A business dinner problem

TL;DR

This paper addresses an optimization problem involving scheduling dinners so that each customer meets each supplier exactly once, with constraints on table sizes and meeting repetitions, providing bounds and optimal solutions.

Contribution

It introduces bounds and closed-form optimal solutions for a complex scheduling problem involving suppliers, customers, and table constraints.

Findings

Provided lower and upper bounds for the scheduling problem.

Derived closed-form expressions for optimal solutions in specific cases.

Established the minimum number of evenings needed for the given constraints.

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.