Maintenance optimization for second‐hand products following periodic imperfect preventive maintenance warranty period

The maintenance policy for a product's life cycle differs for second‐hand and new products. Although several maintenance policies for second‐hand products exist in the literature, they are rarely investigated with reference to periodic inspection and preventive maintenance action during the warranty period. In this research, we study an optimal post‐warranty maintenance policy for a second‐hand product, which was purchased at age x with a fixed‐length warranty period. During the warranty period, the product is periodically inspected and maintained preventively at a prorated cost borne by the user, while any product failure is only minimally repaired by the dealer. After the warranty expires, the product is self‐maintained by the user for a fixed‐length maintenance period and the costs incurred during this time are fully borne by the user. At the end of the maintenance period, the product is replaced with a product of the user's choice. This study is focused on the determination of an optimal length for the maintenance period after the warranty expiration. As a criterion for the optimality, we adopt the long‐run mean cost during the second‐hand product's life cycle from the user's perspective. Finally, our results are analyzed numerically for sensitive analysis of several relevant factors, assuming that the failure distribution follows a Weibull distribution.     

Optimal maintenance strategy for non‐renewing replacement–repair warranty

In this paper, we study the maintenance policy following the expiration of the non‐renewing replacement–repair warranty (NRRW). For such purposes, we first define the non‐renewing free replacement–repair warranty and the non‐renewing pro rata replacement–repair warranty. Then the maintenance model following the expiration of the NRRW is discussed from the user's point of view. As the criterion to determine the optimal maintenance strategy, we formulate the expected cost rate per unit time from the user's perspective. All system maintenance costs incurred after the warranty is expired are paid by the user. Given the cost structures during the life cycle of the system, we determine the optimal maintenance period following the expiration of the NRRW. Finally, a few numerical examples are given for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.     

基于身份的动态数字签名方案

数字签名是解决信息安全问题的重要途径,用于鉴别用户身份.随着计算机、网络的发展,安全的用户数字签名显得尤为重要.目前,现代的数字签名技术正向智能化、密码化、多因素、大容量和快速响应方向发展.结合数论中的中国剩余定理及RSA公钥体制,提出了一种基于身份的动态数字签名方案.     

An efficient code for the minimization of highly nonlinear and large residual least squares functions

A new code for solving the unconstrained least squares problem is given, in which a Quasi-NEWTON approximation to the second order term of the Hessian is added to the first order term of the GAUSS-NEWTON method and a line search based upon a quartile model is used. The new algorithm is shown numerically to be more efficient on large residual problems than the GAUSS-NEWTON method and a general purpose minimization algorithm based upon BFGS formula. The listing and the user's guide of the code is also given.     

Coevolutionary-based Mechanisms for Network Anomaly Detection

The paper presents an approach based on the principles of immune systems applied to the anomaly detection problem. Flexibility and efficiency of the anomaly detection system are achieved by building a model of the network behavior based on the self–nonself space paradigm. Covering both self and nonself spaces by hyperrectangular structures is proposed. The structures corresponding to self-space are built using a training set from this space. The hyperrectangular detectors covering nonself space are created using a niching genetic algorithm. A coevolutionary algorithm is proposed to enhance this process. The results of experiments show a high quality of intrusion detection, which outperform the quality of the recently proposed approach based on a hypersphere representation of the self-space.      

A Modeling Perspective on the Teaching and Learning of Mathematical Problem Solving

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving.     

Certificateless signature: a new security model and an improved generic construction

Certificateless cryptography involves a Key Generation Center (KGC) which issues a partial key to a user and the user also independently generates an additional public/secret key pair in such a way that the KGC who knows only the partial key but not the additional secret key is not able to do any cryptographic operation on behalf of the user; and a third party who replaces the public/secret key pair but does not know the partial key cannot do any cryptographic operation as the user either. We call this attack launched by the third party as the key replacement attack. In ACISP 2004, Yum and Lee proposed a generic construction of digital signature schemes under the framework of certificateless cryptography. In this paper, we show that their generic construction is insecure against key replacement attack. In particular, we give some concrete examples to show that the security requirements of some building blocks they specified are insufficient to support some of their security claims. We then propose a modification of their scheme and show its security in a new and simplified security model. We show that our simplified definition and adversarial model not only capture all the distinct features of certificateless signature but are also more versatile when compared with all the comparable ones. We believe that the model itself is of independent interest.A conventional certificateless signature scheme only achieves Girault’s Level 2 security. For achieving Level 3 security, that a conventional signature scheme in Public Key Infrastructure does, we propose an extension to our definition of certificateless signature scheme and introduce an additional security model for this extension. We show that our generic construction satisfies Level 3 security after some appropriate and simple modification. A preliminary version of the extended abstract of partial results appeared in ACISP 2006 [9].     

