A characterization of the proportional rule in multi-issue allocation situations

In multi-issue allocation situations, we have to divide a resource among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present an axiomatic characterization of the proportional rule.     

A composite run-to-the-bank rule for multi-issue allocation situations

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations. We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency.     

Distributed personnel scheduling—negotiation among scheduling agents

This paper introduces a model for Distributed Employee Timetabling Problems (DisETPs) and proposes a general architecture for solving DisETPs by using a Multi Agent System (MAS) paradigm. The architecture is composed of a set of autonomous software Scheduling Agents (SAs) that solve the Employee Timetabling Problems (ETP) for each department. Each agent has its own local ETP problem and its own goals. The Scheduling Agents must coordinate their local solution with the other agents in order to achieve a global solution for the whole organization that yields a better result with respect to the organization’s global targets. To achieve a coherent and consistent global solution, the SAs make use of a sophisticated negotiation protocol among scheduling agents that always ends in an agreement (not ensured to be optimal). The main functionalities of this protocol are agent to agent relation definition, a mechanism to approve a chain of Request for Changes and an electronic marketplace for bidding on preferred common time slots. Experimental analysis of the implemented Multi Agent System for the Soroka medical center is presented. The results of our study indicate that the proposed framework has the potential to reduce the cost of transportation for the nurses that traveling to and from the hospital.     

A problem of data mining in E-commerce

Data mining is generally defined as the science of nontrivial extraction of implicit, previously unknown, and potentially useful information from datasets. There are many websites on the Internet that provide extensive information about products and allow users post comments on various products and rate the product on a scale of 1 to 5. During the past decade, the need for intelligent algorithms for calculating and organizing extremely large sets of data has grown exponentially. In this article we investigate the extent to which a product’s average user rating can be predicted, using a manageable subset of a data set. For this we use a linearization-algorithm based prediction model and sketch how an inverse problem can be formulated to yield a smooth local volatility function of user ratings. The MAPLE programs that implement the proposed algorithm show that the method is reasonably accurate for the reconstruction of volatility of user ratings, which is useful both in accurate user predictions as well as computing sensitivity.     

A turnpike result for autonomous variational problems

In this paper we examine the structure of extremals of variational problems with continuous integrands f:R ⁿ ?×?R ⁿ ?→?R ¹ which belong to a complete metric space of functions. Our results deal with the turnpike properties of variational problems. To have this property means that the solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions.     

一种基于 Agent 劝说分类的让步模型及实现

随着电子商务的迅速发展以及Agent理论和方法的引入,出现了关于Agent自动谈判等方面的研究。 A-gent劝说由于能节约商务谈判成本,提高商务谈判效率,使谈判过程更加理性,解决谈判中出现的许多问题,受到了广泛的关注。本文结合人际劝说理论,对Agent劝说进行了分类;结合形式化理论,构建了相应的形式化表述模型和交互机制;然后将两者相结合,在让步影响幅度的基础上,构建了基于Agent劝说分类的让步模型;最后,通过算例和系统实现对模型的可行性、有效性进行了验证。     

A least commitment approach to avoiding protection violations in nonlinear planning

We suggest one alternative approach to creating a valid plan in which all temporal constraints are mutually satisfiable and all preconditions for actions hold where required. While simultaneously maintaining information on the status of protection intervals for all required preconditions in the plan, our approach avoids premature imposition of temporal constraints to correct for protection violations. At the expense of additional bookkeeping, we adopt the least commitment strategy of attempting to correct those protection violations which can be corrected in only one way. By postponing choice as much as possible, we attempt to generate a search tree with fewer nodes. Since scheduling problems which arise in our planning context are inherently intractable, our approach does not rule out the possibility of extensive search. However, it might well be a preferable mechanism for a planner which adopts a general least commitment strategy.     

Entry of online presale of fresh produce: A competitive analysis

The fresh produce market is one of the last unexplored spaces for e-commerce and has attracted the entrance of many e-commerce firms in recent years; these firms are likely to influence the traditional fresh produce sales channels. The online presale of fresh produce can lower the circulation loss rate while traditional sales channels suffer from a huge waste in the circulation. In this paper, we study the online presale model of fresh produce from a competitive perspective. We examine the pricing and order decisions of one online grocery and one physical store. By examining the physical store with and without the online grocery, we investigate the impact of the entry of an online grocery on the physical store. We first identify two pricing strategies, penetration-pricing and skimming-pricing, for the physical store and two pricing strategies for the online grocery, and then identify the conditions under which pricing equilibrium will occur. We find that the store does not necessarily alter its pricing strategy after the online grocery enters the market. When the physical store uses the penetration-pricing strategy to compete with the online grocery for Internet shoppers, it may fail to achieve that goal if the online grocery's delivery cost is low and if the Internet shoppers account for a relatively low proportion of shoppers. Alternatively, the physical store may fail if the online grocery's delivery cost is not high and if the circulation loss rate of fresh produce is high.     

A model of market power and efficiency in private electronic exchanges

We investigate how private electronic markets (PEMs) can be used as a strategic tool by a large producer to compete against a consortium of smaller producers. We model the competition between a Large Producer and Consortium of producers in a two-tier supply chain as a game and characterize the resulting Subgame Perfect Nash Equilibrium. Our results demonstrate that as the costs of inputs to production increase, there are greater returns to ownership of a private exchange. Further, we demonstrate strong welfare enhancing effects of the PEM as the production efficiency of upstream suppliers declines. Finally, from a policy standpoint we show that when upstream suppliers are highly efficient, the creation of a private electronic exchange by the Large Producer will result in significant welfare loss.     

