operations research approach to problem solving

Recognize the Problem

The figure shows the situation with vague outlines because most problems are poorly defined in their original conception. Historical data describing organizational operations and performance may be present in various forms. The data may be immediately relevant to the situation or investigations may reveal the need for additional data collection.

Formulate the Problem

Construct a Model

Find a Solution

Of course, the solution provided by the computer is only a proposal. An analysis does not promise a solution but only guidance to the decision maker. Choosing a solution to implement is the responsibility of the decision maker and not the analyst. The decision maker may modify the solution to incorporate practical or intangible considerations not reflected in the model.

Establish the Procedure

Once a procedure is established (and implemented), the analyst and perhaps the decision maker are ready to tackle new problems, leaving the procedure to handle the required tasks. But what if the situation changes? An unfortunate result of many analyses is a remnant procedure designed to solve a problem that no longer exists or which places restrictions on an organization that are limiting and no longer appropriate. Therefore, it is important to establish controls that recognize a changing situation and signal the need to modify or update the solution.

Implement the Solutio n

The OR Process

There are a number of ways to to test a solution. The simplest determines whether the solution makes sense to the decision maker. Solutions obtained by quantitative studies may not be predictable but they are often not too surprising. Other testing procedures include sensitivity analysis, the use of the model under a variety of conjectured conditions including a range of parameter values, and the use of the model with historical data.

If the testing determines that the solution or model is inappropriate, the process may return to the formulation step to derive a more complex model embodying details of the problem formerly eliminated through abstractions. This may, of course, render the model intractable, and it may be necessary to conclude that an acceptable quantitative analysis is out of reach. It may also be possible to construct a less abstract model and accept less powerful solution methods. In many cases, finding a good or an acceptable solution is almost as satisfactory as obtaining an optimal one. This is particularly true when the quality of the input data is low or when important parameters cannot be specified with certainty.

Different organizations have different ways of approaching a problem, and many do not admit quantitative techniques or analysts as part of the process. It is important to note, however, that in today’s world problems do arise and decisions are made (even inaction is a decision made by default). Many problems are solved in the first step of our process, but there will be cases when complexity, variability or uncertainty suggest that further analysis is necessary. In these cases, the Operations Research process will assist problem solving and decision making.

What is Operations Research? | NC State OR

What is Operations Research?

Last Updated:  08/16/2022 and all information on this page is accurate and up-to-date

The simple answer: Operations Research (OR) is a discipline of problem-solving and decision-making that uses advanced analytical methods to help management run an effective organization. Problems are broken down, analyzed and solved in steps.

• Identify a problem
• Build a model around the real-world problem
• Use the model and data to arrive at solutions
• Test the solution and analyze its success
• Implement the solution

The technical answer: Operations research, also known as management sciences, uses scientific methodology to study systems whose design or operation requires human decision-making. OR provides the means for making the most effective systems design and operation decisions. The strength and versatility of OR stem from its diagnostic power through observation and modeling and its prescriptive power through analysis and synthesis.

OR is interdisciplinary, drawing on and contributing to the techniques from many fields, including mathematics and mathematical sciences, engineering, economics and the physical sciences. OR practitioners have successfully solved a wide variety of real-world problems, varying from the optimal design of telecommunications networks in uncertain demand to the planning for an optimal deployment of armed forces during wartime. Many new applications originate from current societal energy production and distribution problems, environmental pollution control, health maintenance, and software production.

The CEO of the Future is an Engineer

Studies show that three times as many S&P 500 CEOs hold undergraduate degrees in engineering rather than business administration. Operation research practitioners lead that trend among the next generation of engineers and scientists. They are tomorrow’s business leaders.

Operations Research Offers Workplace Freedom

Operations research practitioners have offices and work in the settings they are trying to improve. When collecting data, they may observe the staff working in a restaurant or watch workers assembling parts in a factory. When solving problems, they are in an office analyzing the data they or others have collected.

