Let's suppose you have $m$ bags of groceries that cannot be taken home in a single trip (if $n$ = number of trips, then $n\ge2$) from your car. Let $L$ be the distance from your car to your kitchen. Is it always a good strategy to walk the full path to get the next bags? I mean, suppose I define $L/2$ to be the place I will leave all the groceries before taking them inside. I grab the first $k$ bags from the car and leave them on the point $L/2$, then I return to the car and grab the next $k$ bags and so on. When I'm out of bags to move from the car I start to move them from $L/2$ to the kitchen.
I could define that the optimized variable is distance or energy, for instance, but I caught myself thinking about how to model this problem. It seems fairly trivial (I should always walk all path long and do $2n$ trips) but I can't find a way of showing that this is in fact the best strategy.