Thomas Yeung

Maintaining a system subject to uncertain technological evolution

Maintenance decisions can be directly affected by the introduction of a new asset on the market, especially when the new asset technology could increase the expected profit. However new technology has a high degree of uncertainty that must be considered such as, e.g., its appearance time on the market, the expected revenue and the purchase cost. In this way, maintenance optimization can be seen as an investment problem where the repair decision is an option for postponing a replacement decision in order to wait for a potential new asset. Technology investment decisions are usually based primarily on strategic parameters such as current probability and expected future benefits while maintenance decisions are based on “functional” parameters such as deterioration levels of the current system and associated maintenance costs. In this paper, we formulate a new combined mathematical optimization framework for taking into account both maintenance and replacement decisions when the new asset is subject to technological improvement. The decision problem is modelled as a non-stationary Markov decision process. Structural properties of the optimal policy and forecast horizon length are then derived in order to guarantee decision optimality and robustness over the infinite horizon. Finally, the performance of our model is highlighted through numerical examples.

Optimizing road milling and resurfacing actions

A condition-based maintenance optimization approach is developed for the road-cracking problem in order to derive optimal maintenance policies that minimize a total discounted maintenance cost. The approach is based on a Markov decision process that takes into account multiple actions with varying effects on future road performance. Maintaining the road consists of adding a new asphalt layer; however, as resurfacing actions are constrained by a maximum total road thickness, the maintenance decision is not only how thick a layer to apply, but also how much old road to remove. Each combination of these actions leads to different maintenance costs and different future degradation behaviours. The road state is modelled by a dependent bivariate deterioration variable (the longitudinal cracking percentage and the deterioration growth rate), for taking these different changes in the cracking patterns into account. Moreover, the sensitivity to cracking for existing roads can be reduced with the addition of new layers, and thus actions that can lead to states better than good-as-new have to be considered. A numerical analysis is provided to illustrate the benefits of the introduction of the deterioration speed in the decision framework, as well as the belief that initially building a road to its maximum thickness is not optimal. The trade-offs in the design decisions and the exploitation/maintenance costs are also explored.

Optimal resurfacing decisions for road maintenance: A POMDP perspective

We develop an optimal maintenance policy for a road section to minimize the total maintenance cost over the infinite horizon when some deterioration and decision parameters are not observable. Both perfect and imperfect maintenance actions are possible through the application of various thicknesses of resurfacing layers. We use a two-phase deterioration process based on two parameters: the longitudinal cracking percentage and the deterioration growth rate. Our deterioration model is a state-based model based on the state-dependent Gamma process for the longitudinal cracking percentage and the Bilateral Gamma process for the deterioration growth rate. Moreover the maintenance decision is constrained by a maximum road thickness that makes the maintenance decisions more complex as it becomes how much surface layer to add as well as to remove. Because only one of the two deterioration parameters is observable, we formulate the problem as a partially observed Markov decision process and solve it using a grid-based value iteration algorithm. Numerical examples have shown that our model provides a preventive maintenance policy that slows down the initiation as well as the propagation of longitudinal cracks and that may ameliorate the road state to a better than as-good-as-new one by altering its composition through additive resurfacing layers.

Selecting test sensitivity and specificity parameters to optimally maintain a degrading system

The formulation of a partially observed Markov decision process (POMDP) model to adaptively schedule testing, minimal repairs and overhauls for a two-state process with age-dependent degradation is presented. Structurally, the optimal maintenance policy is of control-limit type with respect to the repair and overhaul actions in both age and the probability of being out-of-control. A tailored solution algorithm is developed that iteratively determines an upper bound on the truncation age under the optimal policy. Numerical examples highlight the flexibility of the model, possible complexities of the optimal policy, and cost savings in comparison with less flexible models.