The World Needs more Operations Research

As companies battle in the competitive world market, the need for operations research practitioners grows. Why? They are the engineers trained to be productivity and quality improvement specialists. They share the common goal of saving companies money and increasing performance.

Operations Research is all about Options

Operations research practitioners work in almost any industry, anywhere in the world. They can work in and out of the office while interacting with people and processes they want to improve. This flexibility gives them a career advantage over other types of engineering. Operations research practitioners have the luxury of not specializing. They can keep their options open. This makes them immune to the ups and downs of any individual industry.

Careers in Operations Research

When considering a career in operations research, it’s logical to ask,  Will I be able to get a job?” Answer:  “YES”

Operation Research Continues to Grow

According to the Bureau of Labor, operations research employment will continue to grow by over 25 percent during the next decade. This is faster than the average for all occupations.

Companies look for new ways to reduce costs and raise productivity every day. They will turn to operation research practitioners to develop more efficient processes and reduce costs, delays and waste. This leads to job growth for these engineers, even in manufacturing industries with slow-growing or declining employment. Because their work is done in management, many operations research practitioners leave the occupation to become managers.

It is a great time to be an operations research practitioner. They solve problems and there’s never a shortage of those!

Approach, Techniques, and Tools of Operations Research: A Comprehensive Guide

Table of Contents

Operations research is a problem-solving approach that utilizes mathematical models and analytical techniques to aid decision-making. It encompasses a wide range of methods and tools that help in solving complex problems, optimizing resources, and improving the efficiency of various systems. In this blog, we will discuss the approach, techniques, and tools used in operations research.

Operations research is an interdisciplinary field that involves the application of mathematical models, statistical analysis, and optimization techniques to complex problems. The ultimate goal of operations research is to improve the efficiency and effectiveness of various systems by aiding in decision-making. The approach, techniques, and tools used in operations research depend on the nature of the problem and the available data.

The approach used in operations research can be broadly classified into two types: the classical approach and the modern approach. The classical approach involves the use of mathematical models to represent the system being analyzed. This approach is based on the assumption that the system under consideration is deterministic and all the parameters of the system are known. On the other hand, the modern approach is based on the assumption that the system under consideration is stochastic, and the parameters of the system are not fully known. This approach utilizes simulation, optimization, and decision-making under uncertainty to analyze the system.

There are several techniques used in operations research, including linear programming, integer programming, dynamic programming, and nonlinear programming. Linear programming is a method used to optimize a linear objective function subject to linear equality and inequality constraints. Integer programming is an extension of linear programming that involves restricting some or all of the decision variables to be integers. Dynamic programming is a method used to solve problems that can be divided into smaller sub-problems. Nonlinear programming is used to optimize a nonlinear objective function subject to nonlinear constraints.

There are several tools used in operations research, including mathematical programming languages such as AMPL, GAMS, and LINGO. These programming languages are used to develop mathematical models and solve optimization problems. Simulation software such as Arena and Simul8 are used to simulate complex systems and evaluate different scenarios. Statistical software such as R and SAS are used to analyze data and develop statistical models.

Operations research is a powerful problem-solving approach that involves the use of mathematical models, analytical techniques, and optimization tools. The approach, techniques, and tools used in operations research depend on the nature of the problem and the available data. By using these methods, decision-makers can make informed decisions and optimize resources to improve the efficiency and effectiveness of various systems.

