Odds of Getting In
Pretty much everyone who deals in physical goods needs someone to shuffle them around efficiently, leaving a massive opening for just about anyone with the right set of skills to swoop in and get paid. Thus, Supply Chain Management is one of the fastest growing fields in the country, with more openings than there are people to fill them. The private sector is niche, meaning you'll definitely need to specialize in a specific kind of product, but hungry, meaning you'll probably find a position.
Even if you can't slip your résumé through one of the big corporations, you can always just pop into your local military recruitment office. "You can effectively move people and items through undesirable conditions, you say? Hmm...that does sound like something we may need in, you know, war. Sign here."
As is the case with most jobs, the most important factor is preparing yourself ahead of time for the career you want. And as this career involves pretty much nothing but critical planning, you should be pretty good at it already.