A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

In this paper, we propose the THESEUS method, a new approach based on fuzzy outranking relations to multi-criteria sorting problems. Compared with other outranking-based methods, THESEUS is inspired by another view of multi-criteria classification problems. It utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined. This way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects. The appropriate assignment is determined by solving a simple selection problem.The capacity of a reference set for making appropriate assignments is related to a good characterization of the categories. A single reference action characterizing a category may be insufficient to achieve well-determined assignments. In this paper, the reference set capacity to perform appropriate assignments is characterized by some new concepts. This capacity may be increased when more objects are added to the reference set. THESEUS is a method for handling the preference information contained in such larger reference sets.     

A different perspective of the teaching philosophy of RL Moore

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to focus on using student participation toward the goal of the conveyance of mathematical knowledge rather than on Dr Moore's goal of teaching students to think. This article proposes that undergraduates would be better served if they took at least one course using Dr Moore's original method and his original goal.     

Combined analysis of unique and repetitive events in quantitative risk assessment

For risk assessment to be a relevant tool in the study of any type of system or activity, it needs to be based on a framework that allows for jointly analyzing both unique and repetitive events. Separately, unique events may be handled by predictive probability assignments on the events, and repetitive events with unknown/uncertain frequencies are typically handled by the probability of frequency (or Bayesian) approach. Regardless of the nature of the events involved, there may be a problem with imprecision in the probability assignments. Several uncertainty representations with the interpretation of lower and upper probability have been developed for reflecting such imprecision. In particular, several methods exist for jointly propagating precise and imprecise probabilistic input in the probability of frequency setting. In the present position paper we outline a framework for the combined analysis of unique and repetitive events in quantitative risk assessment using both precise and imprecise probability. In particular, we extend an existing method for jointly propagating probabilistic and possibilistic input by relaxing the assumption that all events involved have frequentist probabilities; instead we assume that frequentist probabilities may be introduced for some but not all events involved, i.e. some events are assumed to be unique and require predictive – possibly imprecise – probabilistic assignments, i.e. subjective probability assignments on the unique events without introducing underlying frequentist probabilities for these. A numerical example related to environmental risk assessment of the drilling of an oil well is included to illustrate the application of the resulting method.     

Computational aspects of assigning agents to a line

We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. We introduce a general approach to compute aggregate gap-minimizing assignments, as well as gap-egalitarian assignments. The approach relies on an algorithm which is shown to be faster than general purpose algorithms for the assignment problem. We also extend the approach to probabilistic assignments and explore the computational features of existing, as well as new, methods for this setting.     

The efficacy of exclusive territory assignments to delivery vehicle drivers

A supporting logic for having a vehicle driver exclusively assigned to serve the same territory on every delivery trip is the deepening of the driver’s knowledge of the territory and the customers therein. This contributes to the driver’s proficiency in serving that territory. However, in situations of randomness in day-to-day customer demands, the choice of exclusive territory assignments entails the sacrifice of sub-optimal route configuration. This study quantifies the extent of that sacrifice in order to depict the cost implications of exclusive territory assignments vis-à-vis tactics that keep pace with day-to-day demand fluctuations by allowing for flexibility in the assignments. The study’s analysis of exclusive territory assignments covers those that involve territory sharing among a team of drivers.     

An Interdisciplinary Approach to Science,Mathematics, and Reading: Learning as Children Learn

A project was designed to implement an integrated curriculum in mathematics, science, and reading by promoting the professional growth of K-4 in-service teachers through a 6-hour graduate course. The course adopts a view of teachers' knowledge acquisition based on constructivism, a perspective currently more accepted for elementary children than for teachers. The effectiveness of the project in the Ist year was evaluated in part by employing content examinations, portfolios, journals, questionnaires, and course assignments. The findings suggest implications for teacher educators, program administrators, teachers in K-4, and the children served by the educational system.     