Zaremba's problem for elliptic equations in the neighborhood of a singular point or in the infinity

In the present paper the behavior of solutions of the mixed Zaremba's problem in the neighborhood of a boundary point and at infinity is studied. In part I of this paper[4] the concept of Wiener's generalized solution of Zaremba's problem was introduced and the so called Growth Lemma for the class of domains, satisfying isoperimetric condition, was proven. In part II regularity criterion for joining points of Neumann's and Dirichlet's boundary conditions is formulated. Generalized solution in unlimited domains as a limit of Zaremba's problem's solutions in a sequence of limited domains is introduced and a regularity condition allowed to obtain an analogue of Phragmen-Lindeloeff theorem for the solutions of Zaremba's problem. Main results of the present paper are formulated in terms of divergence of Wiener's type series.     

Optimal filtering of piecewise deterministic processes for source detection and separation in electric load monitoring

We wish to compute in discrete real time the best estimate for the composition of the total active power recorded at a customer's house, without any intrusion. A new solution for online characterization of the electric load is proposed. The solution is based on issues from the applied stochastic analysis of Markov processes. We specifically suggest that optimal filtering of a hybrid stochastic differential system covers entirely the detection and separation subproblems underlying the main problem.     

Vehicle routing considerations in distribution system design

In Distribution System Design, one minimizes total costs related to the number, locations and sizes of warehouses, and the assignment of warehouses to customers. The resulting system, while optimal in a strategic sense, may not be the best choice if operational aspects such as vehicle routing are also considered.We formulate a multicommodity, capacitated distribution planning model as anon-linear, mixed integer program. Distribution from factories to customers is two-staged via depots (warehouses) whose number and location must be chosen. Vehicle routes from depots to customers are established by considering the “fleet size and mix” problem, which also incorporates strategic decisions on fleet makeup and vehicle numbers of each type. This problem is solved as a generalized assignment problem, within an algorithm for the overall distribution/routing problem that is based on Benders decomposition. We furnish two version of our algorithm denoted Technique I and II. The latter is an enhaancement of the former and is employed at the user's discretion. Computer solution of test problems is discussed.     

Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming

In this paper, we present a mathematical model for cyclic and non-cyclic scheduling of 12 h shift nurses. The model exploits the fact that a nurse's schedule is made up of an alternating sequence of work-stretch and ‘off-stretch’ patterns. We introduce a concept called a stint, which is a pattern characterized by a start date, a length, a `cost' and the shifts worked. Using the stints as nodes in a network, we construct an acyclic graph on which the nurse's schedules can be defined. The resulting model is essentially a shortest-path problem with side constraints. The model is quite flexible and can accommodate a variety of constraints. With a minor modification, the network is used to define both the cyclic and non-cyclic scheduling problems. The models are illustrated on sample data from a local hospital and solved using CPLEX optimization software on an IBM RISC6000/340 workstation.     

Bayesian decision making and military command and control

We discuss firstly the problem of military decision, in the context of the more general development of ideas in the representation of decision making. Within this context, we have considered a mathematical model—Bayesian Decision—of decision making and military command. Previous work has been extended, and applied to this problem. A distribution of belief in outcome, given that a decision is made, and a Loss function—a measure of the effect of this outcome relative to a goal—are formed. The Bayes' Decision is the decision which globally minimises the resultant bimodal (or worse) Expected Loss function. The set of all minimising decisions corresponds to the surface of an elementary Catastrophe. This allows smooth parameter changes to lead to a discontinuous change in the Bayes' decision. In future work this approach will be used to help develop a number of hypotheses concerning command processes and military headquarters structure. It will also be used to help capture such command and control processes in simulation modelling of future defence capability and force structure.     

Genetic algorithms for the bus driver scheduling problem: a case study

This paper describes an application of genetic algorithms to the bus driver scheduling problem. The application of genetic algorithms extends the traditional approach of Set Covering/Set Partitioning formulations, allowing the simultaneous consideration of several complex criteria. The genetic algorithm is integrated in a DSS but can be used as a very interactive tool or a stand-alone application. It incorporates the user's knowledge in a quite natural way and produces solutions that are almost directly implemented by the transport companies in their operational planning processes. Computational results with airline and bus crew scheduling problems from real world companies are presented and discussed.     

Stress formulation for frictionless contact of an elastic-perfectly-plastic body

A mathematical model for frictionless contact of a deformable body with a rigid moving obstacle is analyzed. The Prandtl–Reuss elastic-perfectly-plastic constitutive law is used to describe the material's behavior, and contact is modeled with a unilateral condition imposed on the surface velocity. The problem is motivated by the process of the plowing of the ground. A variational formulation of the problem is derived in terms of the stresses and the existence of the unique weak solution is proven. The proof is based on arguments for differential inclusions obtained in A. Amassad, M. Shillor and M. Sofonea (2001). A quasistatic contact problem for an elastic perfectly plastic body with Tresca's friction. Nonlin. Anal., 35, 95–109. Finally, a study of the continuous dependence of the solution on the data is presented.     

An Algorithm for the Fixed-Charge Assigning Users to Sources Problem

Given a set of sources with known capacities and a set of users with known demands for a product, the objective is to minimize the cost of assigning the users to the sources. The restrictions are that each user's demand is satisfied by exactly one of the sources, and that the total amount assigned to each source does not exceed its capacity. A fixed-charge version of this problem is formulated as a set partitioning problem and solved by a column-generating branch and bound procedure. Computational results are given.     

Analysis of third-party warehousing contracts with commitments

This paper considers multi-period warehousing contracts under random space demand. A typical contract is specified by a starting space commitment plus a certain number of times at which the commitment can be further modified. Three forms of contracts are analysed: (1) there is a restriction on the range of commitment changes and the schedule for the changes is preset by the warehouser; (2) the same as form (1) but there is no restriction on the range; (3) the same as form (2) but the schedule for the changes is chosen by the user. We explore properties and algorithms for the three problems from the user's perspective. Solutions of simple form are obtained for the first two models and an efficient dynamic programming (DP) procedure is proposed for the last. A numerical comparison of the total expected leasing costs suggests that under certain demand patterns, contract forms (2) and (3) could be cost effective.     

An investigation of the behavior of simulation response surfaces

This paper is part of a research stream whose purpose is to study the effect of simulation response surface behavior on the choice of appropriate simulation optimization search technique. This paper's research lays some groundwork by examining the behavior of simulation response surfaces themselves. The point here is not to criticize existing simulation-optimization techniques (such as Response Surface Methodology (RSM). Rather, one point is to emphasize the care and precision that must be used to invoke extant procedures properly, while another is to demonstrate the need for additional methods such as nonparametric approaches. In particular, this paper examines a simple, inventory-simulation model under various experimental conditions, including some factors under a user's control, and some not. Both point and region estimates of surface characteristics are determined and graphed while such factors as number of replications, simulation run length, and demand and lead-time variances are varied. It is found, for example, that even for this simple surface such optimization techniques as first-order RSM can be inappropriate over 21–98% of the feasible region, depending on the case. Four implications are noted from the research: the care that should be exercised with existing simulation-optimization techniques; the need for a simulation-optimization starter; the importance of examining global, nonparametric-metamodeling approaches to simulation optimization; and the desirability of investigating a multi-strategy approach to optimization. The paper concludes with a call for further research investigating these suggestions.     

Dynamic Programming in Digital Communications: Viterbi Decoding to Turbo Multiuser Detection

Many important signal processing tasks in digital communications are based on integer programming problems whose raw complexity is extremely high. Such problems include the decoding of convolutional codes, channel equalization, multiuser detection, and the joint performance of these tasks. In each of these problems, the high complexity arises from the need to perform simultaneous processing on long sequences of finite-valued symbols in order to optimally detect or decode them. Fortunately, the complexity of these optimization problems can often be greatly reduced through the use of dynamic programming, which efficiently finds optimal [e.g., maximum likelihood (ML) or maximum a posteriori probability (MAP)] decisions in long sequences of symbols. This paper reviews four decades of progress in this area: the Viterbi algorithm for ML decoding of convolutional codes of the 1960s; the ML sequence detectors for channel equalization and the BCJR algorithm for MAP decoding of convolutional codes of the 1970s; the ML and MAP multiuser detectors of the 1980s; and combinations of these through the turbo processing of the 1990s.     

A comparative evaluation of interactive solution methods for multiple objective decision models

This paper describes a laboratory experiment which compares the performance from the user's point of view of four different solution methods for multiple objective decision models with continuous variables. These are the method of Zionts and Wallenius, the surrogate worth tradeoff method, the method of Steuer and Choo and a simplistic ‘naive’ solution method. The users exhibited different preferences among the different solution methods with the method of Steuer and Choo favoured overall. The results highlight a need for solution methods to accommodate the decision making characteristics of the user.     

On a certain seqence of positive linear operators and tow optimization inequalities

In this Paper the approximation of continuous functions by positive linear operators of Bernstein type is investigated. The consideered operators are constructed using a system of rational functions with prescribed matrix of real poles. A certain general problem of S Bernstein concerning a scheme of construction of a sequence of positive linear operators is discussed. The answer on the Bernstein's hypothesis is given. The optimal limiting relations for the norm of the second central moment of our sequence of operators are established.