Bag rationalisation for a food manufacturer

A food manufacturer has decided to rationalise the types of bags used to pack their products with a view to achieving economies of scale and improved efficiency. Under the new regime, the name and characteristics of the product are to be printed on the bag during packaging, with the bag colour as a secondary distinctive feature. There are several ways of describing the director's conflicting objectives of minimising both cost and customer colour conflicts. We model the problem in two ways: as a Zero–One Integer Program, and as a variant of a classical Graph Colouring Problem. Problem-specific observations, and data pre-processing, enable us to decompose the originally intractable problem, and to solve it using commercial integer programming software. Our solution compares favourably with that from a heuristic for graph colouring and our recommended allocation of eight colours was accepted for implementation.