Field Of Operations Research Research Articles

Editorial for the Special Issue: "Novel Solutions and Novel Approaches in Operational Research"

Abstract This special issue of Business Systems Research (SI of the BSR) is being co-published by the Slovenian Society INFORMATIKA – Section for Operational Research (SSI -SOR). It focuses on recent advances in Operations Research and Management Science (OR / MS), with a particular emphasis on linking OR / MS with other areas of quantitative and qualitative methods in the context of a multidisciplinary framework. The ten papers that were chosen for this Special Issue of the BSR present advancements and new techniques (methodology) in the field of Operations Research (OR), as well as their application in a variety of fields, including risk management, mathematical programming, game theory, gravity, spatial analysis, logistics, circular economy, continuous improvement, sustainability, e-commerce, forecasting, Gaussian processes, linear regression, multi-layer perceptron, and machine learning.

An Improved MOEA/D with an Auction-Based Matching Mechanism

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm.

Average Waiting Time of Customers in Single-Server Uncertain Queueing System

Uncertain queueing system is an important research object in the field of operations research, and widely exists in logistics, production, insurance and other fields. In order to further analyze the performance of the single-service uncertain queueing system, this paper derives the generalized inverse uncertainty distributions of the waiting times of customers, and provides the calculation formulas for the average waiting times of customers on this basis. Finally, this paper also provides two examples to illustrate the generalized inverse uncertainty distributions of waiting times and the calculation formulas of the average waiting times under specific uncertainty distributions.

Regression Machine Learning Models for the Short-Time Prediction of Genetic Algorithm Results in a Vehicle Routing Problem

Machine learning techniques have advanced rapidly, leading to better prediction accuracy within a short computational time. Such advancement encourages various novel applications, including in the field of operations research. This study introduces a novel way to utilize regression machine learning models to predict the objectives of vehicle routing problems that are solved using a genetic algorithm. Previous studies have generally discussed how (1) operations research methods are used independently to generate optimized solutions and (2) machine learning techniques are used independently to predict values from a given dataset. Some studies have discussed the collaborations between operations research and machine learning fields as follows: (1) using machine learning techniques to generate input data for operations research problems, (2) using operations research techniques to optimize the hyper-parameters of machine learning models, and (3) using machine learning to improve the quality of operations research algorithms. This study differs from the types of collaborative studies listed above. This study focuses on the prediction of the objective of the vehicle routing problem directly given the input and output data, without optimizing the problem using operations research algorithms. This study introduces a straightforward framework that captures the input data characteristics for the vehicle routing problem. The proposed framework is applied by generating the input and output data using the genetic algorithm and then using regression machine learning models to predict the obtained objective values. The numerical experiments show that the best models are random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation.

A Constraint Programming Approach for Discrete Time–Cost Tradeoff Problems in a Time-Constrained Activity Network

The discrete time-cost tradeoff problem (DTCTP) is a well-researched topic in the field of operations research. The majority of existing DTCTP models are based on traditional activity networks, which permit the execution of an activity as soon as all its predecessors have been completed. This assumption is reasonable, but it is important to note that there are always exceptions. The main work of this study was threefold. Firstly, we expanded the analysis of the DTCTP to encompass time-constrained activity networks (DTCTPTC), which encompassed three different types of time constraints. The first constraint was the time-window constraint, which limited the time interval during which an activity could be executed. The second constraint was the time-schedule constraint, which specified the times at which an activity could begin execution. The third constraint was the time-switch constraint, which required project activities to start at specific times and remain inactive during designated time periods. Secondly, a constraint programming (CP) model was developed for the purpose of solving the DTCTPTC. The model employed interval variables to define the activity and its potential time constraints, while CP expressions were utilized to ensure the feasibility of the solution. The objective was to identify the optimal execution mode for each activity, the optimal start times for time-scheduled activities, and the optimal work/rest patterns for time-switch activities, with the aim of minimizing the total cost of the project. Finally, the efficacy of the proposed CP model was validated through two case studies based on two illustrative projects of varying sizes. The outcomes were then compared against existing algorithms. The results demonstrated that time constraints were important factors affecting schedule optimization, and the proposed CP model had the ability to solve large-scale DTCTPTC.

A Learnheuristic Algorithm Based on Thompson Sampling for the Heterogeneous and Dynamic Team Orienteering Problem

The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to 25% better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems.

