/* Food Manufacture 2, section 12.2 in

  * Williams, "Model Building in Mathematical Programming"

  *

  * Sebastian Nowozin <nowozin@gmail.com>

  */

 set oils;

 set month;

 /* Buying prices of the raw oils in the next six month. */

 param buyingprices{month,oils};

 /* Actual amount bought in each month. */

 var buys{month,oils} >= 0;

 /* Stock for each oil. */

 var stock{month,oils} >= 0;

 /* Price of the produced product */

 param productprice >= 0;

 param storagecost;

 param oilhardness{oils} >= 0;

 param M >= 0;

 /* Actual amount of output oil produced in each month */

 var production{m in month} >= 0;

 var useoil{m in month, o in oils} >= 0, <= M;

 var useoilb{m in month, o in oils}, binary;

 maximize totalprofit:

     sum{m in month} productprice*production[m]

     - sum{m in month, o in oils} buyingprices[m,o]*buys[m,o]

     - sum{m in month, o in oils} storagecost*stock[m,o];

 /* Constraints */

 /* 1. Starting stock */

 s.t. startstock{o in oils}:

     stock[1,o] = 500;

 s.t. endstock{o in oils}:

     stock[6,o] + buys[6,o] - useoil[6,o] >= 500;

 /* 2. Stock constraints */

 s.t. stocklimit{m in month, o in oils}:

     stock[m,o] <= 1000;

 s.t. production1{m in month, o in oils}:

     useoil[m,o] <= stock[m,o] + buys[m,o];

 s.t. production2{m1 in month, m2 in month, o in oils : m2 = m1+1}:

     stock[m2,o] = stock[m1,o] + buys[m1,o] - useoil[m1,o];

 s.t. production3a{m in month}:

     sum{o in oils} oilhardness[o]*useoil[m,o] >= 3*production[m];

 s.t. production3b{m in month}:

     sum{o in oils} oilhardness[o]*useoil[m,o] <= 6*production[m];

 s.t. production4{m in month}:

     production[m] = sum{o in oils} useoil[m,o];

 /* 3. Refining constraints */

 s.t. refine1{m in month}:

     useoil[m,"VEG1"]+useoil[m,"VEG2"] <= 200;

 s.t. refine2{m in month}:

     useoil[m,"OIL1"]+useoil[m,"OIL2"]+useoil[m,"OIL3"] <= 250;

 /* 4. Additional conditions:

  *    i) The food may never be made up of more than three oils every month

  */

 s.t. useoilb_calc{m in month, o in oils}:

     M*useoilb[m,o] >= useoil[m,o];

 s.t. useoilb_limit{m in month}:

     sum{o in oils} useoilb[m,o] <= 3;

 /* ii) If an oil is used in a month, at least 20 tons must be used.

  */

 s.t. useminimum{m in month, o in oils}:

     20*useoilb[m,o] <= useoil[m,o];

 /* iii) If either of VEG1 or VEG2 is used in a month, OIL2 must also be used

  */

 s.t. use_oil2a{m in month}:

     useoilb[m,"VEG1"] <= useoilb[m,"OIL3"];

 s.t. use_oil2b{m in month}:

     useoilb[m,"VEG2"] <= useoilb[m,"OIL3"];

 solve;

 for {m in month} {

     printf "Month %d\n", m;

     printf "PRODUCE %4.2f tons, hardness %4.2f\n", production[m],

         (sum{o in oils} oilhardness[o]*useoil[m,o]) / (sum{o in oils} useoil[m,o]);

     printf "\tVEG1\tVEG2\tOIL1\tOIL2\tOIL3\n";

     printf "STOCK";

     printf "%d", m;

     for {o in oils} {

         printf "\t%4.2f", stock[m,o];

     }

     printf "\nBUY";

     for {o in oils} {

         printf "\t%4.2f", buys[m,o];

     }

     printf "\nUSE";

     printf "%d", m;

     for {o in oils} {

         printf "\t%4.2f", useoil[m,o];

     }

     printf "\n";

     printf "\n";

 }

 printf "Total profit: %4.2f\n",

     (sum{m in month} productprice*production[m]

     - sum{m in month, o in oils} buyingprices[m,o]*buys[m,o]

     - sum{m in month, o in oils} storagecost*stock[m,o]);

 printf "      turnover: %4.2f\n",

     sum{m in month} productprice*production[m];

 printf "      buying costs: %4.2f\n",

     sum{m in month, o in oils} buyingprices[m,o]*buys[m,o];

 printf "      storage costs: %4.2f\n",

     sum{m in month, o in oils} storagecost*stock[m,o];

 data;

 param : oils : oilhardness :=

     VEG1    8.8

     VEG2    6.1

     OIL1    2.0

     OIL2    4.2

     OIL3    5.0 ;

 set month := 1 2 3 4 5 6;

 param buyingprices

 :           VEG1    VEG2    OIL1    OIL2    OIL3    :=

 1           110     120     130     110     115

 2           130     130     110     90      115

 3           110     140     130     100     95

 4           120     110     120     120     125

 5           100     120     150     110     105

 6           90      100     140     80      135 ;

 param productprice := 150;

 param storagecost := 5;

 param M := 1000;

 end;