On application of multi-criteria decision making with ordinal information in elementary education

In the Czech Republic each elementary or secondary school decides which textbook will be used for a given class and a given subject of education. As a supply of textbooks is wide, a selection of the most suitable textbook by a teacher is a typical case of multi-criteria decision making situation where an evaluation of different textbooks on selected criteria is rather ordinal in nature than cardinal: it is not possible to assign textbooks some numerical value with regard to criteria such as content, comprehensibility, adequacy to children’s age and knowledge, etc. (with the exception of textbook’s price), but textbooks can be ranked from the best to the worst by such criteria, and the best textbook can be found by a new and simple mathematical method developed for this purpose in this paper. The aim of the paper is to show how this multi-criteria decision making method with ordinal information can be used for the selection of the most appropriate textbook for elementary science education, because a right choice of a textbook plays an important role in children’s education. And we shall not forget that decisions made today influence the world tomorrow, and the World of Tomorrow is also a World of Our (well-educated) Children

On application of multi-criteria decision making with ordinal information in elementary education

In the Czech Republic each elementary or secondary school decides which textbook will be used for a given class and a given subject of education. As a supply of textbooks is wide, a selection of the most suitable textbook by a teacher is a typical case of multi-criteria decision making situation where an evaluation of different textbooks on selected criteria is rather ordinal in nature than cardinal: it is not possible to assign textbooks some numerical value with regard to criteria such as content, comprehensibility, adequacy to children’s age and knowledge, etc. (with the exception of textbook’s price), but textbooks can be ranked from the best to the worst by such criteria, and the best textbook can be found by a new and simple mathematical method developed for this purpose in this paper. The aim of the paper is to show how this multi-criteria decision making method with ordinal information can be used for the selection of the most appropriate textbook for elementary science education, because a right choice of a textbook plays an important role in children’s education. And we shall not forget that decisions made today influence the world tomorrow, and the World of Tomorrow is also a World of Our (well-educated) Children

On a preference analysis in a group decision making

The aim of the paper is to provide several quantitative measures concerning preference structure in a group decision making setting. These measures enable to assess group and individual discord, core preferences and outliers, or to find a consensus, where a consensus is defined as a preference with a minimum sum of distances to other preferences. Also, it is shown that a distance of a consensus to a median preference is upper bounded, which might reduce a search for a consensus significantly

On a preference analysis in a group decision making

The aim of the paper is to provide several quantitative measures concerning preference structure in a group decision making setting. These measures enable to assess group and individual discord, core preferences and outliers, or to find a consensus, where a consensus is defined as a preference with a minimum sum of distances to other preferences. Also, it is shown that a distance of a consensus to a median preference is upper bounded, which might reduce a search for a consensus significantly

Formulating and Solving Sustainable Stochastic Dynamic Facility Layout Problem: A Key to Sustainable Operations

Facility layout design, a NP Hard problem, is associated with the arrangement of facilities in a manufacturing shop floor, which impacts the performance, and cost of system. Efficient design of facility layout is a key to the sustainable operations in a manufacturing shop floor. An efficient layout design not only optimizes the cost and energy due to proficient handling but also increase flexibility and easy accessibility. Traditionally, it is solved using meta-heuristic techniques. But these algorithmic or procedural methodologies do not generate effective and efficient layout design from sustainable point of view, where design should consider multiple criteria such as demand fluctuations, material handling cost, accessibility, maintenance, waste and more. In this paper, to capture the sustainability in the layout design these parameters are considered, and a new Sustainable Stochastic Dynamic Facility Layout Problem (SDFLP) is formulated and solved. SDFLP is optimized for material handling cost and rearrangement cost using various meta-heuristic techniques. The pool of layouts thus generated is then analyzed by Data Envelopment Analysis (DEA) to identify efficient layouts. A novel hierarchical methodology of consensus ranking of layouts is proposed which combines the multiple attributes/criteria. Multi Attribute decision-making (MADM) Techniques such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Interpretive Ranking Process (IRP) and Analytic hierarchy process (AHP), Borda-Kendall and Integer Linear Programming based rank aggregation techniques are applied. To validate the proposed methodology data sets for facility size N=12 for time period T=5 having Gaussian demand are considered

A Hybrid Distance-Based Ideal-Seeking Consensus Ranking Model

Ordinal consensus ranking problems have received much attention in the management science literature. A problem arises in situations where a group of k decision makers (DMs) is asked to rank order n alternatives. The question is how to combine the DM rankings into one consensus ranking. Several different approaches have been suggested to aggregate DM responses into a compromise or consensus ranking; however, the similarity of consensus rankings generated by the different algorithms is largely unknown. In this paper, we propose a new hybrid distance-based ideal-seeking consensus ranking model (DCM). The proposed hybrid model combines parts of the two commonly used consensus ranking techniques of Beck and Lin (1983) and Cook and Kress (1985) into an intuitive and computationally simple model. We illustrate our method and then run a Monte Carlo simulation across a range of k and n to compare the similarity of the consensus rankings generated by our method with the best-known method of Borda and Kendall (Kendall 1962) and the two methods proposed by Beck and Lin (1983) and Cook and Kress (1985). DCM and Beck and Lin's method yielded the most similar consensus rankings, whereas the Cook-Kress method and the Borda-Kendall method yielded the least similar consensus rankings