I am currently a Supply Chain Major in my final semester. I am attempting a Lp model in Lingo and I'm having trouble with the syntax. It's a pretty simple model. When I "solve" it, I get error code 81 and no feasible solution found. Any help would be greatly appreciated.
You should check your model with some small instance (as small as possible). You should be able to check by hand if it has a feasible solution or not. Then compare results. An error code doesn't implicate that you have a syntax error.
To summarize, problem might lie in LP formulation. Double check it.
I checked the model in lp solve. The same result - infeasibility.
Maybe the problem really does not have a feasible solution that can satisfy all the constraints!!
However, check these:
https://www.lindo.com/doc/online_help/lingo15_0/81_nofeasiblesolutionfound_.htm
https://www.lindo.com/doc/online_help/lingo15_0/debug.htm
I implemented the model in Excel (without the objective function but it doesn't matter for infeasibility).
I'm pretty sure now that it is infeasible. I'll explain why.
First, we have 49 "x" variables. The sums in formulas make the constraints similar to the transportation problem with 7 sources (indexed 1,2,3,4,5,6,7) and 7 destinations (indexed 8,9,10,11,12,13,14). The destination constraints are
X18+X28+X38+X48+X58+X68+X78=60000 to
X114+X214+X314+X414+X514+X614+X714=50000.
They are equality constraints so each demand must be fully satisified.
The total demand of all the destinations is 175000. This obviously means that the total supply from the sources must be 175000 or more. But it isn't! Because "y" binary variables sum up to one, then only one of them can take the value of 1. Following the construction principles of sources constraint I would say that the largest supply can be 15000 if one of Y5, Y7, Y9, Y11 or Y13 is equal to one.
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