In this article, we have presented a method for finding the approximate center of a linear programming polytope. This method provides a point near the center of a polytope in few simple and easy steps. Geometrical interpretation and some numerical examples have also been presented to demonstrate the proposed approach and comparison of quality of the center obtained by using the new method with existing methods of finding exact and approximate centers. At the end, we also presented computational results on the randomly generated polytopes to compare the quality of the center obtained by using the new method.

Syed Inayatullah

Maria Aman

Asma Rani

Hina Zaheer

Tanveer Ahmed Siddiqi

A New Technique for Determining Approximate Center of a Polytope

This paper presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multiple aspiration levels to achieve, and the parameters of supply and demand are random variables which are not predetermined. The random variables shall be assumed to follow extreme value distribution, and the demand and supply constraints will be converted from a probabilistic case to a deterministic one using a stochastic approach. A transformation method using binary variables reduces the MCMOTP into a multiobjective transportation problem (MOTP), selecting one aspiration level for each objective from multiple levels. The reduced problem can then be solved with goal programming. The novel adapted approach is significant because it enables the decision maker to handle the many objectives and complexities of real-world transportation problem in one model and find an optimal solution. Ultimately, a mixed-integer mathematical model has been formulated by utilizing GAMS software, and the optimal solution of the proposed model is obtained. A numerical example is presented to demonstrate the solution in detail.

Hadeel Al Qahtani

Ali El&#x2013;Hefnawy

Maha M. El&#x2013;Ashram

Aisha Fayomi

A Goal Programming Approach to Multichoice Multiobjective Stochastic Transportation Problems with Extreme Value Distribution

Simulated annealing is a stochastic local search method, initially introduced for global combinatorial mono-objective optimisation problems, allowing gradual convergence to a near-optimal solution. An extended version for multiobjective optimisation has been introduced to allow a construction of near-Pareto optimal solutions by means of an archive that catches nondominated solutions while exploring the feasible domain. Although simulated annealing provides a balance between the exploration and the exploitation, multiobjective optimisation problems require a special design to achieve this balance due to many factors including the number of objective functions. Accordingly, many variants of multiobjective simulated annealing have been introduced in the literature. This paper reviews the state of the art of simulated annealing algorithm with a focus upon multiobjective optimisation field.

Khalil Amine

Multiobjective Simulated Annealing: Principles and Algorithm Variants

The Pareto optimality is a widely used concept for the multicriteria decision-making problems. However, this concept has a significant drawback&#x2014;the set of Pareto optimal alternatives usually is large. Correspondingly, the problem of choosing a specific Pareto optimal alternative for the decision implementation is arising. This study proposes a new approach to select an &#x201c;appropriate&#x201d; alternative from the set of Pareto optimal alternatives. The proposed approach is based on ranking-theory methods used for ranking participants in sports tournaments. In the framework of the proposed approach, we build a special score matrix for a given multicriteria problem, which allows the use of the mentioned ranking methods and to choose the corresponding best-ranked alternative from the Pareto set as a solution of the problem. The proposed approach is particularly useful when no decision-making authority is available, or when the relative importance of various criteria has not been evaluated previously. The proposed approach is tested on an example of a materials-selection problem for a sailboat mast.

Joseph Gogodze

Ranking-Theory Methods for Solving Multicriteria Decision-Making Problems

Development of credit scoring models is important for financial institutions to identify defaulters and nondefaulters when making credit granting decisions. In recent years, artificial intelligence (AI) techniques have shown successful performance in credit scoring. Support Vector Machines and metaheuristic approaches have constantly received attention from researchers in establishing new credit models. In this paper, two AI techniques are reviewed with detailed discussions on credit scoring models built from both methods since 1997 to 2018. The main discussions are based on two main aspects which are model type with issues addressed and assessment procedures. Then, together with the compilation of past experiments results on common datasets, hybrid modelling is the state-of-the-art approach for both methods. Some possible research gaps for future research are identified.

R. Y. Goh

L. S. Lee

Credit Scoring: A Review on Support Vector Machines and Metaheuristic Approaches

Safety is paramount in the construction industry and the fixed sprinkler and water spray systems used in firefighting involve networks of pipes of various lengths. Manufacturers of such fixed firefighting systems need to either cut the existing stocks to length&#x2014;a (one-dimensional) cutting-stock problem&#x2014;or lengthen the existing stocks or leftover segments through welding, a (one-dimensional) cutting-stock problem with welding. Best industry practice safety requirements allow only one weld per length of pipe. The case of a Hungarian manufacturer of fixed firefighting systems motivates this article, which argues that the cutting-stock problem with welding (with single- or multiple-size stocks) may be converted to an equivalent cutting-stock problem (with multiple-size stocks). Readily available algorithms and software may then be used to generate an optimal cutting plan for the equivalent cutting-stock problem. Subject to certain restrictions, the optimal cutting plan for the equivalent cutting-stock problem may then be converted to cutting patterns for the original cutting-stock problem with welding.

Kolos Csaba &#xc1;goston

The Effect of Welding on the One-Dimensional Cutting-Stock Problem: The Case of Fixed Firefighting Systems in the Construction Industry

An overview of current debates and contemporary research devoted to modeling decision making processes and their facilitation directs attention to techniques based on pairwise judgments. At the core of these techniques are various judgment consistency measures which, in a sense, control the prioritization process which leads to the establishment of decision makers&#x2019; unknown preferences. If judgments expressed by decision makers were perfectly consistent (cardinally transitive), all available prioritization techniques would deliver the same solution. However, human judgments are consistently inconsistent, as it were; thus the preference estimation quality significantly varies. The scale of these variations depends, among others, on the chosen consistency measure of pairwise judgments. That is why it seems important to examine relations among various consistency measures and the preferences estimation quality. This research reveals that there are consistency measures whose performance may confuse decision makers with the quality of their ranking outcome. Thus, it introduces a measure which is directly related to the quality of the preferences estimation process. The main problem of the research is studied via Monte Carlo simulations executed in Wolfram Mathematica Software. The research results argue that although the performance of examined consistency measures deviates from the exemplary ones in relation to the estimation quality of decision makers preferences, solutions proposed in this paper can significantly improve that quality.

Paul Thaddeus Kazibudzki

An Examination of Ranking Quality for Simulated Pairwise Judgments in relation to Performance of the Selected Consistency Measure

Marta Bottero

Chiara D&#x2019;Alpaos

Alessandra Oppio

Decision-Making for Urban Planning and Regional Development

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Advances in Operations Research publishes original research and review articles contributing to the theory and methodology of operational research.

Advances in Operations Research