Travel Salesman Problem Using Dynamic Programming

In the fields of operations research and computer science, the traveling salesman problem (also known as TSP) is a classic algorithmic issue. One method for solving TSP is dynamic programming, which identifies the optimal path at the lowest possible cost. It starts by determining the shortest path between two points, and then it expands to identify routes to other sites. In order to solve the Travel salesman Problem, Dynamic Programming was used in this study as a a solution technique. In addition to a real-world application from AM-EXPRESS NIGERIA LIMITED, illustrative examples of travel salesman difficulties were taken into consideration and handled utilizing the dynamic programming technique. The finding's outcome showed that the least amount of money needed to provide logistical services is ₦6500, and the shortest possible paths or routes were found.

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.

A Review of Sports Analytics

Abstract: Due to the lack of review papers published in the field of operations research in sports analytics, the central aim of the authors of this paper is to conduct a bibliometric review of publications on the application of Operations research in sports analytics between 2000 and 2022. Through this bibliometric analysis, this paper aims to identify research gaps for future academicians to enable them to work on the topic. The data (130 papers) used for the paper comprises various central as well as interlinked disciplines and topics like sports scheduling, decision-making, and mathematical models used in sports. To present the data cleanly and allow the reader to visualize it, the authors have used various types of different graphs, tables, and figures. The present bibliometric review would be instrumental in helping academicians and students in identifying areas of research as well as helping tournament organizers and team managers, among others, by enumerating various areas that they can use to optimize decision-making in sports further.

Two-Stage Probe-Based Search Optimization Algorithm for the Traveling Salesman Problems

As a classical combinatorial optimization problem, the traveling salesman problem (TSP) has been extensively investigated in the fields of Artificial Intelligence and Operations Research. Due to being NP-complete, it is still rather challenging to solve both effectively and efficiently. Because of its high theoretical significance and wide practical applications, great effort has been undertaken to solve it from the point of view of intelligent search. In this paper, we propose a two-stage probe-based search optimization algorithm for solving both symmetric and asymmetric TSPs through the stages of route development and a self-escape mechanism. Specifically, in the first stage, a reasonable proportion threshold filter of potential basis probes or partial routes is set up at each step during the complete route development process. In this way, the poor basis probes with longer routes are filtered out automatically. Moreover, four local augmentation operators are further employed to improve these potential basis probes at each step. In the second stage, a self-escape mechanism or operation is further implemented on the obtained complete routes to prevent the probe-based search from being trapped in a locally optimal solution. The experimental results on a collection of benchmark TSP datasets demonstrate that our proposed algorithm is more effective than other state-of-the-art optimization algorithms. In fact, it achieves the best-known TSP benchmark solutions in many datasets, while, in certain cases, it even generates solutions that are better than the best-known TSP benchmark solutions.

Vehicle Routing Optimization Algorithms for Pharmaceutical Supply Chain: A Systematic Comparison

Abstract Nowadays, supply chain and road networks are full of complexity. Companies can differentiate themselves by offering superior customer service. Therefore, pharmaceutical distributors need to optimize route distribution for efficient and effective delivery to pharmacies, enhancing their competitiveness. In the field of operations research (OR), efficient route optimization is a significant function of the Vehicle Routing Problem (VRP) where the goal is to find the optimal distance travelled. The VRP can be solved using a range of algorithms, comprising exact methods, heuristics and meta-heuristics. This paper gives the basic concepts of some algorithms and these algorithms are compared based on the results. This study also extends its focus to the variation known as the Vehicle Routing Problem with Time Windows (VRPTW), that closely mirrors real-world scenarios, allowing for a more practical assessment of pharmaceutical distribution challenges and optimization solutions.

Incorporation of poverty principles into goal programming

This paper presents a methodology for the incorporation of poverty related concepts into the goal programming paradigm. The concepts of poverty line, absolute poverty and relative poverty are discussed in the context of their potential usage in the field of Operations Research. The synergy between goal programming and poverty lines is examined. Two additional meta-goals are proposed for inclusion in a meta-goal programming framework based around absolute and relative poverty respectively. The resulting poverty incorporating meta-goal programming model is compared against other goal programming variants over a test set of school budget allocation models. The results demonstrate how the incorporation of poverty principles allows for greater modelling flexibility in the goal programming framework. This in turn allows decision makers to avoid solutions that are below threshold levels for a subset of stakeholders in either a relative or absolute sense. Appropriate conclusions and suggestions for future research are given.

