestRate)^iPeriods); 0077 0078 %d4 is a matrix holding the discounted penalty cost from deviating 0079 %positively from the dyke material target for all periods 0080 d4(1, iPeriods)= d4(1,iPeriods)/... 0081 ((1+interestRate)^iPeriods); 0082 end 0083 0084 %the model assumes that there exists a pre-emptive priority structure among 0085 %the goals. the most important goal is mining capacity, P1; then processing 0086 %capacity, P2; and then dyke material requirement, P3; refer your notes. 0087 %P1=50; P2=40; P3=30; %Order of goal importance using abitrary values. 0088 d1 = P1*d1; 0089 d2 = P2*d2; 0090 d3 = P3*d3; 0091 d4 = P3*d4; 0092 0093 % We need to calcualte a single norm for v, p, q, d1, d2, d3, d4 matrices. 0094 % See the documentation of the code for the format of the objective 0095 % function. After optimization the value of the objective function must 0096 % be multiplied with the norm to get the real disounted cash flow values 0097 % of the production schedule. 0098 combinedVPQ = [v; p; q; d1; d2; d3; d4]; 0099 normVPQ = norm(combinedVPQ); 0100 0101 %Normalizing the v matrix (ore value vector norm) 0102 v = v/normVPQ; 0103 0104 %Normalizing the p matrix (dyke construction cost vector norm) 0105 p = p/normVPQ; 0106 0107 %Normalizing the q matrix (mining cost vector norm) 0108 q = q/normVPQ; 0109 0110 %Normalizing the deviational variables matrix (d1, d2, d3, d4) 0111 d1 = d1/normVPQ; 0112 d2 = d2/normVPQ; 0113 d3 = d3/normVPQ; 0114 d4 = d4/normVPQ; 0115 0116 %Reshape v matrix into a vector 0117 v = reshape(v,numBlocks*numOfPeriods, 1); 0118 0119 %Reshape p matrix into a vector 0120 p = reshape(p,numBlocks*numOfPeriods, 1); 0121 0122 %Reshape q matrix into a vector 0123 q = reshape(q,numBlocks*numOfPeriods, 1); 0124 0125 %Reshape deviational variables matrix into a vector 0126 d1 = reshape(d1,numOfPeriods, 1); 0127 d2 = reshape(d2,numOfPeriods, 1); 0128 d3 = reshape(d3,numOfPeriods, 1); 0129 d4 = reshape(d4,numOfPeriods, 1); 0130 0131 % this is the coefficient of the objective function. The zeros are for the 0132 % mining precedence relationship decision variable, b, in the formulation. 0133 % This enables mining and processing at high resolution (continuous 0134 % variables) and mining precedence at lower resolution (integer variables) 0135 c=[zeros(numBlocks*numOfPeriods,1); v; p; q; d1; d2; d3; d4]; 0136 0137 %You need to formulate the entire goal function for all the variables and 0138 %then find the norm of this matrix and use it to scale down the values. 0139 %This case, the priority relationship of all the goals will be preserved. 0140 0141 end