A dyadic age-replacement policy for a periodically inspected equipment item subject to random deterioration

A periodic review replacement system is considered. The amount of deterioration over successive periods forms a sequence of i.i.d. random variables. A replacement policy of the dyadic type is in effect whereby the used equipment item is discarded and immediately replaced by a new identical equipment item if at the end of a period the old equipment has service aged by an amount in excess of S or has been in operation for exactly N periods whichever comes first. Using a theorem on renewal reward processes, an expression for the total steady-state expected cost per period is derived, consisting of a fixed replacement cost and a linear cost of operation. Optimal values of S and N that minimize this steady state cost are computed for a few numerical examples, when the service aging per period has a gamma distribution.     

Maintenance scheduling of a protection system subject to imperfect inspection and replacement

An inspection and replacement policy for a protection system is described in which the inspection process is subject to error, and false positives (false alarms) and false negatives are possible. We develop two models: one in which a false positive implies renewal of the protection system; the other not. These models are motivated by inspection of a protection system on the production line of a beverage manufacturer. False negatives reduce the efficiency of inspection. Another notion of imperfect maintenance is also modelled: that of poor installation of a component at replacement. These different aspects of maintenance quality interact: false alarms can, in a worst case scenario, lead to the systematic and unnecessary replacement of good components by poor components, thus reducing the availability of the system. The models also allow situations in which maintenance quality differs between alternative maintainers to be investigated.     

An approach for solving nonlinear multi-objective separable discrete optimization problem with one constraint

We propose an exact solution approach for solving nonlinear multi-objective optimization problems with separable discrete variables and a single constraint. The approach converts the multi-objective problem into a single objective problem by using surrogate multipliers from which we find all the solutions with objective values within a given range. We call this the surrogate target problem which is solved by using an algorithm based on the modular approach. Computational experiments demonstrate the effectiveness of this approach in solving large-scale problems. A simple example is presented to illustrate an interactive decision making process.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

A finite-element approach to solving a thermal conductivity problem for thick plates

A method is proposed for the numerical solution of a problem in the thermal conductivity a plate heated by a moving heat source, taking into account the dependence of the thermal properties of the material on temperature. A hypothesis of N. N. Rykalin concerning the state of the thermal field is adopted. The method is based on a spline variant of the finite-element method; this is based on the synthesis of parametrization and finite elements with splines. A FORTRAN algorithm is given for performing the method on an ES series computer.Translated from Matematichekie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 58–62, 1989.     

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Traditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so‐called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.     

A multi-objective programming approach to 1.5-dimensional assortment problem

In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches.     

A fully subjective approach to capital equipment replacement

The timing of replacement of equipment is dependent on factors like replacement costs, discount factors and differences in productivity, reliability and safety of existing and new equipment. Predictions related to these factors are, however, normally subject to uncertainties, and in this paper we discuss how two subjective approaches to representing uncertainties related to future events—the classical Bayesian approach and the fully subjective approach—can be used as a basis for decision-making about replacement. Some key features of the approaches are discussed, including integration of engineering judgements, uncertainty treatment and type of performance measures to be used. In the fully subjective approach, we advocate the direct subjective assessment of uncertainty in a quantity of interest, which should be observable, with decisions made on the basis of this uncertainty. The fully subjective approach is illustrated using an example in capital equipment replacement.     

A Bayesian approach to the triage problem with imperfect classification

A collection of jobs (or customers, or patients) wait impatiently for service. Each has a random lifetime during which it is available for service. Should this lifetime expire before its service starts then it leaves unserved. Limited resources mean that it is only possible to serve one job at a time. We wish to schedule the jobs for service to maximise the total number served. In support of this objective all jobs are subject to an initial triage, namely an assessment of both their urgency and of their service requirement. This assessment is subject to error. We take a Bayesian approach to the uncertainty generated by error prone triage and discuss the design of heuristic policies for scheduling jobs for service to maximise the Bayes’ return (mean number of jobs served). We identify problem features for which a high price is paid in number of services lost for poor initial triage and for which improvements in initial job assessment yield significant improvements in service outcomes. An analytical upper bound for the cost of imperfect classification is developed for exponentially distributed lifetime cases.     