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Operations Research

1 Operations Research-An Overview

• History of O.R.
• Approach, Techniques and Tools
• Phases and Processes of O.R. Study
• Typical Applications of O.R
• Limitations of Operations Research
• Models in Operations Research
• O.R. in real world

2 Linear Programming: Formulation and Graphical Method

• General formulation of Linear Programming Problem
• Optimisation Models
• Basics of Graphic Method
• Important steps to draw graph
• Multiple, Unbounded Solution and Infeasible Problems
• Solving Linear Programming Graphically Using Computer
• Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

• Principle of Simplex Method
• Computational aspect of Simplex Method
• Simplex Method with several Decision Variables
• Two Phase and M-method
• Multiple Solution, Unbounded Solution and Infeasible Problem
• Sensitivity Analysis
• Dual Linear Programming Problem

4 Transportation Problem

• Basic Feasible Solution of a Transportation Problem
• Modified Distribution Method
• Stepping Stone Method
• Unbalanced Transportation Problem
• Degenerate Transportation Problem
• Transhipment Problem
• Maximisation in a Transportation Problem

5 Assignment Problem

• Solution of the Assignment Problem
• Unbalanced Assignment Problem
• Problem with some Infeasible Assignments
• Maximisation in an Assignment Problem
• Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

• Concepts of goal programming
• Goal programming model formulation
• Graphical method of goal programming
• The simplex method of goal programming
• Using Excel Solver to Solve Goal Programming Models
• Application areas of goal programming

8 Integer Programming

• Some Integer Programming Formulation Techniques
• Binary Representation of General Integer Variables
• Unimodularity
• Cutting Plane Method
• Branch and Bound Method
• Solver Solution

9 Dynamic Programming

• Dynamic Programming Methodology: An Example
• Definitions and Notations
• Dynamic Programming Applications

10 Non-Linear Programming

• Solution of a Non-linear Programming Problem
• Convex and Concave Functions
• Kuhn-Tucker Conditions for Constrained Optimisation
• Quadratic Programming
• Separable Programming
• NLP Models with Solver

11 Introduction to game theory and its Applications

• Important terms in Game Theory
• Saddle points
• Mixed strategies: Games without saddle points
• 2 x n games
• Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

• Reasons for using simulation
• Monte Carlo simulation
• Limitations of simulation
• Steps in the simulation process
• Some practical applications of simulation
• Two typical examples of hand-computed simulation
• Computer simulation

13 Queueing Models

• Characteristics of a queueing model
• Notations and Symbols
• Statistical methods in queueing
• The M/M/I System
• The M/M/C System
• The M/Ek/I System
• Decision problems in queueing

• Prospective Cadets
• Faculty & Staff

Operations Research Major

Operations research.

Operations research is a scientific approach to decision-making with a focus on how to best design and operate systems, usually under conditions requiring the allocation of scarce resources.

Offered by the Department of Mathematics Sciences .

Operations research is a scientific approach that applies quantitative methods to decision-making with a focus on how best to design and operate systems, usually under conditions requiring the allocation of scarce resources. However, whether one means the term to be a professional designation, a label for a body of methods, or an approach to problem-solving, operations research is today inextricably linked to the direction and management of large systems of people, machines, materials, and money in government, industry, business, and defense.

Since its inception during WWII, the interdisciplinary field of operations research has set itself apart as an applied mathematical science and engineering discipline with a diverse range of applications. Because of the increased demand for operations research analyses within the Army, the operations research specialty continues to enjoy steady growth in membership, and is associated with superb educational and promotion opportunities throughout an officer's military career. West Point remains the single largest source of operations research officers for the Army.

Graduates of the operations research program at USMA are well prepared to tackle some of the Army's most challenging problems and to pursue graduate study in support of the operations research career field.

The operations research curriculum offers a combination of mathematical optimization, statistics, systems engineering, engineering management, computer science, and economics. This broad foundation of problem-solving skills and knowledge afford an adept perspective when confronting the challenging and complex problems that face military, government, and industry leaders.

The major offers an honors option.

Military Applications of Operations Research

The military specifically uses Operations Research at the strategic, operational, and tactical levels. The applications cover a full spectrum of military activities including national policy analysis, resource allocation, force composition and modernization, logistics, human resources, battle planning, and maintenance and replenishment.

