An algorithm to calculates an allocation maximizing the leximin order on the utility profiles of the agents

Abstract

Allocating a limited set of resources equitably and efficiently to agents each with their own preferences is a general problem of considerable significance. Many examples of this problem are commonly found, among which we can cite the construction of schedules, the sharing of communication networks, the management of airport resources involving several companies, the sharing of airspace between different users, sharing of satellite resources. In the context of constraint programming, we propose an algorithm solving the following problem: allocate in an equitable and efficient way a finite set of objects to agents each having their own utilities, under admissibility constraints. The algorithm calculates an allocation maximizing the leximin order on the utility profiles of the agents. We also describe the field of application that motivated this work: the sharing of satellite resources. We extract from it a simple and precise problem of fair allocation, which serves as a basis, thanks to a generator of test sets, for the evaluation of the proposed algorithm. Two implementations of the algorithm are compared, one in "pure" constraint programming, with Choco, the other in mixed linear programming with Cplex.