A generalized Weiszfeld method for the multi-facility location problem

An iterative method is proposed for the K facilities location problem. The problem is relaxed using probabilistic assignments, depending on the distances to the facilities. The probabilities, that decompose the problem into K single-facility location problems, are updated at each iteration together with the facility locations. The proposed method is a natural generalization of the Weiszfeld method to several facilities.     

A pseudo-Bayesian model in financial decision making with implications to market volatility,under- and overreaction

This paper develops a model of weight assignments using a pseudo-Bayesian approach that reflects investors’ behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors’ conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors’ behavioral biases. The seriousness of an anomaly can be quantitatively assessed by investigating into its dependency on weights. New results other than the short-run underreaction and long-run overreaction can be derived and new hypotheses can be formed.     

A heuristic approach for airport gate assignments for stochastic flight delays

To make good flight to gate assignments, not only do all the relevant constraints have to be considered, but stochastic flight delays that occur in actual operations also have to be taken into account. In past research, airport gate assignments and stochastic disturbances have often been handled in the planning and the real-time stages separately, meaning that the interrelationship between these stages, as affected by such delays, has been neglected. In this research, we develop a heuristic approach embedded in a framework designed to help the airport authorities make airport gate assignments that are sensitive to stochastic flight delays. The framework includes three components, a stochastic gate assignment model, a real-time assignment rule, and two penalty adjustment methods. The test results are based on data supplied by a Taiwan international airport, and show that the proposed framework performs better than the current manual assignment process and the traditional deterministic model.     

Analysis of the effectiveness of the theseus multi-criteria sorting method: theoretical remarks and experimental evidence

The effectiveness of the THESEUS multi-criteria sorting method is characterized, here, by (i) its capacity for suggesting precise and appropriate assignments; (ii) the probability of suggesting imprecise assignments; and (iii) the probability of suggesting incorrect assignments. We study how these important features are influenced by the number of criteria and categories, the cardinality of the reference set and the level of decision-maker consistency. We present a theoretical characterization and a wide range of experimental results that confirm and complement the formal analysis. The proposed way of analyzing effectiveness may be applied to other multi-criteria sorting methods.     

DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality

In this paper, we present a new preference disaggregation method for multiple criteria sorting problems, called DIS-CARD. Real-life experience indicates the need of considering decision making situations in which a decision maker (DM) specifies a desired number of alternatives to be assigned to single classes or to unions of some classes. These situations require special methods for multiple criteria sorting subject to desired cardinalities of classes. DIS-CARD deals with such a problem, using the ordinal regression approach to construct a model of DM’s preferences from preference information provided in terms of exemplary assignments of some reference alternatives, together with the above desired cardinalities. We develop a mathematical model for incorporating such preference information via mixed integer linear programming (MILP). Then, we adapt the MILP model to two types of preference models: an additive value function and an outranking relation. Illustrative example is solved to illustrate the methodology.     

Representation stability for the cohomology of arrangements associated to root systems

From Smyth’s classification, modular compactifications of the moduli space of pointed smooth rational curves are indexed by combinatorial data, the so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a finite union of atomic extremal assignments. We discuss a connection with the birational geometry of the moduli space of stable pointed rational curves. As applications, we study three special classes of extremal assignments: smooth, toric, and invariant with respect to the symmetric group action. We identify them with three combinatorial objects: simple intersecting families, complete multipartite graphs, and special families of integer partitions, respectively.     

A Collaborative Effort to Improve University Engineering Instruction

This study focused on the instructional development of an assistant professor of environmental engineering in collaboration with science education and higher education faculty members. One semester of data was collected in the assistant professor's environmental engineering laboratory class as he endeavored to address his teaching goals. Data collection included pre and post interviews with the assistant professor, students, and program coordinator, and collection of course documents, such as the course syllabus and assignments. In addition, all of the classroom sessions were observed and videotaped, and a midsemester video stimulated‐recall interview was conducted. Results show the assistant professor made growth in the areas of questioning strategies, “think time” for students, increased class participation, and the implementation of a student‐designed field research project. Implications include that new professors can benefit from peer faculty support, and they and their students can benefit when the new professors recognize the complementary nature of research and teaching.     