Program of Study

Operations Research applies quantitative methods to decision-making. The Operations Research curriculum offers a combination of mathematical optimization, statistics, systems engineering, engineering management, computer science, and economics. This broad foundation of problem-solving skills and knowledge afford an adept perspective when confronting the challenging and complex problems that face military, government, and industry leaders.

Student Outcomes

The student outcomes of the operations research major include:    

• Identifying and articulating assumptions, metrics and constraints
• Applying appropriate solutions techniques
• Interpreting results within the appropriate context
• Argue and inquire soundly and rigorously; become independent questioners and learners
• Understand and apply probabilistic and statistical models and methods
• Understand and apply simulation methods
• Understand and apply optimization methods
• Communicate effectively - orally and in writing
• Use technology to model, visualize, and solve complex problems
• Creative and curious
• Experimental disposition
• Critical thinking and reasoning
• Commitment to life-long learning
• Understand the role of operations research in interdisciplinary problem solving

Contact a Department of Mathematical Sciences Academic Counselor:

• Head DAC: MAJ Si Park, Instructor, [email protected]
• Math DAC: MAJ Jacques Kassa, Instructor, [email protected]

To learn more about this area of study, visit the Department of Mathematical Sciences .

Required Courses

• MA371  LINEAR ALGEBRA 
• MA376  APPLIED STATISTICS 
• MA381  NONLINEAR OPTIMIZATION 
• MA476  MATHEMATICAL STATISTICS 
• MA477  THEORY & APPL OF DATA SCIENCE 
• MA481  LINEAR OPTIMIZATION 
• MA486  MATHEMATICAL COMPUTATION 
• SE385  DECISION ANALYSIS

Sample Electives

• EM381  ENGINEERING ECONOMY 
• EM411  PROJECT MANAGEMENT 
• EM420  PRODUCTION OPERATIONS MGMT 
• EM482  SUPPLY CHAIN ENG & INFO MGMT 
• SE370  COMPUTER AIDED SYSTEMS ENG
• SE489  AD IND STY IN SYS ENG/ENG MGMT
• CS393  DATABASE SYSTEMS  
• CS486  ARTIFICIAL INTELLIGENCE 
• CY300  PROGRAMMING FUNDAMENTALS 
• MA388  SABERMETRICS 
• MA478  GENERALIZED LINEAR MODELS 
• CS384  DATA STRUCTURES 
• CS393  DATABASE SYSTEMS 
• CS486  ARTIFICIAL INTELLIGENCE  
• CY460  CYBER POLICY, STRATEGY, & OPNS 
• MA372  INTRODUCTION TO DISCRETE MATH 
• MA394  FUNDAMENTALS/NETWORK SCIENCE 
• MA461  GRAPH THEORY AND NETWORK
• SE485  COMBAT MODELING 
• SM484  SYSTEM DYNAMICS SIMULATION
• MG410  MANAGERIAL FINANCE 
• SS368  ECONOMETRICS I 
• SS382  MICROECONOMICS 
• SS388  MACROECONOMICS 
• SS469  ECONOMETRICS II

This major offers an honors track. 

To learn more, view the full Operations Research Major Curriculum .

Cadets who choose this major have the opportunity to publish in journals like Mathematica Militaris , become a member of the Pi Mu Epsilon Mathematics Honor Society, Alpha Zeta Chapter , and work with the mathematical science center as they conduct summer internships/research at various laboratories and agencies. 

Other Honor Societies: Golden Key - International Honour Society Phi Kappa Phi - Oldest and Largest Collegiate Honor Society

To learn more about enrichment for this area of study, visit the Department of Mathematical Sciences or the Mathematical Sciences Center .

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Scope of Operation Research

• Updated on  
• Aug 19, 2022

What is the scope of operational research? To answer this, we will first have to understand what operations research means. Operational Research can be simply formulated as the science of rational decision-making along with the study of the synthesis of intricate problematic situations. Thus, the nature of operations research is purely scientific as it aims at determining the systematic behaviour and hence optimizing the results. The scope and applications of operations research empower decision-making in those business aspects where there is a larger concern of allocation of scarce resources especially like capital, investment, labour, etc.