A filtering system to solve the large-scale shared autonomous vehicles Dial-a-Ride Problem

Shared autonomous vehicles are rapidly becoming one of the most popular topics in the fields of transportation and operations research. This paper studies a prospective transportation system in which shared autonomous vehicles (SAVs) providing Dial-a-Ride services in urban and rural areas must meet a large number of passenger requests (at least 105 per day). We consider those SAVs likely to replace, in the future, most of the individual vehicles inside urban areas. We address this very large-scale problem with a greedy insertion heuristic that involves a specific filtering system design in order to speed up the decision process and relies on an original network-driven encoding of the routes. Experimental results show that en-route vehicles can be drastically reduced by such systems using a fleet of SAVs of capacity 10, decreasing the vehicle number by more than 98%, compared to a situation where all travel demands would rely on personal vehicles. In addition, thanks to the filtering system, the total execution time can be reduced by almost 97% compared to the classic best-fit insertion heuristic, while maintaining the quality of the solution. This opens the way to the adaptation of our algorithms to a dynamic real-time context.

A Self-Adaptive Memetic Algorithm for Distributed Job Shop Scheduling Problem

Distributed scheduling has become a common manufacturing mode, and the distributed job scheduling problem (DJSP) has attracted more manufacturers and researchers in the field of operation research. For the distributed scheduling problem, it emphasizes the flexibility of factory assignment and determines the sequence of operation related to each machine in related factories. In this paper, a mixed-integer linear programming model for the DJSP is formulated to be optimized by an SMA. Also in this paper, a self-adaptive memetic algorithm (SMA) is proposed to obtain a near-optimal solution in a limited time for the DJSP. To strengthen the effectiveness of the SMA, an independent encoding is designed with jobs assigned to factories and the sequence of operation. In the proposed algorithm, various local search strategies related to the critical path in the critical factory are designed to enhance the quality of the solution. Moreover, the self-adaptive scheme for solution improvement is formulated to reduce the search time and avoid prematurity effectively. To demonstrate the performance of the proposed algorithm, numerical experiments are carried out on 120 different instances extended from the well-known job shop scheduling benchmarks. The proposed SMA has updated 30 instance records in 120 instances and it has obtained the 91 best records in 120 instances. According to the comparison, an SMA is a more effective algorithm that could update several records of benchmarks.

Finding a Basic Feasible Solution for Neutrosophic Linear Programming Models: Case Studies, Analysis, and Improvements


 Since the inception of operations research, linear programming has received the attention of researchers in this field due to the many areas of its use. The focus was on the methods used to find the optimal solution for linear models. The direct simplex method, with its three basic stages, begins by writing the linear model in standard form and then finding a basic solution that is improved according to the simplex steps until We get the optimal solution, but we encounter many linear models that do not give us a basic solution after we put it in a standard form, and here we need to solve a rule through which we reach the optimal solution. For these models, researchers and scholars in the field of operations research introduced the simplex method with an artificial basis, which helped to Find the optimal solution for linear models, given the importance of this method and as a complement to the previous research we presented using the concepts of neutrosophic science. In this research, we will reformulate the simplex algorithm with an artificial basis using concepts of neutrosophic science.

Estimating the International Cocaine Market: A Novel Combination of Excess Compensation and Stochastic Frontier Analysis

Abstract Although there are different ways to estimate the value of the illicit drug markets, the main issue remains that one cannot estimate the unseized or floating value of drugs at the country- and international-level markets. This study applies a novel estimation method that combines excess compensation estimation (from the financial field) and stochastic frontier analysis (from the operations research field) to estimate the value of the international cocaine market in 2019. Our estimations show that in 2019, the unseized market accounted for 32.16 % of the total market of cocaine and was smaller than the ratio of 48 % in 2007, indicating that the effectiveness of countries in disrupting the illicit cocaine market has improved. More importantly, we show that improvement in dealing with money laundering risks could also help reduce the illicit market of cocaine since illicit cocaine/drug proceeds must be laundered before they can be used by criminal organisations.

Robust data envelopment analysis with variable budgeted uncertainty

Including uncertainty in data envelopment analysis (DEA) is vital to achieving stable and reliable performance evaluations for the field of operational research as business environments are becoming increasingly volatile and unpredictable. Robust DEA models with budgeted uncertainty have been drawing particular attention in the DEA literature for modelling uncertainties, aiming to obtain robust efficiency scores in a way that guarantees the feasibility of solutions. A concern with such robust DEA models – which has been largely ignored in the literature – is that incorporating high uncertainty levels might result in too conservative efficiency measures, possibly reducing the decision support value of such information. To address this concern, this paper tackles uncertainties by employing variable budgeted uncertainty, which is a generalisation of the budgeted uncertainty. We introduce a novel robust DEA model with variable budgeted uncertainty that is less conservative than extant robust DEA models. Furthermore, we suggest a solution for specifying the probabilistic bounds for constraint violations of the uncertain parameters in robust DEA models. A comparison of the introduced robust DEA model with existing robust DEA models based on a numerical example shows an average reduction in the price of robustness by approximately 20%. Finally, the usefulness and applicability of the suggested model are demonstrated by using a large-scale data set in the context of grocery retailing.

