Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension while ensuring their coordination. Each subproblem consists in optimizing the maintenance on a single component. Decomposition-coordination techniques are based on variational techniques but the maintenance optimization problem is a mixed-integer problem. Therefore, we relax the dynamics and the cost functions of the system. The resulting algorithm iteratively solves the subproblems on the relaxed system with a blackbox method and coordinates the components. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. An admissible maintenance strategy is then derived from the resolution of the relaxed problem. We apply the decomposition algorithm on a system with 80 components. It outperforms the reference blackbox method applied directly on the original problem.
This paper considers the simultaneous high-speed train assignment and maintenance scheduling problem. For the maintenance scheduling module, our focus is the second-level maintenance, which is carried out once a month on average. We propose a binary non-linear programming model to mathematically describe the problem. The objective aims to minimize the mileage losses for all high-speed trains and the constraints cover various operational requirements and capacity restrictions. To model the difficult operational requirements, a novel cumulative mileage update function is developed; meanwhile, to…
During the life of a wind farm, various types of costs arise. A large share of the operational cost for a wind farm is due to maintenance of the wind turbine equipment; these costs are especially pronounced for offshore wind farms and provide business opportunities in the wind energy industry. An effective scheduling of the maintenance activities may reduce the costs related to maintenance. We combine mathematical modelling of preventive maintenance scheduling with corrective maintenance strategies. We further consider different types of contracts between the wind farm owner and a maintenance …
We suggest a mathematical model for computing and regularly updating the next preventive maintenance plan for a wind farm. Our optimization criterium takes into account the current ages of the key components, the major maintenance costs including eventual energy production losses as well as the available data monitoring the condition of the wind turbines. We illustrate our approach with a case study based on data collected from several wind farms located in Sweden. Our results show that preventive maintenance planning gives some effect, if the wind turbine components in question live significa…
We consider a problem concerning a network and a set of maintenance requests to be undertaken. We wish to schedule the maintenance in such a way as to minimise the impact on the total throughput of the network. We apply disaggregated Benders cuts and lazy constraints to solve the problem to optimality, as well as exploring the strengths and weaknesses of the technique. We prove that our Benders cuts are pareto optimal. Solutions to the LP relaxation also provide further valid inequalities to reduce total solve time. We implement these techniques on simulated data presented in previous papers, …
We consider a problem that marries network flows and scheduling, motivated by the need to schedule maintenance activities in infrastructure networks, such as rail or general logistics networks. Network elements must undergo regular preventive maintenance, shutting down the arc for the duration of the activity. Careful coordination of these arc maintenance jobs can dramatically reduce the impact of such shutdown jobs on the flow carried by the network. Scheduling such jobs between given release dates and deadlines so as to maximize the total flow over time presents an intriguing case to study t…
This paper proposes a dynamic game-based maintenance scheduling mechanism for the asset owners of the natural gas grid and the power grid by using a bilevel approach. In the upper level, the asset owners of the natural gas grid and the power grid schedule maintenance to maximize their own revenues. This level is modeled as a dynamic game problem, which is solved by the backward induction algorithm. In the lower level, the independent system operator (ISO) dispatches the system to minimize the loss of power load and natural gas load in consideration of the system operating conditions under main…
Maintenance planning plays a key role in power system operations under uncertainty by helping system operators ensure a reliable and secure power grid. This paper studies a short-term condition-based integrated maintenance planning with operations scheduling problem while considering the unexpected failure possibilities of generators as well as transmission lines. We formulate this problem as a two-stage stochastic mixed-integer program with failure scenarios sampled from the sensor-driven remaining lifetime distributions of the individual system elements whereas a joint chance-constraint cons…
A large part of the operational cost for a wind power farm is due to the cost of equipment maintenance, especially for offshore wind farms. How to reduce the maintenance cost, and hence increase profitability, is this article's focus. It presents a binary linear optimization model whose solution may suggest the wind turbine owners which components, and when, should undergo the next preventive maintenance (PM) replacements. The suggested short-term scheduling strategy takes into account eventual failure events of the multi-component system, in that after the failed system is repaired, the previ…
The approach presented in this article is a contribution to research relating to the optimization of the scheduling of the spots of maintenance. This work answers the following objectives: Decision in time-reality (planning and scheduling), Allowance/assignment of resources, To ensure a minimum availability required, To minimize times delay while inserting the dynamic tasks "corrective maintenance"
Due to increasing railway use, the capacity at railway yards and maintenance locations is becoming limiting. Therefore, the scheduling of rolling stock maintenance and the choice regarding optimal locations to perform maintenance is increasingly complicated. This research introduces a Maintenance Scheduling and Location Choice Problem (MSLCP). It simultaneously determines maintenance locations and maintenance schedules of rolling stock, while it also considers the available capacity of maintenance locations, measured in the number of available teams. To solve the MSLCP, an optimization framewo…
