In a previous model we used cuts to find all solutions (http://yetanothermathprogrammingconsultant.blogspot.com/2013/03/there-are-293-ways-to-make-change-for.html). This time we use the solution pool in Cplex. This is quite an adventure:
- The documentation on the solution pool in http://www.gams.com/dd/docs/solvers/cplex.pdf is really bad. It also contains some things I think are wrong or confusing.
- The solution pool does not work with a constant objective.
- But eventually, we got it to work and then it is very fast. We find all 293 integer solutions in just 46 simplex pivots:
MIP Solution: 1.000000 (46 iterations, 1162 nodes)
The final results shows all solutions:
---- 71 PARAMETER allcount
dollar halfdollar quarter dime nickel penny