Scope and Application of Operations Research

Operation Research centrally focuses on simplifying complicated business problems into well-defined mathematical constructs and works specifying expected behaviour as well as goals. The key application of Operations Research is that it facilitates decision making in those aspects of a business where resource allocation is paramount, i.e. capital, labour, time and other business resources. Given that it is rooted in computer science and analytics, there is an immense scope of operation research in every business enterprise.

Here are the key areas of the scope and application of operations research:

• Healthcare Management and Hospital Administration
• Financial Management , Budgeting and Investments
• Government Development / Public Sector Units
• Energy and Environment
• Marketing and Revenue Management

Agriculture

• Telecommunication Networks
• Military Defences
• Supply Chain Management
• Purchasing / Procurement / Logistics
• National Plans / Budgets

Find out everything about Operations Management MBA !  

Nature of Operations Research

When it comes to the nature of operations research, business experts and scholars describe it as a science as operations research takes a mathematical and scientific approach to decision-making and problem-solving. Let’s understand the nature of operations research through these key definitions:

• “Operations Research is a scientific approach to problem-solving for executive management.” – H.M Wagner
• “Operations Research is the systematic, method oriented study of the basic structure, characteristics, functions and relationships of an organization to provide the executive with a sound, scientific and quantitative basis for decision making.” – E.L. Arnoff and M.J. Netzorg
• “Operations Research is an aid for the executive in making his decision by providing him with the needed quantitative information based on the scientific method of analysis.” – C. Kittel
• “O.R. is an experimental and applied science devoted to observing, understanding and predicting the behavior of purposeful man-machine systems and operations research workers are actively engaged in applying this knowledge to practical problems in business, government and society.” – Operations Research Society of America

Limitations of Operations Research

There are certain limitations and disadvantages of operations research that you must also know about. Here are the limitations of operations research:

• Operation Research can be costly in terms of implementation as well as using the best technology and tools for simulations.
• Operation Research also requires a team of analysts or experts to carry out every step of the process and thus needs a team of properly qualified professionals to find the best results and solutions.
• Operation Research also relies heavily on technology as software applications and tools play an imperative part in data analysis and predictions.

Characteristics of Operations Research

Given below are the 3 main characteristics of Operations Research, i.e. Optimization, Stimulation and Probability & Statistics.

Optimization The objective of Operations Research is to provide better performance in any given situation. The process of doing this involves a lot of data collection and analysis of possible outcomes. The process of optimization involves a critical analysis of all the available options and selecting the highly relevant ones. 

Simulation Before you move on with selected options or methods to improve the overall result, you must be sure that the selected method is going to be beneficial. This part is ensured by the process of simulation.

Probability and Statistics Mathematical algorithms are the best way to evaluate potential risks and predict the possible outcomes beforehand. Thus, Operation Research involves intensive use of statistical and mathematical approach to cover all the circumstances.

Phases of Operation Research

There are three phases in an operation research study –

• Determining the operation and objectives
• It also includes determining the effectiveness of different steps, the type of problem, its origin and the causes behind it.
• Formulating the hypothesis and models
• Next step is analyzing the information collected and verifying the hypothesis.
• The last step in this phase is the production and generation of results and considering all the other alternatives.
• Giving recommendations for the solution to the problem including the assumptions, scope, limitations and other alternatives.
• Lastly, the solution has to be put to work.

Where is Operation Research Used?

Here are the most common problems that can be solved by Operation Research:

Methodologies

When operation research is carried out in a business enterprise, there are three major steps followed to complete the OR process. These steps are:

• Judgement : At this phase, the clarification of the problem happens. First, the problem is defined in a simple manner and then the objectives and ways for measuring the final results and success are also determined.
• Research : Once you have defined what the problem is, the research phase carries out the accumulation of data about the problem and then determining the hypothesis, validating the hypothesis and then developing the model(s) and thus making possible predictions.
• Action : After getting the predictions, results are incorporated and the necessary improvements and changes take place.

