Benjamin
Leveque
Title:
Optimizing diversity
Abstract:
We consider a problem originating in the optimization of the
diversity of industrial production. Companies have to
determine the
semi-finished products that they stock in order to be able to
assemble any possible finished product in at most a given number
of
operations. The goal is to reduce the size of the stock for
decreasing stockage costs. We do not know about any previous
result
concerning the underlying combinatorial problem. We propose
a
simple construction providing a feasible solution, and conjecture
its optimality; we then raise some other questions related to a
possible proof of this conjecture. The questions are answered and
the conjecture is proved in some cases that occur to be
interesting.