I developed a MIP on LINGO. My objective is minimizing makespan (time). When I run it using the LP solver using a set of data, the objective value is 237. But when I run it using the global solver and the same data, it gives me an objective value of 600. I thought that global optima should be smaller than Local optima in this case. What is the reasoning behind this?
In general, yes a local solution won’t be better than the global. Because this is occurring, this probably indicates that there is an issue with the way you’re using the solvers or that the model implementation isnt consistent (ie solving different models).
When you say you’re running with the LP solver, does this mean it allows the solution to take on non-integer values? Does the global solver require integer solutions? If both are yes, then you’re probably getting these results because the LP solver is solving a relaxed version of the problem (with a larger feasible region that includes both integer and non-integer values) and the other solver is only considering integer variables.
One way to check this is to see if the solution (the decision variables) the LP solver is giving you is feasible for the original problem.
If both the LP and global solvers are producing non-integer results, I recommend finding an integer programming solver.