Roles & Responsibilities in Operation Research 

If you imagine yourself working in the field of Operational Research, there are many essential responsibilities that you will be expected to handle. Hence, you need to be well-versed with the qualities and attributes required to apprehend critical situations and problems. So, before moving to the scope of Operation Research, take a look at the following roles and responsibilities that you will be carried out under varied career profiles. 

• To analyze and devise the plan using statistical analysis, predictive modelling, simulations and methods to exempt the organizations from business problems. 
• To help organisational teams with in-depth research on various topics. 
• Collect the required information for the company from co-workers and utilize it in situations to come up with decisions. 
• Preparing reports by performing critical analyses of the key matrices. 
• Support the company with advantageous financial decisions while comprehending the budgets.

Find our how to make a career in Operational Research !

Career Scope of Operation Research: Employment Areas

With a degree in Operation Research or its related field, candidates can enter many employment areas. These leading job destinations can carve your career and provide you with a high-end growth ahead. To help you understand the scope of operation research, let’s elaborate some of the top-notch job-sectors that you can explore.

Defence Services

Industrial sector.

• Logistics and Supply Chain Management
• Marketing Management

There are several departments in the defence services like administrations, training, supply etc. which involves in-depth knowledge of operations. To perform warfare tasks in the Army, Navy, Air Force with promptness, there is always a constant demand for candidates with a degree in operation research. Thus, in the defence services, there is a wide scope of operation research as candidates get the opportunity to work in a dynamic environment and under higher roles facilitating the formulation of policies and strategies.

Being brought up in a country like India where agriculture is a colossal part of the economy, we often think that this domain is only for farmers or rather scientists. But, with the dire need to ensure optimum utilization of resources, there is a greater scope of operation research in this field. With sky-rocketing population, operation research can ensure optimization in agriculture and potential graduates in this field can avail the opportunities to work as research assistants under this domain.

In the advent of globalization, the industrial sector is experiencing an upheaval across the globe. To frame and handle the ever-rising demands of the organizations, candidates with brainstorming abilities are selected for various profiles in operation research. You can also opt for a specialised role like an Operational Research Analyst, who is expected to tackle the upcoming discrepancies in a business.

Have a look at the Job Oriented Courses After MBA

Scope of Operational Research: Job Profiles 

In the above-mentioned sectors, there is a multitude of career profiles available for those wanting to kickstart their career in operation research. Below we have brought you some of the key job roles which depict the varied scope of operation research: 

• Operations Analyst   
• Research Analyst 
• Operation Research Analyst 
• Project Manager 
• Data Analyst
• Consultant 
• System Analyst 
• Senior Analyst 
• Operations Officer
• Project Analyst 
• Quality Assurance Analyst

It is the research process from which management provides support for their decisions. While the name of this method is relatively new, the method used for this is not a new one. Operation Analysis is concerned with applying the concepts and techniques of science to strategic issues.

In its latest years of organized growth, O.R. Several research proceedings for the military, government and industry have been successfully resolved. In most developing countries in Asia and Africa, the underlying issue is that poverty and hunger should be removed as soon as possible. There is also a tremendous opportunity for economists , statisticians, managers, politicians and technicians working in a team to address this issue through an O.R. Approaching.

