Operations Research Problems Research Articles

Rebalancing the assembly lines with total squared workload and total replacement distance objectives

Assembly line balancing is an important and well recognised operations research problem. The current line balance may not stay optimal, even feasible, due to the disruptions in one or more workstations. In this study, after the disruption, we aim to rebalance the assembly line by considering the trade-off between workload balancing (fairness measure) and total replacement distance for the tasks assigned to the different workstations (stability measure). We try to generate all non-dominated objective function vectors for the defined fairness and stability measures. Two algorithms are developed: exact algorithm (classical approach) and tabu search algorithm. The results of the experiments have shown that the classical approach returns exact non-dominated objective vectors with up to 40 tasks and 7 workstations in one hour, and the tabu search algorithm returns approximate non-dominated objective vectors that are very close to their exact counterparts and can solve large sized instances with up to 94 tasks and 7 workstations in less than 10 s.

Analysis of Mathematic Representation Ability of Informatics Engineering Students in Assignment Problems

Mathematics is a field of science that can improve a person's ability to think logically, critically, rationalistically, effectively, carefully and efficiently. To find out a person's ability to think logically, critically, rationalistically, effectively, carefully and efficiently in solving mathematical problems, an analysis of mathematical representations is needed. Mathematical representation is needed in solving Operations Research problems, because operations research uses a mathematical model as a problem-solving approach. This research discusses the mathematical representation ability of informatics engineering students at Nusantara University PGRI Kediri in solving assignment problems in Operations Research courses. The research method used includes descriptive research with a qualitative research approach. Data were taken directly from the research location using interviews and tests on 3 research subjects, namely students with high, medium and low abilities. The subject selection is based on the results of the dialogue between the researcher and the student's mathematics subject lecturer. Based on the results of research, high-ability students can complete multiple representations both visually, symbolically and verbally. Likewise for the mathematical representation of moderate-capable students is having multiple representations, but there are steps in solving that are missed in verbal representations. Low-ability students only provide visual and verbal representations, while symbolic representations still have errors. However, all three are still lacking in terms of the implementation of the final results

English

(max, +)-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form f(x1, …, xh) = max(aj + xj), where aj, j = 1, …, h, are real numbers. Similarly (min, +)-linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have (max, +)-linear functions of variables x on one side and (min, +)-linear functions of variables y on the other side. Such systems can be applied e.g. to operations research problems in which we need to coordinate or synchronize release and completion times of operations or departure and arrival times of passengers. A motivation example is presented and the proposed solution method is demonstrated on a small numerical example.

Study on intelligent algorithm of guide partition for emergency evacuation of a subway station

In order to improve the efficiency of emergency evacuation of subway passengers, the concept of ‘guide partition’ is put forward, and an intelligent algorithm of guide partition for emergency evacuation of subway stations is proposed according to the theory of allocation problem in operational research. First an evacuation partition optimization algorithm based on the shortest path principle and based on exit capacity for non-standard allocation problem is proposed, according to the solution of service facility allocation and site selection problem in operational research. Secondly, the passengers evacuation area is divided to partitioned evacuation zones. Combined with the advantages of cellular automata model, the evacuation simulation software of Building Exodus is used for simulation and comparison of the advantages of the proposed intelligent algorithm. Finally, the evacuation partition intelligent algorithm considering the exit capacity is applied to the Military Museum Station of Beijing subway to obtain the numbers and distribution of guiders on each floor. The results show that the proposed algorithm can help the subway station staff to better determine the number, location and influence range of each guider, and effectively improve the utilization rate of evacuation exits, reduce evacuation time and improve evacuation efficiency..