Wind power is one of the most important sources of renewable energy. A large part of the wind energy cost is due to the cost of maintaining the wind power equipment. To further reduce the maintenance cost, one can improve the design of the wind turbine components. One can also reduce the maintenance costs by optimal scheduling of the component replacements. The latter task is the main motivation for this paper. When a wind turbine component fails to function, it might need to be replaced under less than ideal circumstances. This is known as corrective maintenance. To minimize the unnecessary c…
We investigate a novel scheduling problem which is motivated by an application in the Australian railway industry. Given a set of maintenance jobs and a set of train paths over a railway corridor with bidirectional traffic, we seek a schedule of jobs such that a minimum number of train paths are cancelled due to conflict with the job schedule. We show that the problem is NP-complete in general. In a special case of the problem when every job under any schedule just affects one train path, and the speed of trains is bounded from above and below, we show that the problem can be solved in polynom…
Despite the promising outlook, the numerous economic and environmental benefits of offshore wind energy are still compromised by its high operations and maintenance (O&M) expenditures. On one hand, offshore-specific challenges such as site remoteness, harsh weather, transportation requirements, and production losses, significantly inflate the O&M costs relative to land-based wind farms. On the other hand, the uncertainties in weather conditions, asset degradation, and electricity prices largely constrain the farm operator's ability to identify the time windows at which maintenance is possible,…
Short-term hydro-generation management poses a non-convex or even non-continuous optimization problem. For this reason, the problem of systematically obtaining feasible and economically satisfying solutions has not yet been completely solved. Two decomposition methods, which, as far as we know, have not been applied in this field, are here proposed : $\bullet$ the first is based on a decomposition by prediction method and the coordination is a primal-dual relaxation algorithm, $\bullet$ handling the dynamic constraints by duality, the second achieves a price decomposition by an Augmented Lagra…
Planning, scheduling and dispatching play critical roles in the operations of a supply chain. Their definitions are clearly given through a unified view in this paper. The distinction between planning and scheduling is analyzed from the view point of microeconomics and queueing theory. The distinction between scheduling and dispatching is analyzed from the view point of computational complexity and hierarchical decomposition. Based on the elasticity of price and capacity, planning can be separated into demand planning or capacity planning. Scheduling period is the time horizon where price and …
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample average approximation, and develop two enhanced decomposition frameworks that use logic-based Benders (LBBD) optimality cuts and binary decision diagram based Benders cuts. Specifically, to the best of our knowledge, deriving LBBD optimalit…
We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second-stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple nogood cuts as well as analytical logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method, with a branch-and-check variant of LBBD faster by several orders of magnitude, allowing significantly larger instances to be solved. This …
Operations and Maintenance (O&M) constitute a major contributor to offshore wind's cost of energy. Due to the harsh and remote environment in which offshore turbines operate, there has been a growing interest in opportunistic maintenance scheduling for offshore wind farms, wherein grouping maintenance tasks is incentivized at times of opportunity. Our survey of the literature, however, reveals that there is no unified consensus on what constitutes an "opportunity" for offshore maintenance. We therefore propose an opportunistic maintenance scheduling approach which defines an opportunity as eit…
Behind the concept of Industry 4.0, there are a number of principles and ideas; one of them is the integration of problems of different decision levels. In this work, we integrate maintenance with planning problems, aiming to take full advantage of the production capacity providing immediate delivery of products to customers and avoiding failures. We propose a hybrid approach for solving a maintenance problem integrated with the lot-sizing and scheduling problems. The approach is based on the concepts of robustness and simheuristics, considering preventive, predictive and corrective maintenanc…
Redox Flow Batteries are a promising option for large-scale stationary energy storage. The vanadium redox flow battery is the most widely commercialized system thanks to its chemical stability and performance. This work aims to optimize the scheduling of a vanadium flow battery that stores energy produced by a renewable power plant, keeping into account a thorough characterization of the battery performance, with variable efficiencies and capacity fade effects. A detailed characterization of the battery performance improves the calculation of the optimal number of cycles and revenue associated…
Safely serving the school transportation demand with the minimum number of buses is one of the highest financial goals of school transportation directors. To achieve that objective, a good and efficient way to solve the routing and scheduling problem is required. Due to the growth of the computing power, the spotlight has been shed on solving the combined problem of the school bus routing and scheduling problem. We show that an integrated multi-school bus routing and scheduling can be formulated with the help of trip compatibility. A novel decomposition algorithm is proposed to solve the integ…
