Self-tuning regulators with restricted inputs
In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines. The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs is associated with one agent. The K agents compete to perform their jobs on common resources. The objective is to find a schedule that minimizes a global objective function f0, while maintaining the regular objective function of each agent, fk, at a level no greater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This...
In this paper we are exploiting some similarities between Markov and Bellman processes and we introduce the main concepts of the paper: comparison of performance measures, and monotonicity of Bellman chains. These concepts are used to establish the main result of this paper dealing with comparison of Bellman chains.
Several peculiarities of stochastic dynamic programming problems where random vectors are observed before the decision ismade at each stage are discussed in the first part of this paper. Surrogate problems are given for such problems with distance properties (for instance, transportation problems) in the second part.