An approach to solve the minimum expected makespan flow-shop problem subject to breakdowns

Daily, there are multiple situations where machines or workers must execute certain jobs. During a working day it may be that some workers or machines are not available to perform their activities during some time periods. When scheduling models are used in these situations, workers or machines are simply called “machines”, and the temporal absences of availability are known as “breakdowns”. This paper considers some of these cases studying stochastic scheduling models with several machines to perform activities. Machines are specialized and models are flow-shops where breakdowns are allowed. The paper proposes a general procedure that tries to solve these problems. The proposed approach converts breakdowns scheduling problems into a finite sequence of without-breakdowns problems. Thus, we consider random variables, which measure the length of availability periods and repair times, to study availability intervals of machines. We propose partial feasible schedules in these intervals and combine them to offer a final global solution to optimize the expected makespan. Computational experiences are also reported.     

The maximum reliability location problem and α-reliablep-center problem: Derivatives of the probabilistic location set covering problem

In the last several years, the modeling of emergency vehicle location has focussed on the temporal availability of the vehicles. Vehicles are not available for service when they are engaged in earlier calls. To incorporate this dynamic aspect into facility location decisions, models have been developed which provide additional levels of coverage. In this paper, two new models are derived from the probabilistic location set covering problem. These models allow the examination of the relationships between the number of facilities being located, the reliability that a vehicle will be available, and a coverage standard. In addition, these models incorporate sectoral specific estimates of the availability of the vehicles. Solution of these models reveals that the use of sectoral estimates leads to facility locations which are distributed to a greater spatial extent over the region to be serviced.     

Probabilistic modeling of computer system availability

System availability is becoming an increasingly important factor in evaluating the behavior of commercial computer systems. This is due to the increased dependence of enterprises on continuously operating computer systems and to the emphasis on fault-tolerant designs. Thus, we expect availability modeling to be of increasing interest to computer system analysts and for performance models and availability models to be used to evaluate combined performance/availability (performability) measures. Since commercial computer systems are repairable, availability measures are of greater interest than reliability measures. Reliability measures are typically used to evaluate nonrepairable systems such as occur in military and aerospace applications. We will discuss system aspects which should be represented in an availability model; however, our main focus is a state of the art summary of analytical and numerical methods used to solve computer system availability models. We will consider both transient and steady-state availability measures and for transient measures, both expected values and distributions. We are developing a program package for system availability modeling and intend to incorporate the best solution methods.     

Generalized Markov Models of Infectious Disease Spread: A Novel Framework for Developing Dynamic Health Policies

We propose a class of mathematical models for the transmission of infectious diseases in large populations. This class of models, which generalizes the existing discrete-time Markov chain models of infectious diseases, is compatible with efficient dynamic optimization techniques to assist real-time selection and modification of public health interventions in response to evolving epidemiological situations and changing availability of information and medical resources. While retaining the strength of existing classes of mathematical models in their ability to represent the within-host natural history of disease and between-host transmission dynamics, the proposed models possess two advantages over previous models: (1) these models can be used to generate optimal dynamic health policies for controlling spreads of infectious diseases, and (2) these models are able to approximate the spread of the disease in relatively large populations with a limited state space size and computation time.     

面向多阶段任务的武器系统备件优化配置建模

资源优化配置是作战单元维修保障的关键因素.当作战单元执行单阶段任务时,讨论了部件结构为串联系统和k/n系统的任务成功概率建模问题,在此基础上,建立了k/n结构动态变化的多阶段任务系统的任务成功概率模型.在满足系统任务成功概率约束条件下,给出了防空作战单元备件携行量优化模型,并运用边际分析法进行了求解,通过示例表明了模型的正确性.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

一种基于证据推理的信息不完全的多准则决策方法

针对权系数信息不完全、准则值不确定且不完全的多准则决策问题,提出了一种基于证据推理的方法.该方法通过证据推理算法构造方案的目标函数,结合不完全信息的权系数建立非线性规划模型,使用遗传算法求解模型得到效用值的区间数,从而得到整个方案集的排序.最后以实例表明该方法的有效性和可行性.     

On the construction of component importance measures for semi-Markov systems

In this paper we consider semi-Markov reliability models of systems with discrete state space in a setup general enough to cover systems with maintenance and repair. The systems are assumed to consist of several components which can either be up or down in each state. In this framework we propose two different types of component importance measures which are based on transition rates and interval availability, respectively. For these importance measures we study both the time-dependent and the steady state situation, and express them in terms of quantities easily calculated from the building blocks of the semi-Markov process.     

Computation of availability of a real-time system using queueing theory methodology

In this paper we consider a real-time multiserver (such as machine controllers) and multichannel (such as regions and assembly lines) systems involving maintenance. Our objective is to fit these systems into the framework of queueing models and thus to justify the use of the powerful queueing theory analytical methods in the analysis of real-time systems. The main difficulty is that real-time systems by their very nature do not permit queues. To resolve this contradiction we use a dual approach in which we consider jobs as servers and servers as jobs. We adjust the traditional definition of availability for the real-time systems under consideration and show how to compute the system’s availability, when both service and maintenance times are exponentially distributed (birth-and-death process). At this stage we restrict ourselves to a worst case (maximum load regime), which is most typical in high-performance data acquisition and control (production and military) systems.     

Availability of inspected systems subject to shocks – A matrix algorithmic approach

We examine the limiting average availability of a maintained system that deteriorates due to random shock process and as a response to its usage (wear out). System’s failures are not self-announcing, hence, failures must be detected via inspection. We consider randomly occurring shocks that arrive according to a Poisson process and cumulatively damage the system. Two models are considered: in Model 1 the shock and wear out processes are independent of the external environment and in Model 2, the shocks arrival rate, the shock magnitudes and the wear out rate are governed by a random environment which evolves as a Markov process. We obtain the system’s availability for both models.     

