A business dinner problem
Combinatorics
2020-12-24 v2
Abstract
We are given suppliers and customers, and a set of tables. Every evening of the forthcoming days, there will be a dinner. Each customer must eat with each supplier exactly once, but two suppliers may meet at most once at a table. The number of customers and the number of suppliers who can sit together at a table are bounded above by fixed parameters. What is the minimum number of evenings to be scheduled in order to reach this objective? This question was submitted by a firm to the Junior company of a French engineering school some years ago. Lower and upper bounds are given in this paper, as well as proven optimal solutions with closed-form expressions for some cases.
Cite
@article{arxiv.1610.00585,
title = {A business dinner problem},
author = {Alejandra Estanislao and Frédéric Meunier},
journal= {arXiv preprint arXiv:1610.00585},
year = {2020}
}