/* 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;