This problem has been thought about for over thirty years. I encountered it a number of times in the CPG enterprise. You have an amount of product you would like to place on the store shelf which is based on consumer demand. You have the dimensions of shelves and their layout. You also know the dimensions of product packages. How do you fill the shelves with product to maximize retail profit? The problem can be stated mathematically but turns out to be very hard to solve. In addition you also have non-quantitative design constraints that must also be applied and behavioral information about how shoppers buy. The complete problem remains unsolved.
The following CIO article is an overview of how Coca-Cola addresses this and some related vendors.
"The Art, Science and Software Behind Placing Coca-Cola Products on Store Shelves
The team charged with keeping Coca-Cola products stocked and moving from stores uses art and technology to make the most of shelf real estate. New software helps them plan ahead while boosting results.... "
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