The economic order quantity repair and waste disposal model with entropy cost

As markets have become more and more competitive, disorder has become a prevailing characteristic of modern production systems that are operating in complex, dynamic and uncertain environments. Minimizing disorder in these production systems requires stringent control measures by management, with costs that are usually hidden or difficult to estimate. Not accounting for these costs leads to less efficient production systems. This paper postulates that the behaviour of production systems very much resembles that of physical systems. Such a parallel suggests that improvements to production systems may be achievable by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). The applicability of these laws is demonstrated in a simple reverse supply chain context, where products are collected and later repaired at some rate while other products might be disposed outside according to some waste disposal rate. Numerical examples are provided.     

A secure and efficient entropy coding based on arithmetic coding

A novel security arithmetic coding scheme based on nonlinear dynamic filter (NDF) with changeable coefficients is proposed in this paper. The NDF is employed to generate the pseudorandom number generator (NDF-PRNG) and its coefficients are derived from the plaintext for higher security. During the encryption process, the mapping interval in each iteration of arithmetic coding (AC) is decided by both the plaintext and the initial values of NDF, and the data compression is also achieved with entropy optimality simultaneously. And this modification of arithmetic coding methodology which also provides security is easy to be expanded into the most international image and video standards as the last entropy coding stage without changing the existing framework. Theoretic analysis and numerical simulations both on static and adaptive model show that the proposed encryption algorithm satisfies highly security without loss of compression efficiency respect to a standard AC or computation burden.     

Estimating generalized state density of near-extreme events and its applications in analyzing stock data

This paper studies the generalized state density (GDOS) of near-historical extreme events of a set of independent and identically distributed (i.i.d.) random variables. The generalized density of states is proposed which is defined as a probability density function (p.d.f.). For the underlying distribution in the domain of attraction of the three well-known extreme value distribution families, we show the approximate form of the mean GDOS. Estimates of the mean GDOS are presented when the underlying distribution is unknown and the sample size is sufficiently large. Some simulations have been performed, which are found to agree with the theoretical results. The closing price data of the Dow-Jones industrial index are used to illustrate the obtained results.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

1.ExtendedEntropyModelEntropymodelsarewidelyusedasaforecastingtechniqueinregionalplanning,see11]and[7].Theydescribeinacertainwaythemostprobablespatialinteractionandcanbeusedtoestimateorigin-destinationtripmatrices.Butthemodelsaretoosimple,soitisdifficulttomeetpracticalrequirements.HallefjordandJo..stenl2]putforwardthegeneralizationofthestandardentropymodels.Onthebasisofthisandaccordingtothedemandofthepredictionofthetripamountfortransportationplanning,wearriveatthefollowing:wherep,μandnarepo…     

Software for the analysis of extreme events: The current state and future directions

The last few years have seen a significant increase in publicly available software specifically targeted to the analysis of extreme values. This reflects the increase in the use of extreme value methodology by the general statistical community. The software that is available for the analysis of extremes has evolved in essentially independent units, with most forming extensions of larger software environments. An inevitable consequence is that these units are spread about the statistical landscape. Scientists seeking to apply extreme value methods must spend considerable time and effort in determining whether the currently available software can be usefully applied to a given problem. We attempt to simplify this process by reviewing the current state, and suggest future approaches for software development. These suggestions aim to provide a basis for an initiative leading to the successful creation and distribution of a flexible and extensible set of tools for extreme value practitioners and researchers alike. In particular, we propose a collaborative framework for which cooperation between developers is of fundamental importance. AMS 2000 Subject Classification Primary—62P99     

A New Extreme Point Algorithm and Its Application in PSQP Algorithms for Solving Mathematical Programs with Linear Complementarity Constraints

In this paper, we present a new extreme point algorithm to solve a mathematical program with linear complementarity constraints without requiring the upper level objective function of the problem to be concave. Furthermore, we introduce this extreme point algorithm into piecewise sequential quadratic programming (PSQP) algorithms. Numerical experiments show that the new algorithm is efficient in practice.     

A note on multiple summing operators and applications

We prove a new result on multiple summing operators and, among other results and applications, we provide a new extension of Littlewood’s 4 / 3 inequality to m-linear forms.     

Forward dynamic utility functions: A new model and new results

A major obstacle in the existing models of forward dynamic utilities and investment performance evaluation is to establish the existence and uniqueness of the optimal solutions. Consequently, we present a new model of forward dynamic utilities. In doing so, we establish the existence and uniqueness of the solutions for a general (smooth) utility function, and we show that the assumptions needed for such solutions are similar to those under the backward formulation. Moreover, we provide unique viscosity solutions. We also provide discontinuous viscosity solutions. In addition, we introduce Hausdorff-continuous viscosity solutions to the portfolio model.     

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach.     

