Optimization of the maintenance of a large bridge system.

摘要

n the first part of this research, one proposes a mathematical model for the dynamical and probabilistic behavior of the deterioration and maintenance of a large bridge system and one shows how this model can be used for making better decisions on its maintenance. The model integrates the budgetary constraints and the level of safety and good functionality, and uses the mathematical framework of Markov Decision Processes (MDP). As an alternative to the solution of the usual optimization problem, for the finite horizon, associated with an MDP, a new class of solutions called "the effective strategies" are introduced and studied. An algorithm for their construction is provided.;In the second part of this research, one studies the problem of the optimal allocation of funds for each bridge separately. The purpose is to maximize the user benefit constrained by a given total amount of funds available for the whole system. The problem reduces to optimally partition a set of bridges of various sizes in M groups, each group having a specified total size. Both, the exact and the approximate partitionings are discussed. In the case of the exact partitioning, a method for obtaining a (locally) optimal partition, starting with a feasible one, is provided. In the case of the approximate partitioning, the concepts of