I wasn't able to reproduce the problem on my mac.

Normally when I see something like this, the cause is that a different variable name is used for something between the two runs. In symbolic computing the choice of a variable name matters, which is counterintuitive for most programmers in most languages. Another common cause is that a method isn't specified for a numerical function. I didn't see that though in your notebook, but please check that both of these aren't being done.

The problem does not occur on my MacBookAir, which makes me think it is not a coding problem but a problem related to the operating system. When I run packing problems with MathOptimizer Professional, which compiles the objective function and and constraints to Fortran or C, I get slightly different results with different compilers, but consistent results for one compiler.

Well, my impression of Windows 8 is that your results might depend on what's currently available on Taylor Swift's facebook page. ;-)