An efficient and simple model for multiple criteria supplier selection problem

Simply looking for vendors offering the lowest prices is not “efficient sourcing” any more. Selection of suppliers is a multiple criteria decision. We propose a weighted linear program for the multi-criteria supplier selection problem. In addition to mathematical formulation, this paper studies a transformation technique which enables our proposed model to be solved without an optimizer. The model for multi-criteria supplier selection problem can be easily implemented with a spreadsheet package. The model can be widely applied to practical situations and does not require the user with any optimization background.     

Restoring infrastructure systems: An integrated network design and scheduling (INDS) problem

We consider the problem of restoring services provided by infrastructure systems after an extreme event disrupts them. This research proposes a novel integrated network design and scheduling problem that models these restoration efforts. In this problem, work groups must be allocated to build nodes and arcs into a network in order to maximize the cumulative weighted flow in the network over a horizon. We develop a novel heuristic dispatching rule that selects the next set of tasks to be processed by the work groups. We further propose families of valid inequalities for an integer programming formulation of the problem, one of which specifically links the network design and scheduling decisions. Our methods are tested on realistic data sets representing the infrastructure systems of New Hanover County, North Carolina in the United States and lower Manhattan in New York City. These results indicate that our methods can be used in both real-time restoration activities and long-term scenario planning activities. Our models are also applied to explore the effects on the restoration activities of aligning them with the goals of an emergency manager and to benchmark existing restoration procedures.     

Global existence and blow-up problems for reaction diffusion model with multiple nonlinearities

In this paper, we study the following reaction diffusion model,

     

A hybrid Pareto model for asymmetric fat-tailed data: the univariate case

Density estimators that can adapt to asymmetric heavy tails are required in many applications such as finance and insurance. Extreme value theory (EVT) has developed principled methods based on asymptotic results to estimate the tails of most distributions. However, the finite sample approximation might introduce a severe bias in many cases. Moreover, the full range of the distribution is often needed, not only the tail area. On the other hand, non-parametric methods, while being powerful where data are abundant, fail to extrapolate properly in the tail area. We put forward a non-parametric density estimator that brings together the strengths of non-parametric density estimation and of EVT. A hybrid Pareto distribution that can be used in a mixture model is proposed to extend the generalized Pareto (GP) to the whole real axis. Experiments on simulated data show the following. On one hand, the mixture of hybrid Paretos converges faster in terms of log-likelihood and provides good estimates of the tail of the distributions when compared with other density estimators including the GP distribution. On the other hand, the mixture of hybrid Paretos offers an alternate way to estimate the tail index which is comparable to the one estimated with the standard GP methodology. The mixture of hybrids is also evaluated on the Danish fire insurance data set.      

PROMISE: A DSS for multiple objective stochastic linear programming problems

Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.     

Coding for a multiple access OR channel: A survey

The signature coding for M active users out of T total users over a multiple access OR channel is considered. The mathematical problem is equivalent to the M-cover-free problem of extremal set theory. We survey the upper and lower bounds on the minimal code word length n(T,M), and present some code constructions. According to the current state of the theory, for 1MT

so there is a huge gap between the upper and lower bounds. Moreover, there is no known construction approaching the upper bound.     

A generating function for sums of multiple zeta values and its applications

A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.

     

A one- and two-dimensional generalized Pareto model for a river flow

The main objective of this paper is to find a two-dimensional model for the flow of the Romaine River in Québec, Canada, which could be used to forecast the flow one day after the currently observed flow. The 2D density function proposed must be such that the correlation coefficient between the two variables can be chosen close to 1, since the river flows on two consecutive days are very highly correlated. We find that a generalized Pareto distribution provides a good fit to the data. We then propose 2D versions of this distribution. Finally, a linear combination of two such 2D distributions is used to obtain the required model. In the case of the Romaine River, the model considered works very well. It could be used with or modified for other rivers.     

A scenario-based stochastic model for supplier selection in global context with multiple buyers,currency fluctuation uncertainties,and price discounts

Suppliers network in the global context under price discounts and uncertain fluctuations of currency exchange rates have become critical in today’s world economy. We study the problem of suppliers’ selection in the presence of uncertain fluctuations of currency exchange rates and price discounts. We specifically consider a buyer with multiple sites sourcing a product from heterogeneous suppliers and address both the supplier selection and purchased quantity decision. Suppliers are located worldwide and pricing is offered in suppliers’ local currencies. Exchange rates from the local currencies of suppliers to the standard currency of the buyer are subject to uncertain fluctuations overtime. In addition, suppliers offer discounts as a function of the total quantity bought by the different customer’ sites over the time horizon irrespective of the quantity purchased by each site.     

A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP

The difficulty to solve multiple objective combinatorial optimization problems with traditional techniques has urged researchers to look for alternative, better performing approaches for them. Recently, several algorithms have been proposed which are based on the ant colony optimization metaheuristic. In this contribution, the existing algorithms of this kind are reviewed and a proposal of a taxonomy for them is presented. In addition, an empirical analysis is developed by analyzing their performance on several instances of the bi-criteria traveling salesman problem in comparison with two well-known multi-objective genetic algorithms.