Optimal highway maintenance policies under uncertainty

We develop an inspection and maintenance policy to minimize the cost of maintaining a given section of road or highway when there is a great deal of uncertainty in the degradation process. We propose to model the degradation of a section of road based on the proliferation and growth of cracks. We utilize a combination of a Poisson and gamma process to account for the tremendous amount of uncertainty and difficulty in predicting the proliferation of cracks. Our policy defines the optimal inspection interval as well as the minimum threshold at which to perform crack repairs. Furthermore, our policy contains a safety constraint to prevent the probability of a ldquocatastrophicrdquo failure from exceeding a pre-determined reliability value. Numerical calculations have shown that our model will extend the lifecycle of the road by performing preventive, conditioned-based maintenance to slow down the growth of cracks. Classical preventive maintenance policies usually shorten the lifecycle by forcing earlier renewals.

Acquisition of new technology information for maintenance and replacement policies

In this paper, we propose the first model that considers the option to acquire information on the profitability of a new technology that is not yet available on the market for asset maintenance and replacement decisions. We consider the uncertainty of future asset characteristics by incorporating information acquisition decisions into a non-stationary Markov decision process framework. Using this framework, we optimise asset maintenance and replacement decisions as well as the optimal timing of new technology adoption. Through mathematical analyses, the monotone properties and convexity of the value function and optimal policy are deduced. Deeper numerical analyses highlight the importance of considering the acquisition of information on future technology when formulating a maintenance and replacement policy for the asset. We also deduce a non-intuitive result: an increase in the arrival probability of new technology does not necessarily make the acquisition of additional information more attractive.

A risk-oriented degradation model for maintenance of reinforced concrete structure subjected to cracking

This article is within the context of decision models aimed for maintenance of structures and infrastructures in civil engineering. The contribution relies on the construction of a degradation model oriented toward risk analysis. The proposed model can be defined as a meta-model in the sense that it is based on observations while incorporating key features from the degradation process necessary for the maintenance decision. We propose to stimulate the construction of the degradation model based on the crack propagation of a submerged reinforced concrete structure subject to chloride-induced corrosion. Furthermore, a set of numerical illustrations is performed to demonstrate the advantages and applicability of the proposed approach in risk management and maintenance contexts.

Integrating Dynamic Control Charts and Maintenance Policies

Abstract Statistical process control and maintenance optimization have an intuitive relationship, but the literature has largely treated them as separate entities. We formulate a partially observable Markov decision process (POMDP) that integrates these two fields by jointly optimizing the conditioned-based maintenance policy and dynamic control chart parameters used to observe the system. We present an insightful numerical example that demonstrates the flexibility of the policy as well it promising structural properties and practical implementation.

Multimodal multi-flow problem with transformation : Application to waste supply chain

This paper presents a new tactical optimization problem for non-hazardous waste and end-life product supply chain. Waste transport and recycling become crucial in our modern society, with a huge environmental and economic impact for industrials and communities. Operations on products during transport such as grinding or sorting allows companies to densify transports and reduce the overall supply cost. Integrating these new aspects, we introduce a new problem we term the multi-commodity, multi-flow problem with transformations and propose a linear mathematical model to solve it. With an application to a waste transport company and a performance benchmark on a linear solver, we show the pertinence of the model in a real case study and its scalability for more complex situations.

Dynamic lot-sizing-based Working Capital Requirement minimization model with infinite capacity

Tactical planning consists of developing production plans to fulfill client demands with a minimal logistic cost. However, plans generated by classical models for tactical planning do not consider a minimum financial need in terms of Working Capital Requirements (WCR) to maintain the activities related to the operating cycle. In this paper, we introduce a first link between tactical planning and the financial aspects of WCR. The concept of WCR is widely used in practice to assess the financial situation at any time. We propose a new generic WCR model which allows us to evaluate the companys financial situation during the planning horizon. In addition, we develop a dynamic lot-sizing-based model with WCR modeling for singlesite, single-level, single-product and infinite capacity cases. An exact algorithm is also presented with numerical tests in order to compare our approach with the traditional dynamic lot-sizing model.