The NATO strategic commanders' assessment of requirements for strategic sea and airlift

With the end of the Cold War and the adoption of a new NATO strategic concept, NATO nations now emphasize the use of mobile, flexible, and multinational military forces to be deployed for a myriad of crisis response operations outside the normal NATO treaty area. One critical shortfall for a number of NATO members has been the ready availability of strategic sea and airlift assets. Most NATO nations rely on the civilian transport market to provide dry cargo vessels and wide-body cargo aircraft. The two NATO strategic commands, Supreme Headquarters Allied Powers Europe (SHAPE) and Headquarter Supreme Allied Command Atlantic (SACLANT), have been assessing the requirements for sea and airlift and have proposed to nations a variety of measures to improve their movement and transport capability. SACLANT staff has been developing the operations research methods to assist in this assessment. The current paper conveys the methodology and the mathematical programming model used in this analysis, using ship, aircraft, and port availability constraints. Furthermore, the paper presents a framework of the modeling and simulation capability of the NATO commands and agencies in the movement and transportation area. Additionally, the paper provides an example of the use of simulation models in follow-up activities such as high-level seminars in which national military force planners and movement and transport staff participate. During these events, participants are provided with the results from a number of transportation simulation models, in an attempt to steer the decision making process in NATO.     

Efficient formulations for pricing under attraction demand models

We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.     

Explicit solutions of boundary-value problems for (2 + 1)-dimensional integrable systems

Two nonlinear integrable models with two space variables and one time variable, the Kadomtsev-Petviashvili equation and the two-dimensional Toda chain, are studied as well-posed boundary-value problems that can be solved by the inverse scattering method. It is shown that there exists a multitude of integrable boundary-value problems and, for these problems, various curves can be chosen as boundary contours; besides, the problems in question become problems with moving boundaries. A method for deriving explicit solutions of integrable boundary-value problems is described and its efficiency is illustrated by several examples. This allows us to interpret the integrability phenomenon of the boundary condition in the traditional sense, namely as a condition for the availability of wide classes of solutions that can be written in terms of well-known functions.     

Product forms for availability models

This paper shows and illustrates that product form expressions for the steady state distribution, as known for queueing networks, can also be extended to a class of availability models. This class allows breakdown and repair rates from one component to depend on the status of other components. Common resource capacities and repair priorities, for example, are included. Conditions for the models to have a product form are stated explicitly. This product form is shown to be insensitive to the distributions of the underlying random variables, i.e. to depend only on their means. Further it is briefly indicated how queueing for repair can be incorporated. Novel product form examples are presented of a simple series/parallel configuration, a fault tolerant database system and a multi-stage interconnection network.     

Metaheuristics for multi-mode capital-constrained project payment scheduling

This paper involves the multi-mode capital-constrained project payment scheduling problem, where the objective is to assign activity modes and payments so as to maximize the net present value (NPV) of the contractor under the constraint of capital availability. In the light of different payment patterns adopted, four optimization models are constructed using the event-based method. For the NP-hardness of the problem, metaheuristics, including tabu search and simulated annealing, are developed and compared with multi-start iterative improvement and random sampling based on a computational experiment performed on a data set generated randomly. The results indicate that the loop nested tabu search is the most promising procedure for the problem studied. Moreover, the effects of several key parameters on the contractor’s NPV are investigated and the following conclusions are drawn: The contractor’s NPV rises with the increase of the contractor’s initial capital availability, the payment number, the payment proportion, or the project deadline; the contractor has a decreasing marginal return as the contractor’s initial capital availability goes up; the contractor’s NPVs under the milestone event based payment pattern are not less than those under the other three payment patterns.     

Repairable inventory theory: Models and applications

Repairable inventory theory involves designing inventory systems for items which are repaired and returned to use rather than discarded. Such systems are composed of items which are typically less expensive to repair than to replace, and are considerably more complicated than traditional inventory systems. The typical problem is concerned with the optimal stocking of the repairable parts and the location of these stocks, given that there may be multiple locations. An added dimension to the problem is the determination of the size and location(s) of the repair capacity for these parts. Further, different performance measures may be used, such as cost, backorders, and availability. There are many complicating factors in the design of repairable inventory systems, for example, not all failed units can be repaired and put back into service, some will be condemned and have to be replaced by new procurements. Various solution approaches have been developed to solve the problem, few have been implemented in practice, and no single model has addressed all or most of the complicating factors. Recent trends in the repairable inventory environment, environmental trends and regulations, and trends in product design are calling some of the assumptions of earlier models into question. In this paper we discuss the existing body of literature on repairable inventory, examine the various models proposed and the major assumptions made in those models, and classify them according to their solution methodology, single versus multi-echelon, and exact versus approximate solutions. It is intended to aid practitioners and researchers in identifying the sources for existing methods and the suitability of those to their application, as well as identify areas for additional research.     

The Use of Corporate Planning Models: Past,Present and Future

The use of corporate planning models is widespread and will continue to expand greatly in the future. The proliferation of these models has been due to the increasing availability of computer-macro and micro-and also to management's awareness of D.S.S. (decision support systems) and M.I.S. (management information systems), which quickly enhanced the applications and practicality of modelling for all types and sizes of business. This paper provides an overview of the concept, developments and the future of corporate planning models.     

Optimal designs for weighted rational models

This paper is concerned with constructing optimal designs for rational models which are used for modeling problems in Agriculture and other disciplines. Homoscedastic and weighted models are considered. An analytical characterization of these designs is obtained as zeros of a polynomial solution of a second order differential equation.