Revisiting the minimum set cover, the maximal coverage problems and a maximum benefit area selection problem to make climate‐change‐concerned conservation plans effective

Abstract Informed decisions for the selection of protected areas (PAs) are grounded in two general problems in Operations Research: the minimum set covering problem (minCost), where a set of ecological constraints are established as conservation targets and the minimum cost PAs are found, and the maximal coverage problem (maxCoverage) where the constraint is uniquely economic (i.e. a fixed budget) and the goal is to maximize the number of species having conservation targets adequately covered. We adjust minCost and maxCoverage to accommodate the dynamic effects of climate change on species’ ranges. The selection of sites is replaced by the selection of time‐ordered sequences of sites (climate change corridors), and an estimate of the persistence of each species in corridors is calculated according to the expected suitability of each site in the respective time period and the capacity of species to disperse between consecutive sites along corridors. In these problems, conservation targets are expressed as desired (and attainable) species persistence levels. We also introduce a novel problem (minShortfall) that combines minCost and maxCoverage. Unlike these two problems, minShortfall allows persistence targets to be missed and minimizes the sum of those gaps (i.e. target shortfalls), subject to a limited budget. We illustrate the three problems with a case study using climatic suitability estimates for 10 mammal species in the Iberian Peninsula under a climate change scenario until 2080. We compare solutions of the three problems with respect to species persistence and PA costs, under distinct settings of persistence targets, number of target‐fulfilled species and budgets. The solutions from different problems differed with regard to the areas to prioritize, their timings and the species whose persistence targets were fulfilled. This analysis also allowed identifying groups of species sharing corridors in optimal solutions, thus allowing important financial savings in site protection. We suggest that enhancing species persistence is an adequate approach to cope with habitat shifts due to climate change. We trust the three problems discussed can provide complementary and valuable support for planners to anticipate decisions in order that the negative effects of climate change on species’ persistence are minimized.

Operations Research Problems and Data Envelopment Analysis in Agricultural Land Processing – A Review

Research Question: This paper aims at specifying the contribution of operations research (OR) methods and techniques to agricultural land processing. Motivation: Agricultural production is performed on an agricultural land, which has to be exploited in the best possible way, given the increasing human population and the limited availability of the land. Considering the importance of this issue, a large number of research studies dealing with problems in agriculture can be found in the literature, and many of these problems are solved by OR methods and techniques. However, to our knowledge, there are no review papers that deal with this specific area, so the main motivation is to provide a detailed review of selected OR methods application in the agricultural land processing area. Idea: The core idea behind this research is to perceive a real impact of OR methods and techniques implementation in the agricultural land processing. The research is based on detailed literature review for the period 2014-2019 and performed statistics involving publication by year, publication by journal and statistics involving keywords in articles. Data: The review was conducted using online repositories of the papers published in SCI and SCIe journals with impact factors in the period from 2014-2019. Tools: Analyzed papers are divided into three groups according to the OR method applied: linear optimization problems, DEA method and other OR methods (non linear, multicriteria, mixed integer programming, dynamic programming). Papers within the groups are analyzed according to the type of problems solved. Statistical analyses of all collected data were used to get a good insight into the applications of operations research problems and data envelopment analysis in agricultural land processing. Findings: The number of published papers in this specific area has a growing trend over the observed years (with some minor decrease in 2016 and 2019 in comparison with the previous year). All of the articles are related to specific application of the given methods to solving problems in the agricultural land processing, and this is the reason for many different keywords appearing in the articles. Some very important keywords such as “operations research” or “OR” does not appear in any article as a keyword. Inclusion of such common keywords may result in a faster search in repositories of all articles. Contribution: The primary contribution of this paper is a detailed review of application of linear optimization, data envelopment analysis and other OR methods in agricultural land processing in the period 2014-2019.

A Novel Improved Data Envelopment Analysis Model Based on SBM and FDH Models

During the past decade, applying nonparametric operation research problems such as Data Envelopment Analysis(DEA) has received significant consideration among researchers. In this paper, a new DEA-based SBM-FDH model is introduced. Finally, productivity evaluation for banking systems in Malmquist Productivity Index (MPI) based on the proposed model has been compared with Slack Based Measurement (SBM) and Free Disposal Hull (FDH). The obtained results confirm the high performance of the proposed model in comparison to the other models used in this paper.