Over the next ten years, the employment of operational research analysts is expected to rise by 25 percent, far faster than the average for all occupations. As technology progresses and businesses are pursuing efficiency and cost savings, the market for analysis of operations research should continue to rise. Therefore, it is a good career option

Here are the advantages of Operation Research – 1. Effective Decisions 2. Better Coordination 3. Facilitates Control 4. Improves Productivity

Hence, we hope that this blog has helped you understand the career scope of operation research as well as an array of opportunities that you can discover in this specialised domain. If you are allured by the fascinating above-listed job profiles and want to start a career in this field, then you should definitely opt for an academic degree to understand the intricacies of this domain. Take the help of Leverage Edu ’s AI-based tool to browse through a plethora of specialised programs in this field and find the best course and university combination that can equip you with the required knowledge and exposure to establish your career in Operation Research.

Team Leverage Edu

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Home » Management Science » Operations Research approach of problem solving

Operations Research approach of problem solving

Optimization is the act of obtaining the best result under any given circumstance. In various practical problems we may have to take many technical or managerial decisions at several stages. The ultimate goal of all such decisions is to either maximize the desired benefit or minimize the effort required. We make decisions in our every day life without even noticing them. Decision-making is one of the main activity of a manager or executive. In simple situations decisions are taken simply by common sense, sound judgment and expertise without using any mathematics. But here the decisions we are concerned with are rather complex and heavily loaded with responsibility. Examples of such decision are finding the appropriate product mix when there are large numbers of products with different profit contributions and production requirement or planning public transportation network in a town having its own layout of factories, apartments, blocks etc. Certainly in such situations also decision may be arrived at intuitively from experience and common sense, yet they are more judicious if backed up by mathematical reasoning. The search of a decision may also be done by trial and error but such a search may be cumbersome and costly. Preparative calculations may avoid long and costly research. Doing preparative calculations is the purpose of Operations research. Operations research does mathematical scoring of consequences of a decision with the aim of optimizing the use of time, efforts and resources and avoiding blunders.

The application of Operations research methods helps in making decisions in such complicated situations. Evidently the main objective of Operations research is to provide a scientific basis to the decision-makers for solving the problems involving the interaction of various components of organization, by employing a team of scientists from different disciplines, all working together for finding a solution which is the best in the interest of the organization as a whole.

The solution thus obtained is known as optimal decision. The main features of Operations Research are:

• It is System oriented: Operations Research studies the problem from over all points of view of organizations or situations since optimum result of one part of the system may not be optimum for some other part.
• It imbibes Inter-disciplinary team approach. Since no single individual can have a thorough knowledge of all fast developing scientific know-how, personalities from different scientific and managerial cadre form a team to solve the problem.
• It makes use of Scientific methods to solve problems.
• OR increases the effectiveness of a management Decision making ability.
• It makes use of computer to solve large and complex problems.
• It gives Quantitative solution.
• It considers the human factors also.

The first and the most important requirement is that the root problem should be identified and understood. The problem should be identified properly, this indicates three major aspects:

• A description of the goal or the objective of the study,
• An identification of the decision alternative to the system, and
• A recognition of the limitations, restrictions and requirements of the system.

Limitations of Operations Research:

• The limitations are more related to the problems of model building, time and money factors.
• Magnitude of computation: Modern problem involve large number of variables and hence to find interrelationship, among makes it difficult.
• Non-quantitative factors and Human emotional factor cannot be taken into account.
• There is a wide gap between the managers and the operation researches.
• Time and Money factors when the basic data is subjected to frequent changes then incorporation of them into OR models are a costly affair.
• Implementation of decisions involves human relations and behavior.

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• Introduction to Transportation Problem
• Construction of Mathematical Decision Model
• Modeling Techniques in Management Science
• Waiting Lines and Queuing System in Management Science
• Introduction to Crtical Path Analysis
• Transportation and Assignment Models in Operations Research
• Economic interpretation of linear programming duality
• Introduction to Linear Programming (L.P)
• Procedure for finding an optimum solution for transportation problem

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The Robots That Will Change the World Are Already Among Us

Climate change more like ecosocial crisis, openmind books, scientific anniversaries, kary mullis, the genius of a scientist, the eccentricity of a celebrity, featured author, latest book, solving problems visually.

