Adam Wojciechowski

The stochastic opportunistic replacement problem, part II: a two-stage solution approach

In Almgren et al. (The opportunistic replacement problem: analysis and case studies, preprint, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2011) we studied the opportunistic replacement problem, which is a multi-component maintenance scheduling problem with deterministic component lives. The assumption of deterministic lives is a substantial simplification, but valid in applications where critical components are assigned a technical life after which replacement is enforced. Here, we study the stochastic opportunistic replacement problem, which is a more general setting in which component lives are allowed to be stochastic. We consider a stochastic programming approach for the minimization of the expected cost over the remaining planning horizon. Further, we present a means to compute lower bounds on the recourse function. The lower bounds are used in the construction of a decomposition method which extends the integer L-shaped decomposition method to incorporate stronger optimality cuts. In order to obtain a computationally tractable model, a two-stage sample average approximation scheme is utilized. Numerical experiments on problem instances from the wind power and aviation industry as well as on two test instances are performed. The results show that the decomposition method is faster than solving the deterministic equivalent on all four instances considered. Furthermore, the numerical experiments show that decisions based on the stochastic programming approach compared with simpler maintenance policies yield maintenance decisions with a significantly lower expected total maintenance cost on two out of the four instances tested, and an equivalent maintenance cost compared to the best policy on the remaining two instances.

A stochastic model for opportunistic maintenance planning of offshore wind farms

A sound maintenance planning is of crucial importance for wind power farms, and especially for offshore locations. This paper presents a stochastic optimization model for opportunistic service maintenance of offshore wind farms. The model takes advantage of 7 days wind production ensemble forecast and opportunities at corrective maintenance activities in order to perform the service maintenance tasks at the lowest cost. The model is based on a rolling horizon, i.e. the optimization is performed on a daily basis to update the maintenance planning based on the updated production and weather forecasts. An example based on real wind data is used to demonstrate the value of the proposed approach. In this example, it is shown that 32% of the cost for production losses and transportation could be saved.

An opportunistic maintenance optimization model for shaft seals in feed-water pump systems in nuclear power plants

Nuclear power is one of the main electricity production sources in Sweden today. Maintenance management is one tool for reducing the costs for operation of a power plant. Driving forces for cost-efficiency has pushed the development of new methods for maintenance planning and optimization forward. Reliability Centered Asset Management (RCAM) is one of these new approaches, and maintenance optimization is one way to perform quantitative analysis which is a feature of RCAM. This paper proposes a model for opportunistic maintenance optimization where replacement schedules for shaft seals in feed-water pump systems in nuclear power plants are constructed. The feed-water pump system is important for the availability of the entire nuclear power plant. Results show that the optimization model is dependent on e.g. the discount interest and a limit for when the optimal solution goes from non-opportunistic to opportunistic is calculated. The circumstances for which opportunistic maintenance could be used have been investigated given different values of discount rates and remaining life at start of the planning period.

A comparison of several models for the hamiltonian p-median problem

The Hamiltonian p-median problem consists of determining p disjoint cycles of minimum total cost covering all vertices of a graph. We present several new and existing models for this problem, provide a hierarchy with respect to the quality of the lower bounds yielded by their linear programming relaxations, and compare their computational performance on a set of benchmark instances. We conclude that three of the models are superior from a computational point of view, two of which are introduced in this article.

New models for and numerical tests of the Hamiltonian p-median problem

The Hamiltonian p-median problem (HpMP) was introduced by [Branco90]. It is closely related to two well-known problems, namely the Travelling Salesman problem (TSP) and the Vehicle Routing problem (VRP). The HpMP is to find exactly p node-disjoint cycles of minimum edge cost, such that each node of the graph is contained in exactly one cycle. We present three new models for the HpMP problem which differ with regard to the constraints that enforce a maximum number of cycles. We demonstrate that one of the models (SEC) is dominated by another model (PCON) with regard to the LP relaxation. Further, we introduce a class of symmetry breaking constraints. We present results regarding the quality of the lower bounds provided by the respective LP relaxations for two of the models, and provide computational results that demonstrate the computational efficiency.

An evaluation approach for opportunistic maintenance optimization models for nuclear power plants

Nuclear power constitutes one of the main electricity production sources in several countries, e.g. in Sweden, with about half of todays electricity production. Driving forces for cost-efficiency have pushed the development of new methods for maintenance planning and optimization forward. Reliability Centered Asset Management (RCAM) is one of these new approaches, and maintenance optimization is one way to perform quantitative analysis which is a feature of RCAM. This paper proposes a stochastic framework for evaluating opportunistic maintenance optimization models for the generation of replacement schedules for shaft seals in feed-water pump systems in nuclear power plants. Results show that the extended discounted model has a good overall performance, when compared to other strategies. Moreover, it is shown that it is the best strategy for high values of the constant cost for maintenance and the second best for lower values of the constant cost.