Swarm Intelligence Algorithms for Weapon-Target Assignment in a Multilayer Defense Scenario: A Comparative Study

Weapon-target assignment (WTA) is a kind of NP-complete problem in military operations research. To solve the multilayer defense WTA problems when the information about enemy’s attacking plan is symmetric to the defender, we propose four heuristic algorithms based on swarm intelligence with customizations and improvements, including ant colony optimization (ACO), binary particle swarm optimization (BPSO), integer particle swarm optimization (IPSO) and sine cosine algorithm (SCA). Our objective is to assess and compare the performance of different algorithms to determine the best algorithm for practical large-scale WTA problems. The effectiveness and performance of various algorithms are evaluated and compared by means of a benchmark problem with a small scale, the theoretical optimal solution of which is known. The four algorithms can obtain satisfactory solutions to the benchmark problem with high quality and high robustness, while IPSO is superior to BPSO, ACO and SCA with respect to the solution quality, algorithmic robustness and computational efficiency. Then, IPSO is applied to a large-scale WTA problem, and its effectiveness and performance are further assessed. We demonstrate that IPSO is capable of solving large-scale WTA problems with high efficiency, high quality and high robustness, thus meeting the critical requirements of real-time decision-making in modern warfare.

Rainbow domination numbers of generalized Petersen graphs

Abstract Domination and its variations in graphs are natural models for the location problems in operations research. In this paper, we investigate the rainbow domination number of graphs, which was introduced by Bresar, Henning and Rall. Given a graph G and a positive integer t, a t-rainbow dominating function of G is a function f from vertex set to the set of all subsets of {1, 2, ⋅⋅⋅, t} such that for any vertex v with f ( v ) = ϕ , we have ⋃ u ∈ N ( v ) f ( u ) = { 1 , 2 , ⋯ , t } . The t-rainbow domination problem is to determine the t-rainbow domination number γrt(G) of G, that is the minimum value of ∑v ∈ V(G)|f(v)|, where f runs over all t-rainbow dominating functions of G. The domination number and its variations of generalized Petersen graphs P(n, k) are widely investigated. The exact values of γr2(P(n, 1)) and γr3(P(n, 1)) are already determined in [11, 12]. In this paper, we determine the exact values of γrt(P(n, 1)) for any t ≥ 8 and t = 4 and prove that γ r t ( P ( 2 k , k ) ) = 4 k for t ≥ 6, where P(2k, k) is a special graph.

Resilience of Complex Adaptive Systems: A Pedagogical Framework for Engineering Education and Research

Abstract The discourse on resilience, currently at the forefront of research and implementation in a wide variety of fields, is confusing because of its multi-disciplinary/spatial/temporal nature. Resilience analysis is a discipline that allows the assessment and enhancement of the coping and recovery behaviors of systems when subjected to short-lived high-impact external shocks leading to partial or complete failure. This paper, meant for pedagogical teaching and research formulation, starts by providing an overview of different aspects of resilience in general and then focuses on communities and regions that are complex adaptive systems (CAS) involving multiple engineered infrastructures providing essential services to local inhabitants and adapted to available natural resources and social requirements. Next, for objective analysis and assessment, it is proposed that resilience be characterized by four different quantifiable sub-attributes. This paper then describes the standard technocentric manner in which different temporal phases during and in the aftermath of disasters are generally visualized and analyzed, and discusses how these relate to reliability and risk analyses. Subsequently, two prevalent types of frameworks are described and representative literature reviewed: (i) those that aim at improving general resilience via soft methods such as subjective means (interviews, narratives) and census data, and (ii) those that are meant to enhance specific resilience under certain threat scenarios using hard/objective methods such as data-driven analysis and performance-predictive modeling methods, akin to resource allocation problems in operations research. Finally, the need for research into an integrated framework is urged; one that could potentially combine the strengths of both approaches.

