Integration and propagation of a multi-criteria decision making model in constraint programming

In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem.     

Multi-criteria optimization model integrated with AHP for evaluation and selection of COTS components

This paper deals with COTS evaluation and selection for developing a modular software system under single application development task. We consider both quantitative and qualitative criteria which fulfils the specific needs of a software system. We use analytical hierarchy process (AHP) technique for evaluating the fitness of COTS components based upon various criteria and sub-criteria thereby providing overall score of each COTS component. We develop optimization models integrating AHP and multi-criteria decision-making, which aim at: (i) maximize the total value of purchasing (TVP) subject to budget, compatibility and reliability constraints, and (ii) maximize TVP and minimize the total cost of purchase simultaneously subject to compatibility and reliability constraints. The efficiency of the models is illustrated by means of numerical illustrations.     

A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.     

A new robust mixed integer-valued model in DEA

The mixed integer linear programming (MILP) models are proposed to estimate the performance of decision making units (DMUs) including both integer and real values in data envelopment analysis (DEA). There are several studies to propose MILPs in the literature of DEA; however, they have some major shortcomings unfortunately. This study firstly mentioned the shortcomings in the previous researches and secondly suggests a robust MILP based on the Kourosh and Arash Method (KAM). The proposed linear model, integer-KAM (IKAM), has almost all capabilities of the linear KAM and significantly removes the shortcomings in the current MILPs. For instance, IKAM benchmarks and ranks all technically efficient and inefficient DMUs at the same time. It detects outliers, and estimates the production frontier significantly. A numerical example of 39 Spanish airports with four integer inputs and three outputs including two integer values and a real value also represents the validity of the statements.     

线性混合模型方差分量的检验

对于含有两个方差分量的随机效应设计阵为任意阵的线性混合模型的方差分量单边检验问题给出了精确的F检验和基于广义p值的检验.对于给出的精确的F检验给出检验存在条件以及是一致最优无偏检验的条件.通过数值模拟,基于广义p值检验的功效和犯第一类错误的概率被讨论,由模拟结果可以看出基于广义p值的检验很好地控制了犯第一类错误的概率.     

Decomposing the efficient frontier of the DEA production possibility set into a smallest number of convex polyhedrons by mixed integer programming

This paper extends the works by Olesen and Petersen (2003), Russell and Schworm (2006) and Cooper et al. (2007) about describing the efficient frontier of a production possibility set by the intersection of a finite number of closed halfspaces, in several ways. First, we decompose the efficient frontier into a smallest number of convex polyhedrons, or equivalently into a new class of efficient faces, called maximal efficient faces (MEFs). Second, we show how to identify all MEFs even if full dimensional efficient faces do not exist. Third, by applying the MEF decomposition to various real-world data sets, we demonstrate the validity of the MEF decomposition and how it can contribute to the DEA literature. Finally, we illustrate how to use the identified MEFs in practice.     

On the number of cycles in local tournaments

A digraph without loops, multiple arcs and directed cycles of length two is called a local tournament if the set of in-neighbors as well as the set of out-neighbors of every vertex induces a tournament. A vertex of a strongly connected digraph is called a non-separating vertex if its removal preserves the strong connectivity of the digraph in question.In 1990, Bang-Jensen showed that a strongly connected local tournament does not have any non-separating vertices if and only if it is a directed cycle. Guo and Volkmann extended this result in 1994. They determined the strongly connected local tournament with exactly one non-separating vertex. In the first part of this paper we characterize the class of strongly connected local tournaments with exactly two non-separating vertices.In the second part of the paper we consider the following problem: Given a strongly connected local tournament D of order n with at least n+2 arcs and an integer 3≤r≤n. How many directed cycles of length r exist in D? For tournaments this problem was treated by Moon in 1966 and Las Vergnas in 1975. A reformulation of the results of the first part shows that we have characterized the class of strongly connected local tournaments with exactly two directed cycles of length n−1. Among other things we show that D has at least n−r+1 directed cycles of length r for 4≤r≤n−1 unless it has a special structure. Moreover, we characterize the class of local tournaments with exactly n−r+1 directed cycles of length r for 4≤r≤n−1 which generalizes a result of Las Vergnas.     

Asymptotic properties of the growth curve model with covariance components

We consider a multivariate regression (growth curve) model of the form , where and are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters {B _ij} estimating simultaneously the first and the second order parameters.     

A bi-objective weighted model for improving the discrimination power in MCDEA

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.     

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.     

Optimization of design tolerances using nonlinear programming

A possible mathematical formulation of the practical problem of computer-aided design of electrical circuits (for example) and systems and engineering designs in general, subject to tolerances onk independent parameters, is proposed. An automated scheme is suggested, starting from arbitrary initial acceptable or unacceptable designs and culminating in designs which, under reasonable restrictions, are acceptable in the worst-case sense. It is proved, in particular, that, if the region of points in the parameter space for which designs are both feasible and acceptable satisfies a certain condition (less restrictive than convexity), then no more than 2 ^k points, the vertices of the tolerance region, need to be considered during optimization.This paper was presented at the 6th Annual Princeton Conference on Information Sciences and Systems, Princeton, New Jersey, 1972. The author has benefitted from practical discussions with J. F. Pinel and K. A. Roberts of Bell-Northern Research. V. K. Jha programmed some numerical examples connected with this work. C. Charalambous, P. C. Liu, and N. D. Markettos have made helpful suggestions. The work was supported by Grant No. A-7239 from the National Research Council of Canada.     

