An integer programming model for hierarchical workforce scheduling problem

In this paper, an integer programming model for the hierarchical workforce problem under the compressed workweeks is developed. The model is based on the integer programming formulation developed by Billionnet [A. Billionnet, Integer programming to schedule a hierarchical workforce with variable demands, European Journal of Operational Research 114 (1999) 105–114] for the hierarchical workforce problem. In our model, workers can be assigned to alternative shifts in a day during the course of a week, whereas all workers are assigned to one shift type in Billionnet’s model. The main idea of this paper is to use compressed workweeks in order to save worker costs. This case is also suitable for the practice. The proposed model is illustrated on the Billionnet’s example problem and the obtained results are compared with the Billionnet’s model results.     

Case Influence Analysis in Bayesian Inference

Abstract

We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Applications to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances between posterior or predictive distributions.     

Modeling subjective evaluation for fuzzy group multicriteria decision making

This paper presents a new fuzzy multicriteria decision making (MCDM) approach for evaluating decision alternatives involving subjective judgements made by a group of decision makers. A pairwise comparison process is used to help individual decision makers make comparative judgements, and a linguistic rating method is used for making absolute judgements. A hierarchical weighting method is developed to assess the weights of a large number of evaluation criteria by pairwise comparisons. To reflect the inherent imprecision of subjective judgements, individual assessments are aggregated as a group assessment using triangular fuzzy numbers. To obtain a cardinal preference value for each decision alternative, a new fuzzy MCDM algorithm is developed by extending the concept of the degree of optimality to incorporate criteria weights in the distance measurement. An empirical study of aircraft selection is presented to illustrate the effectiveness of the approach.     

A multi-criteria model for auditing a Predictive Maintenance Programme

Auditing tools can play a key role in the continuous improvement of maintenance policies, in particular to enhance predictive maintenance (PM). This paper proposes a multi-criteria model for auditing a Predictive Maintenance Programme (PMP) developed and implemented in the General Hospital of Ciudad Real (GHCR) in Spain. The model has a two-level structure, with top level auditing areas specified by second level auditing criteria on which the performance of the PMP should be appraised. This structure resulted from the analysis and discussion of an internal questionnaire to the management, technical and consulting staff of GHCR. This also guided the association of a performance scale with each criterion, describing several reference levels of accomplishment. Using the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) approach, a hierarchical additive value model was constructed, with criteria weights and value scales derived from staff judgments of comparison of different reference levels and profiles of performance. This model enables managers to measure the performance of the PMP and its added value for the hospital, not only against each audit criterion individually, but also on each area and in overall terms. Integrated in a management “tableau de bord”, the model outputs permit the identification of PMP deficiencies requiring urgent intervention and corrective measures for its continuous improvement.     

Estimation of missing judgments in AHP pairwise matrices using a neural network-based model

Selecting relevant features to make a decision and expressing the relationships between these features is not a simple task. The decision maker must precisely define the alternatives and criteria which are more important for the decision making process. The Analytic Hierarchy Process (AHP) uses hierarchical structures to facilitate this process. The comparison is realized using pairwise matrices, which are filled in according to the decision maker judgments. Subsequently, matrix consistency is tested and priorities are obtained by calculating the matrix principal eigenvector. Given an incomplete pairwise matrix, two procedures must be performed: first, it must be completed with suitable values for the missing entries and, second, the matrix must be improved until a satisfactory level of consistency is reached. Several methods are used to fill in missing entries for incomplete pairwise matrices with correct comparison values. Additionally, once pairwise matrices are complete and if comparison judgments between pairs are not consistent, some methods must be used to improve the matrix consistency and, therefore, to obtain coherent results. In this paper a model based on the Multi-Layer Perceptron (MLP) neural network is presented. Given an AHP pairwise matrix, this model is capable of completing missing values and improving the matrix consistency at the same time.     

