1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/examples/food2.mod Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,150 @@
1.4 +/* Food Manufacture 2, section 12.2 in
1.5 + * Williams, "Model Building in Mathematical Programming"
1.6 + *
1.7 + * Sebastian Nowozin <nowozin@gmail.com>
1.8 + */
1.9 +
1.10 +set oils;
1.11 +set month;
1.12 +
1.13 +/* Buying prices of the raw oils in the next six month. */
1.14 +param buyingprices{month,oils};
1.15 +
1.16 +/* Actual amount bought in each month. */
1.17 +var buys{month,oils} >= 0;
1.18 +
1.19 +/* Stock for each oil. */
1.20 +var stock{month,oils} >= 0;
1.21 +
1.22 +/* Price of the produced product */
1.23 +param productprice >= 0;
1.24 +param storagecost;
1.25 +
1.26 +param oilhardness{oils} >= 0;
1.27 +param M >= 0;
1.28 +
1.29 +/* Actual amount of output oil produced in each month */
1.30 +var production{m in month} >= 0;
1.31 +var useoil{m in month, o in oils} >= 0, <= M;
1.32 +var useoilb{m in month, o in oils}, binary;
1.33 +
1.34 +maximize totalprofit:
1.35 + sum{m in month} productprice*production[m]
1.36 + - sum{m in month, o in oils} buyingprices[m,o]*buys[m,o]
1.37 + - sum{m in month, o in oils} storagecost*stock[m,o];
1.38 +
1.39 +/* Constraints */
1.40 +
1.41 +/* 1. Starting stock */
1.42 +s.t. startstock{o in oils}:
1.43 + stock[1,o] = 500;
1.44 +s.t. endstock{o in oils}:
1.45 + stock[6,o] + buys[6,o] - useoil[6,o] >= 500;
1.46 +
1.47 +/* 2. Stock constraints */
1.48 +s.t. stocklimit{m in month, o in oils}:
1.49 + stock[m,o] <= 1000;
1.50 +
1.51 +s.t. production1{m in month, o in oils}:
1.52 + useoil[m,o] <= stock[m,o] + buys[m,o];
1.53 +s.t. production2{m1 in month, m2 in month, o in oils : m2 = m1+1}:
1.54 + stock[m2,o] = stock[m1,o] + buys[m1,o] - useoil[m1,o];
1.55 +
1.56 +s.t. production3a{m in month}:
1.57 + sum{o in oils} oilhardness[o]*useoil[m,o] >= 3*production[m];
1.58 +s.t. production3b{m in month}:
1.59 + sum{o in oils} oilhardness[o]*useoil[m,o] <= 6*production[m];
1.60 +
1.61 +s.t. production4{m in month}:
1.62 + production[m] = sum{o in oils} useoil[m,o];
1.63 +
1.64 +/* 3. Refining constraints */
1.65 +s.t. refine1{m in month}:
1.66 + useoil[m,"VEG1"]+useoil[m,"VEG2"] <= 200;
1.67 +s.t. refine2{m in month}:
1.68 + useoil[m,"OIL1"]+useoil[m,"OIL2"]+useoil[m,"OIL3"] <= 250;
1.69 +
1.70 +/* 4. Additional conditions:
1.71 + * i) The food may never be made up of more than three oils every month
1.72 + */
1.73 +s.t. useoilb_calc{m in month, o in oils}:
1.74 + M*useoilb[m,o] >= useoil[m,o];
1.75 +s.t. useoilb_limit{m in month}:
1.76 + sum{o in oils} useoilb[m,o] <= 3;
1.77 +
1.78 +/* ii) If an oil is used in a month, at least 20 tons must be used.
1.79 + */
1.80 +s.t. useminimum{m in month, o in oils}:
1.81 + 20*useoilb[m,o] <= useoil[m,o];
1.82 +
1.83 +/* iii) If either of VEG1 or VEG2 is used in a month, OIL2 must also be used
1.84 + */
1.85 +s.t. use_oil2a{m in month}:
1.86 + useoilb[m,"VEG1"] <= useoilb[m,"OIL3"];
1.87 +s.t. use_oil2b{m in month}:
1.88 + useoilb[m,"VEG2"] <= useoilb[m,"OIL3"];
1.89 +
1.90 +solve;
1.91 +
1.92 +for {m in month} {
1.93 + printf "Month %d\n", m;
1.94 + printf "PRODUCE %4.2f tons, hardness %4.2f\n", production[m],
1.95 + (sum{o in oils} oilhardness[o]*useoil[m,o]) / (sum{o in oils} useoil[m,o]);
1.96 +
1.97 + printf "\tVEG1\tVEG2\tOIL1\tOIL2\tOIL3\n";
1.98 + printf "STOCK";
1.99 + printf "%d", m;
1.100 + for {o in oils} {
1.101 + printf "\t%4.2f", stock[m,o];
1.102 + }
1.103 + printf "\nBUY";
1.104 + for {o in oils} {
1.105 + printf "\t%4.2f", buys[m,o];
1.106 + }
1.107 + printf "\nUSE";
1.108 + printf "%d", m;
1.109 + for {o in oils} {
1.110 + printf "\t%4.2f", useoil[m,o];
1.111 + }
1.112 + printf "\n";
1.113 + printf "\n";
1.114 +}
1.115 +printf "Total profit: %4.2f\n",
1.116 + (sum{m in month} productprice*production[m]
1.117 + - sum{m in month, o in oils} buyingprices[m,o]*buys[m,o]
1.118 + - sum{m in month, o in oils} storagecost*stock[m,o]);
1.119 +printf " turnover: %4.2f\n",
1.120 + sum{m in month} productprice*production[m];
1.121 +printf " buying costs: %4.2f\n",
1.122 + sum{m in month, o in oils} buyingprices[m,o]*buys[m,o];
1.123 +printf " storage costs: %4.2f\n",
1.124 + sum{m in month, o in oils} storagecost*stock[m,o];
1.125 +
1.126 +
1.127 +data;
1.128 +
1.129 +param : oils : oilhardness :=
1.130 + VEG1 8.8
1.131 + VEG2 6.1
1.132 + OIL1 2.0
1.133 + OIL2 4.2
1.134 + OIL3 5.0 ;
1.135 +
1.136 +set month := 1 2 3 4 5 6;
1.137 +
1.138 +param buyingprices
1.139 +
1.140 +: VEG1 VEG2 OIL1 OIL2 OIL3 :=
1.141 +
1.142 +1 110 120 130 110 115
1.143 +2 130 130 110 90 115
1.144 +3 110 140 130 100 95
1.145 +4 120 110 120 120 125
1.146 +5 100 120 150 110 105
1.147 +6 90 100 140 80 135 ;
1.148 +
1.149 +param productprice := 150;
1.150 +param storagecost := 5;
1.151 +param M := 1000;
1.152 +
1.153 +end;