A converse of asymptotic formulae in simultaneous approximation

In the general setting of simultaneous approximation by sequences of linear shape preserving operators, this paper contains a sort of converse result of Voronovskaya-type asymptotic formulae. As a by-product a saturation result is derived. Applications to some very well-known approximation processes are also presented.     

A Multiobjective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, nonlinearities, and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this article introduces the multiobjective genetic algorithm for variable selection (MOGA-VS) that provides the user with an optimal set of regression models for a given dataset. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision-making process is executed which allows the user to choose the most preferred model using visualizations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime Within the United States.     

A frictionless economy with suboptimizing agents

The existence of short-term monetary equilibrium in a frictionless economy with suboptimal agents is proved for any (reasonable) given interest rate. Money is distinguished from monetary assets. Separability ideas (as defined in decision theory) are applied. Two financial markets are in operation: for bank contracts (deposits and credits) and for shares.     

A two-player competitive discrete location model with simultaneous decisions

In this paper we will describe and study a competitive discrete location problem in which two decision-makers (players) will have to decide where to locate their own facilities, and customers will be assigned to the closest open facilities. We will consider the situation in which the players must decide simultaneously, unsure about the decisions of one another, and we will present the problem in a franchising environment. Most problems described in the literature consider sequential rather than simultaneous decisions. In a competitive environment, most problems consider that there is a set of known and already located facilities, and new facilities will have to be located, competing with the existing ones. In the presence of more than one decision-maker, most problems found in the literature belong to the class of Stackelberg location problems, where one decision-maker, the leader, locates first and then the other decision-maker, the follower, locates second, knowing the decisions made by the first. These types of problems are sequential and differ significantly from the problem tackled in this paper, where we explicitly consider simultaneous, non-cooperative discrete location decisions. We describe the problem and its context, propose some mathematical formulations and present an algorithmic approach that was developed to find Nash equilibria. Some computational tests were performed that allowed us to better understand some of the features of the problem and the associated Nash equilibria. Among other results, we conclude that worsening the situation of a player tends to benefit the other player, and that the inefficiency of Nash equilibria tends to increase with the level of competition.     

A simultaneous decomposition of a matrix triplet with applications

Researches on ranks of matrix expressions have posed a number of challenging questions, one of which is concerned with simultaneous decompositions of several given matrices. In this paper, we construct a simultaneous decomposition to a matrix triplet (A, B, C), where A=±A*. Through the simultaneous matrix decomposition, we derive a canonical form for the matrix expressions A?BXB*?CYC* and then solve two conjectures on the maximal and minimal possible ranks of A?BXB*?CYC* with respect to X=±X* and Y=±Y*. As an application, we derive a sufficient and necessary condition for the matrix equation BXB* + CYC*=A to have a pair of Hermitian solutions, and then give the general Hermitian solutions to the matrix equation. Copyright © 2010 John Wiley & Sons, Ltd.     

A research journey through mathematics coaching

Classroom coaching in mathematics is flexible in its definition, complex in its enactment, variable in its outcomes, and dependent on setting and circumstances. Multiple lines of inquiry are required to navigate this subjective terrain: research on coaching encompasses understanding perceptions of coaching held by coaches, teachers, and administrators, measuring the effectiveness of coaching in terms of teachers’ content knowledge and instructional practices, and exploring the nature of coaching within an educational ecosystem. This paper describes a cumulative sequence of research studies that inform current understanding of classroom coaching in mathematics, highlighting methodological decisions made at various crossroads and elaborating on the populations, methods, and instruments used to investigate coaching. A presentation of findings related to the three domains of perception, effectiveness, and nature is followed by reflections on features of coaching that pose particular challenges, questions that remain to be answered, and promising avenues of future inquiry.     

A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems

A network queuing approach is used to estimate performance measures for Autonomous Vehicle Storage and Retrieval (AVS/R) Systems using opportunistic interleaving. The model exploits the distribution of cycle types and random storage assumptions to estimate the proportion of single and dual command cycles in a system. Comparable in accuracy and computational efficiency to procedures based on standard queuing models, the proposed technique provides the additional advantage of flexibility for modeling the interfaces between a storage system and the overall material flow system in a facility. The procedure is demonstrated for a range of problem scenarios.     

A Mixed Integer Linear Programming model for simultaneous design and scheduling of flowshop plants

Models representing batch plants, especially flowshop facilities where all the products require the same processing sequence, have received much attention in the last decades. In particular, plant design and production scheduling have been addressed as disconnected problems due to the tremendous combinatory complexity associated to their simultaneous optimization. This paper develops a model for both design and scheduling of flowshop batch plants considering mixed product campaign and parallel unit duplication. Thus, a realistic formulation is attained, where industrial and commercial aspects are jointly taken into account. The proposed approach is formulated as a Mixed Integer Linear Programming model that determines the number of units per stages, unit and batch sizes and batch sequencing in each unit in order to fulfill the demand requirements at minimum investment cost. A set of novel constraints is proposed where the number of batches of each product in the campaign is an optimization variable. The approach performance is evaluated through several numerical examples.     

A note on some improvements of the simultaneous methods for determination of polynomial zeros

Applying Gauss-Seidel approach to the improvements of two simultaneous methods for finding polynomial zeros, presented in [9], two iterative methods with faster convergence are obtained. The lower bounds of the R-order of convergence for the accelerated methods are given. The improved methods and their accelerated modifications are discussed in view of the convergence order and the number of numerical operations. The considered methods are illustrated numerically in the example of an algebraic equation.     

A continuous review replenishment–disposal policy for an inventory system with autonomous supply and fixed disposal costs

In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment–disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability.