Practical extensions to a minimum cost flow model for level of repair analysis

The level of repair analysis (LORA) gives answers to three questions that are posed when deciding on how to maintain capital goods: (1) which components to repair upon failure and which to discard, (2) at which locations in the repair network to perform each type of repairs, and (3) at which locations in the network to deploy resources, such as test equipment. The goal is to achieve the lowest possible life cycle costs. Various models exist for the LORA problem. However, they tend to be restrictive in that specific business situations cannot be incorporated, such as having repair equipment with finite capacity or the occurrence of unsuccessful repairs or no-fault-founds. We discuss and model such practically relevant extensions to an existing minimum cost flow formulation for the LORA problem. In an extensive numerical experiment, we show that incorporating the model refinements leads to a substantial change in the costs in general. The repair strategy changes substantially only when incorporating finite resource capacities or a probability of unsuccessful repair that is decreasing with an increasing echelon level.     

Some Probabilistic Models of Reinforced Concrete Structures Deterioration

Some probabilistic models for deterioration of reinforced concrete elements (local problem) and whole structures (global problem) caused by the reinforcing steel corrosion and another external and internal influences are proposed. Such problem is important for estimation how the structure reliability changes in time and for planning structure inspections and repairs.     

A Closed Queueing Maintenance Network with Two Repair Centres

In this paper we introduce a model to determine the maintenance float needed to maximize the availability of an operating system with N number of circulating units. An implicit enumeration algorithm is used as a solution technique to the closed queueing maintenance network with two types of repairs: minor and major repairs. It is shown that when there is no differentiation of repair type, this special case is obtained as a by-product of the two-repair-centre model. This paper assumes exponential failure times and exponential repair times with load-independent servers. The approach followed in this paper provides an approximate and simple way to solve the maintenance-float problem of this complex closed-network system.     

Semidefinite relaxations for partitioning,assignment and ordering problems

This paper introduces polymorphic ejection chains, and applies them to the problem of repairing time assignments in high school timetables while preserving regularity. An ejection chain is a sequence of repairs, each of which removes a defect introduced by the previous repair. Just as the elements of a polymorphic list may have different types, so in a polymorphic ejection chain the individual repairs may have different types. Methods for the efficient realization of these ideas, implemented in the author’s KHE framework, are given, and some initial experiments are presented.     

A multi-objective approach for solving a replacement policy problem for equipment subject to imperfect repairs

This paper proposes a multi-objective approach to model a replacement policy problem applicable to equipment with a predetermined period of use (a planning horizon), which may undergo critical and non-critical failures. Corrective replacements and imperfect repairs are taken to restore the system to operation respectively when critical and non-critical failures occur. Generalized Renewal Process (GRP) is used to model imperfect repairs. The proposed model supports decisions on preventive replacement intervals and the number of spare parts purchased at the beginning of the planning horizon. A Multi-Objective Genetic Algorithm (MOGA) coupled with discrete event simulation (DES) is proposed to provide a set of solutions (Pareto-optimum set) committed to the different objectives of a maintenance manager in the face of a replacement policy problem, that is, maintenance cost, rate of occurrence of failures, unavailability, and investment on spare parts. The proposed MOGA is validated by an application example against the results obtained via the exhaustive approach. Moreover, examples are presented to evaluate the behavior of objective functions on Pareto set (trade-off analysis) and the impact of the repair effectiveness on the decision making.     

Iterative algorithms for the curfew planning problem

The curfew planning problem is to design an annual timetable for railway track maintenance teams. Each team is capable of handling certain types of repairs and replacement jobs. The jobs are combined into a set of projects according to their locations and types. The timetable shows which project should be worked on by each team on a weekly basis throughout an entire year. Our objective is to design a schedule with minimum network disruption due to ongoing maintenance projects that require absolute curfew. Absolute curfew projects are those that cause complete closure of the rail traffic. For tackling this problem, we develop four optimization-based iterative algorithms. We also present very promising computational results obtained within a few minutes using data provided by a major North American railroad.     

Approximate solution for two stage open networks with Markov-modulated queues minimizing the state space explosion problem

Analytical solutions for two-dimensional Markov processes suffer from the state space explosion problem. Two stage tandem networks are effectively used for analytical modelling of various communication and computer systems which have tandem system behaviour. Performance evaluation of tandem systems with feedbacks can be handled with these models. However, because of the numerical difficulties caused by large state spaces, considering server failures and repairs at the second stage employing multiple servers has not been possible. The solution proposed in this paper is approximate with a high degree of accuracy. Using this approach, two stage open networks with multiple servers, break downs, and repairs at the second stage as well as feedback can be modelled as three-dimensional Markov processes and solved for performability measures. Results show that, unlike other approaches such as spectral expansion, the steady state solution is possible regardless of the number of servers employed.     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

Optimal number of minimal repairs before ordering spare for preventive replacement

This paper presents a model for determining the optimal number of minimal repairs before ordering spare for preventive replacement. By introducing the costs of ordering, repair, downtime, replacement, and the salvage value of an un-failed system, the expected long-term cost rates and cost effectiveness are derived. It is shown that, under certain conditions, the optimal number of minimal repairs, which minimizes the cost rate or maximizes the cost effectiveness, is given by a unique solution of an equation. A numerical example is also given for illustration of the proposed model.     

Replacement times and costs in a degrading system with several types of failure: The case of phase-type holding times

A reliability system submitted to external and internal failures, that can be repairable or non-repairable, with degradation levels, and with sojourn times phase-type distributed, is considered. Repair is not as good as new, and the repair of internal failure follows policy N, that is, after N completed repairs the system is replaced by a new one to the following failure, repairable or not. For this system, a Markov model is constructed, and the stationary probability vector is calculated. It is shown that the distribution of the time between two consecutive replacements follows a phase-type distribution, whose representation is determined. The costs of these periods are calculated. An optimization problem involving the costs, the availability, and the number of internal repairs is illustrated by a numerical example.     