Optimal Foraging Algorithm That Incorporates Fuzzy Relative Entropy for Solving Many-Objective Permutation Flow Shop Scheduling Problems

Permutation flow shop scheduling problems (PFSPs) with many objectives are highly important scheduling problems in operations research. They have attracted substantial attention from enterprise operators and researchers in recent years. In this article, a membership function is used to connect the function values of many-objective optimization problems with a fuzzy membership degree. An approach for mapping function values to fuzzy sets is presented. Thus, the fuzzy relative entropy (FRE) can be employed in many-objective PFSPs. A many-objective PFSP model with four objectives, namely, the makespan, total tardiness, inventory holding cost, and energy consumption cost, is established. The optimal foraging algorithm (OFA) with FRE (OFA/FRE) is proposed for solving many-objective PFSPs. FRE is used as the fitness strategy of OFA. OFA/FRE is evaluated in three classification experiments and compared with five algorithms on the Walking-Fish-Group test suite, PFSP benchmark instances, and a practical PFSP for machine tool components. The results demonstrate that OFA/FRE is a promising tool for many-objective PFSP. The FRE can be used in scheduling problems and in many-objective optimization problems.

Biological Applications for Online Methods of Resource Allocation

Mathematical methods have improved our understanding of biology over time. For instance, mathematical modeling of the circadian clock has allowed us to analyze the dynamics emerging from networks of coupled circadian oscillators. Operations research, a popular research area in mathematics, is another way we can potentially apply mathematics to biology. One problem in operations research explores how to allocate resources to people who arrive on a shopping website in an online manner in a way that maximizes reward but satisfies budget constraints.

Quickest Multi-Commodity Flow Over Time with Partial Lane Reversals

Routing of more than one different commodity from specific origin nodes to the corresponding destination nodes through the arcs of an underlying network respecting the capacity constraints is one of the main problems in operational research. Among them, the quickest multi-commodity flow problem concerns with minimization of time taken to complete this process. The general multi-commodity and quickest multi-commodity flow problems are computationally hard. By flipping the orientation of lanes towards the demand nodes, the outbound lane capacities are increases. We introduce lane reversals in the quickest multi-commodity flow problem and present two approximation algorithms, one polynomial-time with the help of length-bounded flow and another FPTAS by using ∆-condensed time-expanded graph. Both algorithms prevent reversing arc capacities that are not required by the optimal flows that may be of interest for other purposes.

A New Approach to Solve Fuzzy Data Envelopment Analysis Model Based on Uncertainty

Many problems in operations research including problems from management, production planning and scheduling, transportation, location, and many others necessitate decision making in the presence of uncertainty. Therefore, many theories and methodologies have been developed to deal with optimization problems under uncertainty in general. To understand uncertain data envelopment analysis models, the process was started by introducing the definition of uncertain variables, uncertain vectors, fuzzy linear programming (FLP). Selection criteria of an incoming vector in improving uncertain linear programming is established along with its unbounded nature. This paper based on the established theoretical framework proposes an alternative linear programming model that can include some uncertainty information. Finally, input-oriented CCR model with fuzzy variables is developed and an effective approach for measuring efficiency is demonstrated with a numerical example.

Genetic Algorithm with Comprehensive Sequential Constructive Crossover for the Travelling Salesman Problem

The travelling salesman problem (TSP) is a very famous NP-hard problem in operations research as well as in computer science. To solve the problem several genetic algorithms (GAs) are developed which depend primarily on crossover operator. The crossover operators are classified as distance-based crossover operators and blind crossover operators. The distance-based crossover operators use distances between nodes to generate the offspring(s), whereas blind crossover operators are independent of any kind of information of the problem, except follow the problem’s constraints. Selecting better crossover operator can lead to successful GA. Several crossover operators are available in the literature for the TSP, but most of them are not leading good GA. In this study, we propose reverse greedy sequential constructive crossover (RGSCX) and then comprehensive sequential constructive crossover (CSCX) for developing better GAs for solving the TSP. The usefulness of our proposed crossover operators is shown by comparing with some distance-based crossover operators on some TSPLIB instances. It can be concluded from the comparative study that our proposed operator CSCX is the best crossover in this study for the TSP.

