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Article
Publication date: 12 July 2023

Naiming Xie and Yuquan Wang

This paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval…

Abstract

Purpose

This paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval grey number and its related definitions, properties, and theorems, the single machine scheduling with uncertain processing time and its general forms are studied as the research object. Then several single machine scheduling models are reconstructed, and an actual production case is developed to illustrate the rationality of the research.

Design/methodology/approach

In this paper, the authors first summarize the definitions and properties related to interval grey numbers, especially the transitivity of the partial order of interval grey numbers, and give an example to illustrate that the transitivity has a positive effect on the computational time complexity of multiple interval grey number comparisons. Second, the authors redefine the general form of the single machine scheduling problem with uncertain processing time according to the definitions and theorems of interval grey numbers. The authors then reconstruct three single machine scheduling models with uncertain processing time, give the corresponding heuristic algorithms based on the interval grey numbers and prove them. Finally, the authors develop a case study based on the engine test shop of K Company, the results show that the proposed single machine scheduling models and algorithms with uncertain processing time can provide effective guidance for actual production in an uncertain environment.

Findings

The main findings of this paper are as follows: (1) summarize the definitions and theorems related to interval grey numbers and prove the transitivity of the partial order of interval grey numbers; (2) define the general form of the single machine scheduling problem with interval grey processing time; (3) reconstruct three single machine scheduling models with uncertain processing time and give the corresponding heuristic algorithms; (4) develop a case study to illustrate the rationality of the research.

Research limitations/implications

In the further research, the authors will continue to summarize more advanced general forms of grey scheduling, improve the theory of grey scheduling and prove it, and further explore the application of grey scheduling in the real world. In general, grey scheduling needs to be further combined with grey system theory to form a complete theoretical system.

Originality/value

It is a fundamental work to define the general form of single machine scheduling with uncertain processing time used the interval grey number. However, it can be seen as an important theoretical basis for the grey scheduling, and it is also beneficial to expand the application of grey system theory in real world.

Details

Grey Systems: Theory and Application, vol. 13 no. 4
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 22 October 2019

Jinshan Ma

The purpose of this paper is to investigate a novel generalised grey target decision method (GGTDM) with index and weight involving mixed attribute values.

Abstract

Purpose

The purpose of this paper is to investigate a novel generalised grey target decision method (GGTDM) with index and weight involving mixed attribute values.

Design/methodology/approach

The mixed attribute values are transformed into binary connection numbers and also comprised of two-tuple (determinacy, uncertainty) numbers to fulfil the decision-making task. The proposed method constructs the weight function to convert the mixed attribute-based weights into the certain number-based weights and determines the alternatives ranking by the comprehensive weighted Gini–Simpson indices (CWGSIs).

Findings

The result of decision making regarding the numerical example by the proposed approach is somewhat different from that obtained by the reported vector-based method. The reasons for this are threefold: the decision-making bases are different, the target centre indices are determined by different mechanisms and certain number-based weights are calculated in different ways.

Research limitations/implications

The proposed method ranks an alternative based on the Gini–Simpson index, as derived from the viewpoint of measuring the uncertainty (heterogeneity): however, the vector-based GGTDM makes a decision based on proximity, as is the case when measuring the similarities between index vectors.

Practical implications

The proposed approach is admissible to solving mixed attribute-based decision making especially for alternative indices and attribute weights containing both uncertain numbers.

Originality/value

The proposed method provides a new perspective on measuring the difference of alternatives to the target centre via the CWGSI: the CWGSI is obtained by relying on the pseudo-probabilities achieved by the ratios of the alternative indices to the target centre indices. It also builds a weight function converting the mixed attribute-based weights into certain number-based weights. This method provides a framework that should be tested in terms of its effective decision making using real data and an actual problem.

Details

Data Technologies and Applications, vol. 53 no. 4
Type: Research Article
ISSN: 2514-9288

Keywords

Article
Publication date: 22 February 2021

Jinshan Ma, Di Tian and Jinmeng Yue

This paper is to propose a novel generalized grey target decision method (GGTDM) with index and weight both containing mixed types of data.

Abstract

Purpose

This paper is to propose a novel generalized grey target decision method (GGTDM) with index and weight both containing mixed types of data.

Design/methodology/approach

The decision-making steps of the proposed approach are as follows. First, all mixed attribute values of alternatives and weights are transformed into binary connection numbers and also comprised two-tuple (determinacy, uncertainty) numbers. Then, the two-tuple (determinacy, uncertainty) numbers of target center indices are calculated. Next, the certain weights are determined by the Gini–Simpson (G–S) index-based method. Following this, the comprehensive-weighted Kullback–Leibler distances (CWKLDs) of all alternatives and the target center are obtained. Finally, the alternative ranking relies on the CWKLD considering the smaller value as the better option.

Findings

The certain weights determined by the improved Gini–Simpson index (IGSI) based method are more accurate in compared with that by the proximity-based method and the weight function method. The discrimination ability of alternatives ranking of the proposed approach is stronger than that of the compared comprehensive-weighted proximity (CWP) based method and comprehensive-weighted Gini–Simpson index (CWGSI) based method.

Research limitations/implications

The proposed method fulfills the decision-making task relying on CWKLD, which solves the uncertain measurement from the viewpoint of entropy.

