$ondollar title Tubular Products (LP) Example 4.3 of Rardin(1998)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

sets
p "products" /1*16/,
m "mills" /1*4/;

table c(p,m) "unit cost of p at m"
     1    2    3    4
1   90   75   70   63
2   80   70   65   60
3  104   85   83   77
4   98   79   80   74
5  123  101  110   99
6  113   94  100   84
7       160  156  140
8       142  150  130
9  140  110       122
10 124   96       101
11 160  133       138
12 143  127       133
13 202  150       160
14 190  141       140
15      190       220
16      175       200;

table t(p,m) "unit time for p at m"
     1    2    3    4
1   0.8  0.7  0.5  0.6
2   0.8  0.7  0.5  0.6
3   0.8  0.7  0.5  0.6
4   0.8  0.7  0.5  0.6
5   0.8  0.7  0.5  0.6
6   0.8  0.7  0.5  0.6
7        0.9  0.5  0.6
8        0.9  0.5  0.6
9   1.5  0.9       1.2
10  1.5  0.9       1.2
11  1.5  0.9       1.2
12  1.5  0.9       1.2
13  1.5  0.9       1.2
14  1.5  0.9       1.2
15       1.0       1.5
16       1.0       1.5;

parameter d(p) "weekly demand for p"
/1 100, 2 630, 3 500, 4 980, 5 720, 6 240, 7 75, 8 22,
9 50, 10 22, 11 353, 12 55, 13 125, 14 35, 15 100, 16 10/;

parameter b(m) "mill m capacity"
/1 800, 2 480, 3 1280, 4 960/;

free variable cost "objective value";

positive variable x(p,m) "units of p produced at m";

equations
obj "total cost",
dem(p) "demand for product p",
cap(m) "capacity of mill m";

obj..
cost =e= sum((p,m)$(c(p,m) gt 0.0), c(p,m)*x(p,m));

dem(p)..
sum(m$(c(p,m) gt 0.0), x(p,m)) =g= d(p);

cap(m)..
sum(p$(c(p,m) gt 0.0), t(p,m)*x(p,m)) =l= b(m);

model tubprods /all/;

solve tubprods using lp minimizing cost;