In this work we propose a decomposition approach to solve the quay crane scheduling problem. This is an important maritime transportation problem faced in container terminals where quay cranes are used to handle cargo. The objective is to determine a sequence of loading and unloading operations for each crane in order to minimize the completion time. We solve a mixed integer programming formulation for the quay crane scheduling problem, decomposing it into a vehicle routing problem and a corresponding scheduling problem. The routing sub-problem is solved by minimizing the longest crane complet…
This paper presents a techno-economic optimisation tool to study how the power system expansion decisions can be taken in a more economical and efficient way, by minimising the consequent costs of network reinforcement and reconfiguration. Analyses are performed to investigate how the network reinforcement and reconfiguration should be planned, within a time horizon of several years, by continuously keeping the network feasibility and ability to satisfy the load. The main contribution of this study is the inclusion of key features within the mathematical model to enhance the investment decisio…
Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bi-layer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner's problem) optimizes end-of-day reservoir filling le…
In Part I of this paper we formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize a weighted sum of total travel distance and generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints and AC power flow equations. We propose there a centralized solution based on the second-order cone programming (SOCP) relaxation of optimal power flow (OPF) and gene…
We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models. Specifically, given a set of MFs, a planning horizon, and a service region, our models aim to find the number of MFs to use (i.e., fleet size) within the planning horizon and a route and schedule for each MF in the fleet. The objective is to minimize the fixed cost of establishing the MF fleet plus a risk measure (expectation or mean conditional value-at-risk) o…
The parallel machine scheduling problem has been a popular topic for many years due to its theoretical and practical importance. This paper addresses the robust makespan optimization problem on unrelated parallel machine scheduling with sequence-dependent setup times, where the processing times are uncertain, and the only knowledge is the intervals they take values from. We propose a robust optimization model with min-max regret criterion to formulate this problem. To solve this problem, we prove that the worst-case scenario with the maximum regret for a given solution belongs to a finite set …
Data centers are increasingly using high-speed circuit switches to cope with the growing demand and reduce operational costs. One of the fundamental tasks of circuit switches is to compute a sparse collection of switching configurations to support a traffic demand matrix. Such a problem has been addressed in the literature with variations of the approach proposed by Birkhoff in 1946 to decompose a doubly stochastic matrix exactly. However, the existing methods are heuristic and do not have theoretical guarantees on how well a collection of switching configurations (i.e., permutations) can appr…
This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs to a well-defined interval. Robust optimization requires scenario-based decision-making. A finite subset of feasible scenarios to determine the worst-case regret (a deviation from the optimal makespan) for a particular schedule is indicated. We formulate a mixed-integer nonlinear programming model to solve the underlying problem via three (constructive) gree…
We study a Lagrangian decomposition algorithm recently proposed by Dan Bienstock and Mark Zuckerberg for solving the LP relaxation of a class of open pit mine project scheduling problems. In this study we show that the Bienstock-Zuckerberg (BZ) algorithm can be used to solve LP relaxations corresponding to a much broader class of scheduling problems, including the well-known Resource Constrained Project Scheduling Problem (RCPSP), and multi-modal variants of the RCPSP that consider batch processing of jobs. We present a new, intuitive proof of correctness for the BZ algorithm that works by cas…
This paper addresses the problem of scheduling a set of jobs that are released over the time on a set of identical parallel machines, aiming at the minimization of the total weighted completion time. This problem, referred to as $P|r_j|\sum w_jC_j$, is of great importance in practice, because it models a variety of real-life applications. Despite its importance, the $P|r_j|\sum w_jC_j$ has not received much attention in the recent literature. In this work, we fill this gap by proposing mixed integer linear programs and a tailored branch-and-price algorithm. Our {branch-and-price} relies on the…
Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming problem. It is amenable to a wide variety large-scale problems that decouple or otherwise simplify when certain decision variables are fixed. This chapter presents the basic theory of LBBD and explains how classical Benders decomposition is a special case. It also describes branch and check, a variant of LBBD that solves the master problem only once. It illu…
A Sensor-Driven Optimization Framework for Asset Management in Energy Systems: Implications for Full and Partial Digital Transformation in Hydro Fleets
In this paper, we present a novel approach for solving a maintenance scheduling problem from the French electricity grid company RTE, as presented in the ROADEF 2020 challenge. Our approach combines constraint generation with a new family of cutting planes to address the nonconvexity of the problem. We provide mathematical proofs and separation algorithms for the cutting planes and study the practical impact of our approach on the challenge instances. This method is applicable to a wide range of problems involving the modeling of uncertainty, and is shown to improve results significantly on re…
Deep learning-driven scheduling algorithm for a single machine problem minimizing the total tardiness
Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague（捷克布拉格技术大学信息学、机器人学与控制论学院）；Czech Technical University in Prague（捷克布拉格技术大学）