Originality/value

The proposed approach adopts the IGSI to transform uncertain weights into certain ones and takes the CWKLD as the basis for the decision-making.

Details

Grey Systems: Theory and Application, vol. 12 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 23 October 2018

Pei Liang, Junhua Hu, Yongmei Liu and Xiaohong Chen

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain

Abstract

Purpose

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game.

Design/methodology/approach

First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.

Findings

The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.

Originality/value

In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

Details

Kybernetes, vol. 48 no. 8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 8 June 2012

Yong Tao, Feifei Shen and Mingli Hu

Since the present university leading cadre capability evaluations are mainly static, there is a lack of evaluation methods to address dynamic and multi‐scale‐based situations…

196

Abstract

Purpose

Since the present university leading cadre capability evaluations are mainly static, there is a lack of evaluation methods to address dynamic and multi‐scale‐based situations. Some important factors to address people's performances, such as the developing trends and potentialities are considered. The purpose of this paper is to attempt to propose a dynamic evaluation model based on multivariate delay connection number.

Design/methodology/approach

First, evaluation results of previous periods are taken into the current period and values of uncertain numbers are revised. Next, a dynamic evaluation model is built for university leading cadre. Last, a numerical example is used to prove its feasibility and effectiveness.

Findings

This paper promotes a corrected equal portion value method of uncertain numbers i1(τ), … ,in(τ) from the adjacent two periods to multi periods, and builds a dynamic evaluation model, which proved simple‐structured and easy to apply.

Practical implications

The new model is applied in the evaluation of university leading cadre, and could give a more comprehensive, dynamic, scientific analysis for evaluation by model application.

Originality/value

The paper develops a novel evaluation model based on a multivariate delay connection number, which expands traditional methods from a static situation to a dynamic and multi‐scale‐based situation.

Article
Publication date: 28 January 2014

Qiao-Xing Li, Sifeng Liu and Nai-Ang Wang

This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey…

Abstract

Purpose

This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Design/methodology/approach

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

Findings

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Practical implications

Because the matrix and the linear programming have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

Originality/value

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

Details

Grey Systems: Theory and Application, vol. 4 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 19 August 2011

Nai‐ming Xie and Si‐feng Liu

This paper aims to construct a novel grey relational model based on grey number sequences and to solve the problems which exist in traditional grey relational models, in which the…

Abstract

Purpose

This paper aims to construct a novel grey relational model based on grey number sequences and to solve the problems which exist in traditional grey relational models, in which the uncertain information cannot be described.

Design/methodology/approach

Based on the definition of traditional grey relational models, considering the limited information and knowledge, the algorithm of grey numbers was combined with the grey relational model. A general formula of grey operations and grey distance is defined. A novel grey relational model based on grey number sequences, named grey geometrical relational model, is proposed according to the definition of grey distance. Finally, several properties including parallel, multiple and order‐keeping about the proposed model are discussed.

Findings

The results show that the novel grey relational model satisfies the properties properly. It is useful to calculate the relational degree of two different grey number sequences. And the process of calculating is easier than traditional grey relational models.

Practical implications

The method exposed in the paper can be used to calculate every two sequences. The method can also be used to rank sequences of more than two.

Originality/value

The paper succeeds in constructing a novel grey relational model. The properties of novel model are studied and it is a new development in grey systems theory undoubtedly.

Details

Grey Systems: Theory and Application, vol. 1 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 10 April 2009

Qiao‐Xing Li and Si‐Feng Liu

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey…

566

Abstract

Purpose

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

Design/methodology/approach

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

Findings

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

Research limitations/implications

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

Practical implications

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Originality/value

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

Details

Kybernetes, vol. 38 no. 3/4
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 December 1994

D.J. Smith

Monte Carlo simulation is one of a number of analytical techniquesavailable to enable managers to assess the risks surrounding capitalbudgeting decisions. Although it is covered…

4731

Abstract

Monte Carlo simulation is one of a number of analytical techniques available to enable managers to assess the risks surrounding capital budgeting decisions. Although it is covered in most texts on financial management, surveys have for many years pointed to only limited use of the technique by practising managers making decisions about investment projects. Describes and analyses a simulation model utilizing facilities available to most managers. The model uses a macro to automate the simulation process and generate a frequency distribution of a project′s net present value. The model can be rapidly implemented, uses a large number of individual simulations to provide a reliable frequency distribution and aids managerial decision making by presenting managers with an easily understood perspective on the uncertainty surrounding an investment project.

Details

Management Decision, vol. 32 no. 9
Type: Research Article
ISSN: 0025-1747

Keywords

Article
Publication date: 1 October 1998

Claudio Marcus

This paper introduces the concept of the Customer Value Matrix, a customer segmentation approach that is especially well‐suited for small retail and service businesses. The…

17580

Abstract

This paper introduces the concept of the Customer Value Matrix, a customer segmentation approach that is especially well‐suited for small retail and service businesses. The discussion offers insights into the reasons for the development of this practical approach, a concrete methodology for its implementation, and strategic and tactical applications of the concept. The material is supported with strong evidence from “real‐world” examples featuring a variety of small retail and service businesses. The paper concludes with a discussion of the managerial implications for companies that manage chains of small retail or service businesses as to how they can take advantage of local relationship marketing.

Details

Journal of Consumer Marketing, vol. 15 no. 5
Type: Research Article
ISSN: 0736-3761

Keywords

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