Optimizing the Site Selection of Payment Stations Based on P-median Mathematical Model

Site selection is one of the classic problems in operations research. In this research, starting from a mathematical modeling example, a model was established to solve the site selection problem of 6 toll points in 52 cells. Taking the shortest distance between the residential area and the toll station as the objective function, this paper introduced 0-1 variables, established the P-median site selection model, and transformed the residents’ payment query problem into a linear programming problem. The Lingo software was used to solve the problem of positioning the 6 points as 1, 6, 14, 26, 28 and 36. This paper successfully applies the site selection model to the site selection of toll station, which has certain reference value to the site selection in real life

Sequencing grey games

The job scheduling problem is a notoriously difficult problem in combinatorial optimization and Operational Research. In this study, we handle the job scheduling problem by using a cooperative game theoretical approach. In the sequel, sequencing situations arising grom grey uncertainty are considered. Cooperative grey game theory is applied to analyze these situations. Further, grey sequencing games are constructed and grey equal gain splitting (GEGS) rule is introduced. It is shown that cooperative grey games are convex. An application is given based on Priority Based Scheduling Algorithm. The paper ends with a conclusion.

Location selection of emergency supplies repositories for emergency logistics management: A variable weighted algorithm

With the development of the city, the number of establishments that are proposed or under construction is increasing year by year, and if they are industries that handle flammable, explosive, toxic, harmful, and dangerous substances, the public safety will face great threats, which will bring great challenges to emergency rescue work. Therefore, providing reasonable solutions to the problem of location selection of emergency supplies repositories are necessary for improving the emergency response efficiency in chemical industrial parks. A mathematical model for location selection of emergency supplies repositories in emergency logistics management are presented considering more actual factors. The optimization objectives of the model are to minimize total transport length and cost. And then a Variable Weighted Algorithm is designed to solve the model, where an auxiliary function was constructed with different methods of building weighting factors based on the theory and method of solving multi-objective optimization problems in operational research. Simulation results show the effectiveness and feasibility of the models and algorithms presented in this paper.

An effective artificial fish swarm optimization algorithm for two-sided assembly line balancing problems

Two-sided assembly lines are often used in assembly of large-sized products, such as automobiles, buses and trucks. Compared to the traditional one-sided assembly line, two-sided assembly line has advantages of shorter line and higher utilization of fixture. However, normal balancing method is not applicable to solve the two-sided assembly line balancing problem since the constraint conditions become more complicated. On the other hand, artificial fish swarm algorithm is a relatively new member of swarm intelligence based on swarm behaviors that were inspired from social behaviors of fish swarm in nature. As a typical application of behaviorism in artificial intelligence, artificial fish swarm algorithm can search for the global optimum. So it is a good candidate for developing new search algorithm for solving optimization problems in operational research. In this research, an effective discrete artificial fish swarm algorithm is developed to solve the cost-oriented assembly line balancing problems which aims to minimize the construction cost and at the same time minimize the number of mate-station. Through extensive computational experiments, the performance of the proposed artificial fish swarm algorithm is examined. The experimental results validate the effectiveness and efficiency of the proposed method.

Optimal spatial data matching for conflation: A network flow‐based approach

AbstractSpatial data conflation involves the matching and merging of counterpart features in multiple datasets. It has applications in practical spatial analysis in a variety of fields. Conceptually, the feature‐matching problem can be viewed as an optimization problem of seeking a match plan that minimizes the total discrepancy between datasets. In this article, we propose a powerful yet efficient optimization model for feature matching based on the classic network flow problem in operations research. We begin with a review of the existing optimization‐based methods and point out limitations of current models. We then demonstrate how to utilize the structure of the network‐flow model to approach the feature‐matching problem, as well as the important factors for designing optimization‐based conflation models. The proposed model can be solved by general linear programming solvers or network flow solvers. Due to the network flow formulation we adopt, the proposed model can be solved in polynomial time. Computational experiments show that the proposed model significantly outperforms existing optimization‐based conflation models. We conclude with a summary of findings and point out directions of future research.