Stochastic model for total cost optimization in street lamp maintenance and its probabilistic Lagrangian relaxation method

Optimization models and algorithms for the maintenance policy of components with general failure modes in a finite horizon still remain a challenge.This paper provides a multi-stage stochastic model to optimize the joint replace-ment policy for street lamp components of general failure modes.The major difficulty arises from the stochastic coupling constraints on different component replacement decisions.Instead of relaxing those constraints based on scenarios as in ex-isting methods,we propose the probability Lagrangian relaxation method(PLR) by introducing multipliers associated with the probability distributions of decisions,where the number of multipliers is independent of the exponentially increasing scenarios.A solution method and its sufficient conditions are also provided for a phase-wise policy structure to decouple the correlation among stages due to the time-variant failure rates.In numerical testing with real data,the PLR obtains the lower bound of the optimal solution and a suboptimal solution.The results lead to a significant reduction in the current maintenance cost,and demonstrate the efficiency of the model and PLR in solving practical problems.