A method for processing the unreliable expert judgments about parameters of probability distributions

A method for combining two types of judgments about an object analyzed, which are elicited from experts, is considered in the paper. It is assumed that the probability distribution of a random variable is known, but its parameters may be determined by experts. The method is based on the use of the imprecise probability theory and allows us to take into account the quality of expert judgments, heterogeneity and imprecision of information supplied by experts. An approach for computing “cautious” expert beliefs under condition that the experts are unknown is studied. Numerical examples illustrate the proposed method.     

考虑层次结构的独立董事治理多优势评价方法

针对企业治理中的独立董事治理优势评价问题,提出了一种考虑层次结构的独立董事治理多优势评价方法。该方法以竞优理论为基础,运用其中的个体优势判别方法确定层次结构下各独立董事治理的优势权重;依据确定的权重结果,逐层构建代理评价和民主评价模型,并计算不同层次的比较优势和团体优势;然后采用聚类分析方法提炼共性优势模式,获得该模式下的优势分布和结构;进一步通过求解模型确定独立董事治理的多项优势。此外,以A公司独立董事治理评价为例,证明了该方法的有效性和优越性。     

A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process

The DEAHP method for weight deviation and aggregation in the analytic hierarchy process (AHP) has been found flawed and sometimes produces counterintuitive priority vectors for inconsistent pairwise comparison matrices, which makes its application very restrictive. This paper proposes a new data envelopment analysis (DEA) method for priority determination in the AHP and extends it to the group AHP situation. In this new DEA methodology, two specially constructed DEA models that differ from the DEAHP model are used to derive the best local priorities from a pairwise comparison matrix or a group of pairwise comparison matrices no matter whether they are perfectly consistent or inconsistent. The new DEA method produces true weights for perfectly consistent pairwise comparison matrices and the best local priorities that are logical and consistent with decision makers (DMs)’ subjective judgments for inconsistent pairwise comparison matrices. In hierarchical structures, the new DEA method utilizes the simple additive weighting (SAW) method for aggregation of the best local priorities without the need of normalization. Numerical examples are examined throughout the paper to show the advantages of the new DEA methodology and its potential applications in both the AHP and group decision making.     

Power Measures and Solutions for Games Under Precedence Constraints

Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure.     

Model selection via adaptive shrinkage with t priors

We discuss a model selection procedure, the adaptive ridge selector, derived from a hierarchical Bayes argument, which results in a simple and efficient fitting algorithm. The hierarchical model utilized resembles an un-replicated variance components model and leads to weighting of the covariates. We discuss the intuition behind this type estimator and investigate its behavior as a regularized least squares procedure. While related alternatives were recently exploited to simultaneously fit and select variablses/features in regression models (Tipping in J Mach Learn Res 1:211–244, 2001; Figueiredo in IEEE Trans Pattern Anal Mach Intell 25:1150–1159, 2003), the extension presented here shows considerable improvement in model selection accuracy in several important cases. We also compare this estimator’s model selection performance to those offered by the lasso and adaptive lasso solution paths. Under randomized experimentation, we show that a fixed choice of tuning parameter leads to results in terms of model selection accuracy which are superior to the entire solution paths of lasso and adaptive lasso when the underlying model is a sparse one. We provide a robust version of the algorithm which is suitable in cases where outliers may exist.     

Alignment using genetic programming with causal trees for identification of protein functions

A hybrid evolutionary model is used to propose a hierarchical homology of protein sequences to identify protein functions systematically. The proposed model offers considerable potentials, considering the inconsistency of existing methods for predicting novel proteins. Because some novel proteins might align without meaningful conserved domains, maximizing the score of sequence alignment is not the best criterion for predicting protein functions. This work presents a decision model that can minimize the cost of making a decision for predicting protein functions using the hierarchical homologies. Particularly, the model has three characteristics: (i) it is a hybrid evolutionary model with multiple fitness functions that uses genetic programming to predict protein functions on a distantly related protein family, (ii) it incorporates modified robust point matching to accurately compare all feature points using the moment invariant and thin-plate spline theorems, and (iii) the hierarchical homologies holding up a novel protein sequence in the form of a causal tree can effectively demonstrate the relationship between proteins. This work describes the comparisons of nucleocapsid proteins from the putative polyprotein SARS virus and other coronaviruses in other hosts using the model.     

Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading

Multi-attribute decision-making is usually concerned with weighting alternatives, thereby requiring weight information for decision attributes from a decision maker. However, the assignment of an attribute’s weight is sometimes difficult, and may vary from one decision maker to another. Additionally, imprecision and vagueness may affect each judgment in the decision-making process. That is, in a real application, various statistical data may be imprecise or linguistically as well as numerically vague. Given this coexistence of random and fuzzy information, the data cannot be adequately treated by simply using the formalism of random variables. To address this problem, fuzzy random variables are introduced as an integral component of regression models. Thus, in this paper, we proposed a fuzzy random multi-attribute evaluation model with confidence intervals using expectations and variances of fuzzy random variables. The proposed model is applied to oil palm fruit grading, as the quality inspection process for fruits requires a method to ensure product quality. We include simulation results and highlight the advantage of the proposed method in handling the existence of fuzzy random information.     

基于广义回归估计的校准加权设计效应模型研究

校准是最常用的加权调整方法,然而传统加权调整设计效应模型只考虑有差异权数导致的精度损失,忽略使用辅助信息后的精度改进,因此应用于设计效应计算时存在一定的缺陷。本文在Spencer模型的基础上进行拓展,引入反映辅助变量和调查变量相关关系的广义回归估计量,构建了校准加权设计效应的一般模型。数值分析结果显示,校准加权设计效应模型的效果优于传统加权调整设计效应模型;尤其在调查变量与辅助变量高度相关的情形下,校准加权设计效应模型能够准确地估计出不等概率抽样设计和校准调整的综合效率。     

Assessing research effectiveness: a comparison of alternative nonparametric models

In this paper, we examine three alternative a posteriori weighting schemes with variable, common and restricted weights in order to assess research productivity by means of two seemingly similar nonparametric models: the Benefit-of-the-doubt and the Kao and Hung (2003) model. Our empirical results, based on different types of faculty members’ publications, show that there is more variability in the estimated effectiveness scores among alternative weighting schemes within each model rather than between models for any particular weighting scheme. In addition, we also found that the effectiveness scores from the BoD model are greater than or equal to those from the K&H model for the variable- and the restricted-weights schemes while there is no clear pattern between the BoD and the K&H effectiveness scores from the common-weights scheme.     

A DEA based procedure for the selection of subgroups

Data Envelopment Analysis (DEA) is a nonparametric technique originally conceived for efficiency analysis of a set of units. The main characteristic of DEA based procedures is endogenous determination of weighting vectors, i.e., the weighting vectors are determined as variables of the model. Nevertheless, DEA’s applications have vastly exceeded its original target. In this paper, a DEA based model for the selection of a subgroup of alternatives or units is proposed. Considering a set of alternatives, the procedure seeks to determine the group that maximizes overall efficiency. The proposed model is characterized by free selection of weights and allows the inclusion of additional information, such as agent’s preferences in terms of relative importance of the variables under consideration or interactions between alternatives. The solution is achieved by computing a mixed-integer linear programming model. Finally, the proposed model is applied to plan the deployment of filling stations in the province of Seville (Spain).     