An LDQBD process under degradation,inspection, and two types of repair

A warm standby n-system with operational and repair times following phase-type distributions is considered. The online unit goes through degradating levels, determined by inspections. Two types of repairs are performed, preventive and corrective, depending on the degradation level. The standby units undergo corrective repair. This systems is governed by a level-dependent-quasi-birth-and-death proces (LDQBD process), whose generator is constructed. The availability, rate of occurrence of failures, and other quantities of interest are calculated. A numerical example including an optimization problem and illustrating the calculations is presented. This system extend other previously studied in the literature.     

Network repair crew scheduling for short-term disasters

Casualties and damages caused by disasters occur every year. To reduce further damages in the post disaster period, many types of research have been conducted. The repair crew problem is one of these efforts, and it is used for deciding ways to manage repairs to destroyed roads that connect members of supply chain networks. Especially in rural areas where road networks are sparse and supply chains are limited, road-network repair is particularly important because road destruction can contribute to high rates of rural isolation. In addition, the unpredictable nature of disasters creates concerns for those effecting post-disaster management. Especially in the short-term after a disaster, damage characteristics can dramatically change. Therefore, we considered a repair crew problem in which aspects of damage vary at certain times. A mathematical formulation on the basis of mixed integer programming is introduced to minimize the weighted sum of total damages caused in isolated areas and completion time of a repair crew. To overcome the complexity issue, an ant colony system algorithm was developed. It can be used to solve a multiple repair crew problem. Our study gives new insights into ways to manage problems in the post-disaster period.     

A model for a textile winding process

This paper solves the problem of determining the efficiency of N machines uni-directionally patrolled by one operative when walking time between the machines is constant, and repair time is constant, but repairs are not always successful. The problem arises in the context of a textile winding process and the results are of value in maintaining controls over the process. The increased efficiency that results from the operative repeatedly trying to repair a stopped machine, rather than leaving it stopped and continuing with his patrol is also calculated, and the design implications of this improved strategy are considered.     

Preventive maintenance for homogeneous and heterogeneous systems

We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented.     

A model for maintenance service contract design,negotiation and optimization

A model is presented in this paper for maintenance service contract design, negotiation and optimization. The model was developed under the assumption that there are one customer and one unique service provider who is the Original Equipment Manufacturer (OEM) and is called the agent in this paper. This is typically applied to the situation where the OEM is the only possible service supplier such as in the case of major military equipment in the defense sector. Three contract options were considered, depending on the extent of outsourced maintenance activities. From an agent point of view, they are, (1), the agent carries out all repairs and inspections; (2), the agent carries out failure based repairs, and (3), the agent does inspections and repairs to the defects identified at inspections. For options two and three, the customer does the rest of maintenance. The relationship between inspections and failures was modeled using the delay time concept and a numerical example was illustrated. The cases of perfect information to both parties and information asymmetry were also discussed in the example. The model developed can be used for contract design, negotiation and optimization.     

An Operational Research Approach to Planned Maintenance: Modelling P.M. for a Vehicle Fleet

A methodology is advanced for modelling the problem of planned preventive maintenance, thereby relating plant performance to maintenance activity. Ideas are discussed and developed within the context of a P.M. system for the maintenance of a vehicle fleet. Three specific questions are addressed: first, the omission of any desirable activities from the P.M. schedule, secondly, the presence of redundant items in the schedule, and thirdly, the consequences of different frequencies of application of the P.M. schedule. A fleet model is obtained relating the P.M. period to measures such as proportion of breakdown repairs and the cost per vehicle year.     

Optimal Claiming on Vehicle Insurance

Insurance companies charge reduced premiums to motorists who go through a period of one or more years without making a claim. When an accident occurs the insured frequently finds himself with the option of either making a claim and reverting to a higher premium or paying for the repair himself. Most motorists operate an informal system of "no-claim limits", whereby they only claim for repairs which exceed a certain cost.In this paper it is shown how, under reasonable assumptions regarding the rate of accidents and the distribution of repair costs, optimal no-claim limits can be determined. These minimise the long run average cost of premiums and repairs and show significant savings over the case where all claims are made. The effect of an "excess clause", whereby the insured agrees to pay a first amount of any claim is also studied, and rules for determining whether it is profitable to accept such a clause are presented in the form of a graph.     

A comparison of adaptive and stationary repair-cost limit criteria for a producer's warranty

A producer sells a product together with a warranty valid fora specified duration.Whenever the product fails during the warrantyperiod, the producer is responsible for making the product functional,either by replacing or repairing the equipment,according towhether the anticipated repair cost exceeds or does not exceeda specified repair-cost limit. It is assumed that repairs areminimal repairs, and that the distribution of repair costs isknown, as is the time-to-failure distribution of the product.In this paper, we compare two models in discrete time. The firstone involves an adaptive repair-cost limit which is set dynamicallyaccording to the age of the product, and the length of warrantyremaining. The second model assumes a constant or stationaryrepair-cost limit throughout the warranty period. Empiricalresults are summarized.     

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic τ-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems.     

A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior

The hedging-point policy for a production-inventory system is investigated under the effect of probabilistic machine breakdowns and repairs assuming general discrete distributions for the repair time and the time to failure. Using a methodology whereby inventory levels can assume only discrete values, an optimal safety stock size that minimizes the total expected cost per unit time is determined.