A matheuristic approach for solving a home health care problem

We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

The optimal repair-time limit replacement policy with imperfect repair: Lorenz transform approach

In this paper, we consider a simple repair-time limit replacement problem with imperfect repair, and focus on the problem of determining the optimal repair-time limit which minimizes the expected cost per unit time in the steady-state. Applying the Lorenz transform, we develop a nonparametric method to estimate the optimal repair-time limit from the empirical repair-time data. Numerical examples are considered to calculate the optimal policy and to examine the asymptotic properties of the estimator.     

A new approach for solving the Stokes problem

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate the velocity functions by piecewise linear functions. Then, the approximate values of pressure are obtained by a finite difference scheme.     

A decomposition approach for solving a broadcast domination network design problem

We consider an optimization problem that integrates network design and broadcast domination decisions. Given an undirected graph, a feasible broadcast domination is a set of nonnegative integer powers f _i assigned to each node i, such that for any node j in the graph, there exists some node k having a positive f _k -value whose shortest distance to node j is no more than f _k . The cost of a broadcast domination solution is the sum of all node power values. The network design problem constructs edges that decrease the minimum broadcast domination cost on the graph. The overall problem we consider minimizes the sum of edge construction costs and broadcast domination costs. We show that this problem is NP-hard in the strong sense, even on unweighted graphs. We then propose a decomposition strategy, which iteratively adds valid inequalities based on optimal broadcast domination solutions corresponding to the first-stage network design solutions. We demonstrate that our decomposition approach is computationally far superior to the solution of a single large-scale mixed-integer programming formulation.     

A decomposition approach for a new test-scenario in complex problem solving

Over the last years, psychological research has increasingly used computer-supported tests, especially in the analysis of complex human decision making and problem solving. The approach is to use computer-based test scenarios and to evaluate the performance of participants and correlate it to certain attributes, such as the participant's capacity to regulate emotions. However, two important questions can only be answered with the help of modern optimization methodology. The first one considers an analysis of the exact situations and decisions that led to a bad or good overall performance of test persons. The second important question concerns performance, as the choices made by humans can only be compared to one another, but not to the optimal solution, as it is unknown in general.Additionally, these test-scenarios have usually been defined on a trial-and-error basis, until certain characteristics became apparent. The more complex models become, the more likely it is that unforeseen and unwanted characteristics emerge in studies. To overcome this important problem, we propose to use mathematical optimization methodology not only as an analysis and training tool, but also in the design stage of the complex problem scenario.We present a novel test scenario, the IWR Tailorshop, with functional relations and model parameters that have been formulated based on optimization results. We also present a tailored decomposition approach to solve the resulting mixed-integer nonlinear programs with nonconvex relaxations and show some promising results of this approach.     

A hybrid metaheuristic approach to solving the UBQP problem

This paper presents a hybrid metaheuristic approach (HMA) for solving the unconstrained binary quadratic programming (UBQP) problem. By incorporating a tabu search procedure into the framework of evolutionary algorithms, the proposed approach exhibits several distinguishing features, including a diversification-based combination operator and a distance-and-quality based replacement criterion for pool updating. The proposed algorithm is able to easily obtain the best known solutions for 31 large random instances up to 7000 variables (which no previous algorithm has done) and find new best solutions for three of nine instances derived from the set-partitioning problem, demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency. Furthermore, some key elements and properties of the HMA algorithm are also analyzed.     

Optimal cost and policy for a Markovian replacement problem

We consider the computation of the optimal cost and policy associated with a two-dimensional Markov replacement problem with partial observations, for two special cases of observation quality. Relying on structural results available for the optimal policy associated with these two particular models, we show that, in both cases, the infinitehorizon, optimal discounted cost function is piecewise linear, and provide formulas for computing the cost and the policy. Several examples illustrate the usefulness of the results.This research was supported by the Air Force Office of Scientific Research Grant AFOSR-86-0029, by the National Science Foundation Grant ECS-86-17860, by the Advanced Technology Program of the State of Texas, and by the Air Force Office of Scientific Research (AFSC) Contract F49620-89-C-0044.