A New Approach to Solve Transportation Problems Under Neutrosophic Environment

The transportation problem has received a lot of attention in the field of operations research. In many circumstances, transportation planners may lack clear information on supply, demand, and transportation costs. Fuzzy sets can accept incomplete information by allowing for degrees of membership, which describe the level of certainty or uncertainty associated with each parameter. Three components—truth-membership, indeterminacy-membership, and falsity-membership degrees—are added to fuzzy numbers to create neutrosophic fuzzy numbers, which enables a more complex depiction of uncertainty. In this paper, we discuss the fuzzy transportation problem in a neutrosophic environment. Here the transportation costs, demands, and supplies are represented by neutrosophic trapezoidal fuzzy numbers. The neutrosophic trapezoidal fuzzy numbers are transformed into crisp numbers by using a ranking function and providing numerical examples to show the proposed method's efficiency to get the minimum optimal cost. Finally, we have demonstrated that our proposed method produced a better optimal solution to existing approaches by comparing its results to those of the existing ones.

Optimization of bike-sharing repositioning operations: A reactive real-time approach

One of the critical issues in the operation of vehicle-sharing systems is the optimization of the fleet repositioning movements. Repositioning implies the artificial movement of vehicles from places where they accumulate to others in which they are scarce. This yields a higher vehicle availability, without over dimensioning the vehicle fleet and while increasing the vehicle utilization rates. In the particular case of bike-sharing systems, repositioning implies to deploy a fleet of small trucks or vans able to move groups of bicycles from one location to another, with the purpose of maximizing the users’ level of service while minimizing the operating agency costs. This repositioning optimization problem has been previously addressed in the operations research field through Mixed Integer Programing (MIP) and its variants, generally facing two limitations. First, its high computational cost, which prevents achieving direct solutions in realistically large systems. So, it has been necessary to develop heuristics and approximations. And second, its reliance and sensitivity to demand forecasts, with its inherent level of uncertainty. Aiming to overcome these weaknesses, this paper presents a strategy based on a real-time pairwise assignment between repositioning trucks and tasks, in order to optimize the bike-sharing repositioning operations. The proposed method is conceptually simple, less dependent on demand predictions, easily implementable in any coding language and applicable to large systems at a low computational cost. These properties make the method appealing to address the repositioning task assignment in any vehicle-sharing system. On a simulated case study, based on Bicing, the bicycle-sharing system in Barcelona, the proposed strategy has been implemented and compared to the MIP-based routing approach. Results show that the proposed real-time pairwise assignment method is able to significantly improve the performance of the repositioning operations, especially in scenarios where the demand forecast is not accurate. Being based on real-time information, the proposed strategy is flexible enough to solve unpredictable situations. So, the proposed strategy can be implemented as an alternative to MIP-based solutions, or as a complementary strategy for dynamic real-time adaptation of static long-term solutions.

A state-of-the-art review on D number (2012-2022): A scientometric analysis

D number theory is a relatively new uncertainty reasoning approach and its application has been gaining momentum due to its distinctive features and potential advantages. This theory aims to generalize Dempster-Shafer theory with two properties such that the elements in discernment frame do not require being mutually exclusive and the completeness constraint is also relaxed. Due to these properties, D number theory has found a wide application range, particularly in handling the vagueness nature of linguistic assessment.We aim to provide a systematic review of the application of D numbers since the inception in 2012 in the field of operations research and management science. By searching the term “D numbers” in the title, abstract and keywords of publications, the raw data has been collected on 30th December 2022 from Scopus and Web of Science. To ensure the quality of research, we only focus on the journal articles written in English from peer-reviewed journals with impact factor ≥1.5 located in the first or second SJR quartile. This filtering yields a final set of 72 articles from 40 international journals. The findings of this review indicate that the number of articles on D numbers has been increasing and have attracted cross-disciplinary attention. But it can be realized that there are very challenging tasks such as combination rule, integration function, belief and plausibility functions, distance function and uncertainty/reliability measure which have been far less studied and the lack of attention given to them can dramatically hinder the development of D number theory. The most popular research direction has been “decision making under uncertainty”. “Expert Systems with Applications” is the most prominent journal with most publications and the largest number of influential articles and “China” with the highest number of publications is the traditional leader in this field. Although 20 countries contribute to this study, D numbers research has not attracted widespread attention around the globe and the lack of literature from many countries with high academic influence is clear. Considering the fact that the research on D number theory is still evolving, this work has important guiding significance for the later research. The findings are expected to provide researchers with a comprehensive understanding of research trends of D numbers and promote further and deeper studies in this context.