[Ipopt] Suboptimal solutions with inventory/sales/receipts balance equations

[Mike Bernshteyn]

Hello ipopt experts,

I thought I'd gamble and ask you a question that you might decide is too
unspecific.

We are solving a retail profit maximization problem in which we deal with
inventory/receipts/sales balance equations across several time periods and a
few other business constraints. One of the constraints looks like this:
(demand(i)-sales(i))*Inventory(i+1) =e= 0. The idea of this is to allow
sales being less than demand only when we sell all of the inventory
otherwise the demand will pull the sales according to the demand formula.

The ipopt solver finds a solution that is suboptimal relative to the one
found by minos in roughtly 10% of the cases (retail items).

I'm wondering if you've had some experience with a*b=0 types of constraints.
Should one avoid them and try to replace by something else? Is it OK to use
"0" or is it better to find some non-zero value that is identical to a "0"
in our problem.

Thanks in advance,

Mike.