Fair resource-constrained allocation of task-chains

This work explores a novel resource allocation problem where a limited resource, such as machine time or budget, is distributed among multiple agents over discrete time slots. Each agent has indivisible unit demands and preferences for the order in which their units are served. The study aims to find fair solutions that balance agents' individual preferences and overall efficiency. To tackle this challenge, a Mixed-Integer Linear Programming (MILP) model is proposed to account for both demand allocation and order preferences. Computational experiments assess the model's effectiveness and evaluate the trade-of between fairness and efficiency. Results indicate that in small instances, fair solutions remain close to the system optimum with minimal efficiency loss. However, as complexity increases, maintaining fairness becomes significantly more costly.