The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.     

Improving heuristics for the frequency assignment problem

Lower bounds for the frequency assignment problem can be found from maximal cliques and subgraphs related to cliques. In this paper we show that for many types of problem optimal assignments can be found by a process of assigning these subgraphs first, fixing the assignment and then extending the assignment to the full problem. We demonstrate the advantages of the method for some typical examples. In particular we give the first optimal assignments of several variants of the “Philadelphia” problems. These problems have been used by several authors to assess assignment methods and lower bounds.     

An integrated approach to worker assignment,workforce flexibility acquisition,and task rotation

In a manufacturing environment, workforce flexibility can be achieved by cross-training and improved via job rotation. In firms with a flexible workforce, employees perform different tasks and functions in response to fluctuations in both product demands and labour resources. This paper presents a mathematical programming model that assigns workers to tasks, rotates workers between the tasks, and determines the training schedule. The objective is to minimize the total costs including training cost, flexibility cost, and productivity loss cost. A constructive-search heuristic is also developed to solve the proposed model. The algorithm provides good solutions in two phases: construction and improvement. At the construction phase, a solution is built using some problem-specific information. The quality of the solution is then enhanced by changing worker assignments at a particular time point during a planning horizon. Our computational results for a number of randomly generated test problems confirms the efficiently of the proposed method.     

Work allocation to stations with varying learning slopes and without buffers

In this paper, we address the problem of allocating the work elements, belonging to the products of a lot, to the stations of an assembly line so as to minimize the makespan. The lots that are processed on the assembly line are characterized by a low overall demand for each product. There is no buffer permitted in between the stations, and the line operates under learning. In particular, the stations’ learning slopes are assumed to be different. We present a procedure to determine the optimal assignments of the workload to the stations under learning variability and show that it considerably affects these assignments.     

Computing Normalizing Constants for Finite Mixture Models via Incremental Mixture Importance Sampling (IMIS)

This article proposes a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive importance sampling function which is itself a mixture, with two types of component distributions, one concentrated and one diffuse. The more concentrated type of component serves the usual purpose of an importance sampling function, sampling mostly group assignments of high posterior probability. The less concentrated type of component allows for the importance sampling function to explore the space in a controlled way to find other, unvisited assignments with high posterior probability. Components are added adaptively, one at a time, to cover areas of high posterior probability not well covered by the current importance sampling function. The method is called incremental mixture importance sampling (IMIS).

IMIS is easy to implement and to monitor for convergence. It scales easily for higher dimensional mixture distributions when a conjugate prior is specified for the mixture parameters. The simulated values on which the estimate is based are independent, which allows for straightforward estimation of standard errors. The self-monitoring aspects of the method make it easier to adjust tuning parameters in the course of estimation than standard Markov chain Monte Carlo algorithms. With only small modifications to the code, one can use the method for a wide variety of mixture distributions of different dimensions. The method performed well in simulations and in mixture problems in astronomy and medical research.     

多次分组会议安排的最佳混合方案

本文在仔细分析问题条件和要求的基础上,运用了运筹学、图论、矩阵理论和置换等方面的知识和技巧,建立了一个布尔规划模型。     

A tabu search algorithm for assigning teachers to courses

In this paper we deal with the problem of assigning teachers to courses in a secondary school. The problem appears when a timetable is to be built and the teaching assignments are not fixed. We have developed a tabu search algorithm to solve the problem. The parameters involved in the algorithm have been estimated by using multiple regression techniques. The computational results, obtained on a set of Spanish secondary schools, show that the solutions obtained by this automatic procedure can be favourably compared with the solutions proposed by the experts.