Two-agent scheduling on uniform parallel machines with maximum criteria functions

Donatas Elvikis (1) , Vincent t'Kindt (2)

1 University of Kaiserslautern [Kaiserslautern]
2 LIFAT - Laboratoire d'Informatique Fondamentale et Appliquée de Tours

We consider the problem of scheduling two agents A and B on a set of m uniform parallel machines. Each agent is assumed to be independent from the other: agent A and agent B are made up of n_A and n_B jobs, respectively. Each job is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size jobs, i.e. all jobs share the same processing time. Our goal is to minimize two maximum functions associated with agents A and B and referred to as F_A^max=max_{i∈A} (f^A_i(C_i)) and F_B^max=max_{i∈B} (f^B_i(C_i)), respectively, with C_i the completion time of job i and f^X_i a non-decreasing function. These kinds of problems are called multi-agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of the strict Pareto optima for the (F_A^max,F_B^max) criteria vector. In this paper we develop a minimal complete Pareto set enumeration algorithm with O(n^2_A+n^2_B+n_An_Blog (n_B)) time complexity and O(nn_B) memory requirements

Mots clés: Multi-agent scheduling; Parallel machines; Pareto optimum

Domaines: Recherche opérationnelle [math.OC]

Donatas Elvikis, Vincent t'Kindt. Two-agent scheduling on uniform parallel machines with maximum criteria functions. Annals of Operations Research, 2014, 213, pp.79-94. ⟨10.1007/s10479-012-1099-0⟩. ⟨hal-01004005⟩