Looking at the complexity of two young children's understanding of number

This paper presents a qualitative study that investigated two third-grade students’ understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as the theoretical framework. The results of the video analysis revealed the two students’ understanding of natural numbers as being conceptually complex and existing in several different realms of the Pirie-Kieren model. Significant instances of Primitive Knowing, Image Making, Image Having, Property Noticing, Formalizing, Observing, as well as how the children's understanding existed beyond “Don’t Need” Boundaries are identified and examined in detail. Other features of the model — Structuring, Inventising, Folding Back, and Connected Understanding - are also explained and possible examples illustrating these kinds of mathematical thinking in relation to the two children's understanding of number are offered.     

Order acceptance/rejection policies in determining the sequence in mixed model assembly lines

This study presents a decision support system for order acceptance/rejection in a Make-to-Order production environment with the mixed model assembly line approach. Indeed, variety of orders is the parameter under investigation herein. When the company does not have sufficient capacity or the required resources to accept the entirety of all new arrival orders, the following steps are proposed: At first, the customers are prioritized based on their corresponding profit values (at present and in the future) whereas other orders are rejected by the top manager along with some undesirable ones. Then, prices and delivery dates of the non-rejected orders are determined via a mathematical programming model. Quality levels are also reported to the customers based upon which they are allowed to select their desired blend of main components. Afterwards, in the case of customer’s lack of satisfaction with the offered price and due date, further negotiation is proposed. Finally, if the negotiation leads to an agreement, the order is accepted and added to the production schedule of the shop floor. The schedule of accepted orders is performed based on minimizing the work overload. The present study presumes that the processing times of the tasks are affected by both learning effect and deterioration of the jobs, simultaneously. In the last section of the study afoot, numerical experiments as well as the corresponding methodology are presented in order to solve the models. Moreover, a simulated annealing algorithm is utilized to solve the problem in a large scale with little computational time. Numerical experiments confirm that the simulated annealing algorithm tends to yield rather fine results with little discrepancy compared to those of the exact algorithm in small and medium size.     

Harvest planning in the Brazilian sugar cane industry via mixed integer programming

This work addresses harvest planning problems that arise in the production of sugar and alcohol from sugar cane in Brazil. The planning is performed for two planning horizons, tactical and operational planning, such that the total sugar content in the harvested cane is maximized. The tactical planning comprises the entire harvest season that averages seven months. The operational planning considers a horizon from seven to thirty days. Both problems are solved by mixed integer programming. The tactical planning is well handled. The model for the operational planning extends the one for the tactical planning and is presented in detail. Valid inequalities are introduced and three techniques are proposed to speed up finding quality solutions. These include pre-processing by grouping and filtering the distance matrix between fields, hot starting with construction heuristic solutions, and dividing and sequentially solving the resulting MIP program. Experiments are run over a set of real world and artificial instances. A case study illustrates the benefits of the proposed planning.     

Fluctuations in the number of points on smooth plane curves over finite fields

In this note, we study the fluctuations in the number of points on smooth projective plane curves over a finite field Fq as q is fixed and the genus varies. More precisely, we show that these fluctuations are predicted by a natural probabilistic model, in which the points of the projective plane impose independent conditions on the curve. The main tool we use is a geometric sieving process introduced by Poonen (2004) [8].     

Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds

In this paper we establish an SIR model with a standard incidence rate and a nonlinear recovery rate, formulated to consider the impact of available resource of the public health system especially the number of hospital beds. For the three dimensional model with total population regulated by both demographics and diseases incidence, we prove that the model can undergo backward bifurcation, saddle-node bifurcation, Hopf bifurcation and cusp type of Bogdanov–Takens bifurcation of codimension 3. We present the bifurcation diagram near the cusp type of Bogdanov–Takens bifurcation point of codimension 3 and give epidemiological interpretation of the complex dynamical behaviors of endemic due to the variation of the number of hospital beds. This study suggests that maintaining enough number of hospital beds is crucial for the control of the infectious diseases.     

On the maximum number of feasible ranking sequences in multi-criteria decision making problems

In many decision problems the focus is on ranking a set of m alternatives in terms of a number, say n, of decision criteria. Given are the performance values of the alternatives for each one of the criteria and the weights of importance of the criteria. This paper demonstrates that if one assumes that the criteria weights are changeable, then the number of all possible rankings may be significantly less than the upper limit of m!. As a matter of fact, this paper demonstrates that the number of possible rankings is a function of the number of alternatives and the number of criteria. These findings are important from a sensitivity analysis point of view or when a group decision making environment is considered.