$ondollar title CAM Assignment (LP) Example 10.3 of Rardin (1998)

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

sets
i    "jobs"  /1*8/,
j    "workstations" /1*10/;

table c(i,j) "transport and process time if i goes on j"
   1   2   3   4   5   6   7   8   9  10
1  8      23                       5
2      4      12  15
3         20      13   6       8
4                 19  10
5              8          12          16
6 14                       8       3
7      6                      27      12
8      5  15                  32;

free variable tottime "total time";

positive variable x(i,j) "whether to assign job i to station j";

equations
time    "min total time",
job(i)  "every job assigned",
ws(j)   "every workstation assigned";

time..
tottime =e= sum((i,j)$(c(i,j) gt 0), c(i,j)*x(i,j));

job(i)..
sum(j$(c(i,j) gt 0), x(i,j)) =e= 1;

ws(j)..
sum(i$(c(i,j) gt 0), x(i,j)) =l= 1;

model camasmt /all/;

solve camasmt using lp minimizing tottime;