Multi-level production scheduling for a class of flexible machining and assembly systems

A class of machining and assembly systems characterised by a flat assembly component structure, the existence of families of similar items, non-negligible setups and fast material flow between work-centres is considered. A hierarchical production scheduling framework is proposed for this class of systems. The decision problems at each level of the hierarchy are identified and formulated. The formulations constitute a sufficiently accurate reflection of reality, while at the same time leading to tractable mathematical models that can be handled by carefully chosen and adapted optimisation techniques. The models can, when combined with suitable knowledge bases form the core of an effective multi-pass, hierarchical decision support system. Possible srategies for coordinating the various decision problems at the different levels of the hierarchy are also discussed.This work was supported by the ACME Directorate of the Science and Engineering Research Council of the United Kingdom, Grant No. GR/D 51476, and was carried out in collaboration with Lucas Aerospace (Engines Division), Shaftmoor Lane, Birmingham, U.K.On leave from Warsaw University of Technology, Institute of Automatic Control, Nowowiejska 15/19, 00-665 Warszawa, Poland.     

Integrating expert weighting and multi-criteria decision making into eco-efficiency analysis: the case of US manufacturing

In this paper, the effect of weighting strategies on sustainability performance assessment is addressed. Eco-efficiency is used as the main metric for sustainability performance evaluation. An integrated input-output life cycle assessment (LCA) and multi criteria decision making (MCDM) approach is employed. The US manufacturing sectors’ LCA results are used in conjunction with the proposed MCDM framework to perform the eco-efficiency evaluation of 276 US manufacturing sectors. Five environmental impact categories are considered as the negative factors, namely: greenhouse gas emissions, energy use, water withdrawal, hazardous waste generation and toxic releases into air and the economic output of each manufacturing sector is considered to be the positive output. To study the overall impact of different weighting strategies; twenty weighting scenarios are designed. Five pairs of weights considered for the overall economic versus environmental impacts along with four specific weighting strategies based on Harvard, SAB, EPP and Equal weighting for each pair. According to the results of the statistical analysis, it is concluded that the weighing strategies applied to the overall environmental impacts and economic outputs cause statistically significant differences in the eco-efficiency scores.     

偏好信息为模糊互反判断矩阵的模糊多属性决策法

研究只有部分权重信息且决策者对方案的偏好信息以模糊互反判断矩阵形式给出的模糊多属性决策问题。提出了一种基于目标规划模型的模糊多属性决策方法。该法首先基于模糊互反判断矩阵，利用转换函数将决策信息一致化，建立了一个目标规划模型．通过求解该模型确定属性的权重，然后运用加性加权法求出各方案的模糊综合属性值，并利用已有的三角模糊数排序公式求得决策方案的排序。文章最后把该法应用于解决风险投资领域中的项目评估问题。     

Optimal sensor placement for spatial lattice structure based on three-dimensional redundancy elimination model

Spatial lattice structures are widely applied in engineering fields attributed to their superiorities in weight and reasonable stress. It is essential to select the best sensor placement layout for structural health monitoring and safety purposes, yet it is neither realistic nor efficient to place sensors in every location possible on the structure. To meet the strong requirements for optimal sensor placement in spatial lattice structure, this paper aims to investigate a combined objective function based on effective independence method and three dimensional redundancy elimination model to balance between optimal sensor placement performance and elimination in redundancy. To eliminate redundant information and resource waste caused by the clustered sensor distribution, the three-dimensional redundancy elimination model is constructed with the consideration of nearer nodes and overall sensor distribution ranges in three-dimensional cases. In addition, the combined function is constructed by giving the two component functions equal significance using weighting factors and normalization, and solved by genetic algorithm. Finally, the proposed method for spatial lattice structure is supported by three numerical examples including a simple lattice structure, a ground spatial truss structure and a space docking modular in space solar power satellite.     

Hierarchical Queue Networks with Partially Shared Servicing

The queue network studied consists of n infinite queues in parallel served by independent servers and by other servers all linked to form a hierarchical structure. The total service a unit receives depends partially on other units in service. We call this type of servicing partially shared servicing. All interarrival times as well as service times are assumed exponentially distributed. The characteristic of interest is the traffic intensity of the infinite queues. Some simple formulae are obtained. An application to modelling a disc I/O system is described. The model turns out to be useful and accurate with wide applicability.