What’s the best way to approach (and successfully solve) a mathematical problem statement? Perhaps by drawing a picture? That, at least, is the conclusion of a striking new study by researchers at the Universities of Geneva and Burgundy.

It’s not a trivial assumption. It is thought that when we face a mathematical problem that contains both mathematical information (numbers and arithmetic operations) and non-mathematical information (the context of the problem and the characteristics of the entities involved), our brains process this combination of verbal and numerical information and convert it into a mental representation in order to identify the best strategy for solving it. On the other hand, more and more studies suggest that the schematic drawings that are usually made to solve this type of problem are a reflection of these mental representations.

Game 1: Not a game, an experiment

In the study, participants were asked to solve 12 simple arithmetic problems in as few steps as possible and to draw a picture that would help them understand and solve the problem.

Here are two of these problems, and we invite you to solve them in the same way: in as few steps as possible, and with a drawing to help you understand the problem.

Problem 1 : Paul has five red marbles and also has some blue marbles. In total he has eleven marbles. Julie’s marbles are green and blue. Julie has as many blue marbles as Paul and also has two fewer green marbles than Paul has red marbles. How many marbles does Julie have?

Problem 2 : Lisa takes the train during the day, travels for 5 hours and arrives at her destination at 11am. Fred got on the train at the same time as Lisa and his trip took 2 hours less. What time did Fred arrive at his destination?

Independently of the above, many studies postulate that relying on drawings, diagrams or other types of graphical representations when processing information has numerous benefits: it improves our ability to learn and remember, it helps us to understand complex concepts, it reinforces critical and scientific thinking, and it fosters a transversal and interdisciplinary interpretation. And from a mathematical point of view, using these representations makes it easier to establish the relationships between different data, to visualise the information implicit in the statement and to identify the most direct and simplest solution strategy.

Use the drawings to answer these complex and hieroglyphic questions.

A recent study goes a step further by suggesting that the verbal information in the problem statement influences the type of diagram shown and also the strategy chosen to solve the problem. More specifically, the study has found that the type of diagram preferentially chosen depends on whether the statement is cardinal or ordinal in nature.

Thus, when the context alludes to the cardinal properties of the quantities involved—the number of elements in a set—a drawing based on groupings of entities (crosses, circles, etc.) that sometimes overlap (or intersect) is usually chosen. This in turn leads to a three-step arithmetic strategy. On the other hand, when the statement of the problem focuses on the ordinal properties of numbers—the position they occupy in a set—we usually opt for drawings based on axes, graduations or intervals, which lead to a more direct and simpler one-step solution strategy.

And this is observed even when the problems are analogous from a mathematical point of view: they have the same structure, the same numerical values and can be solved with the same strategy (as in the case of the two problems in Game 1).

But perhaps the most interesting reflection is that, knowing this, it is possible to guide and train the student to apply this second type of diagram, thereby facilitating the identification of the best way to solve it.

Game 3:  A high-flying challenge

Sara wants to travel from Madrid to Tokyo. To do so, she flies first to New York, from where she takes a plane to London and from there to Tokyo.

Paul also wants to go from Madrid to Tokyo, but in his case he flies directly from Madrid to London and then takes a flight to Tokyo.

If Sara flies for a total of 27hrs 15min and Paul for 14hrs 30min, and given that the flight from New York to London takes 4hrs 45min longer than the flight from Madrid to London, and the flight from London to Tokyo takes 12 hours, how long is the flight from Madrid to New York?

And if both Sara and Paul lose only one hour at each stopover, what will the local time be when they each arrive in Tokyo if they both depart Madrid at 2pm?

            M                                 NY    M-L + 4:45   L                    12:00 h                   T

                                                   M           L                                       12:00 h                    T 

14 hrs 30 min

The Madrid-London flight takes 2hrs 30min. New York to London is 2hrs 30min + 4hrs 45min = 7hrs 15min. And the Madrid to New York flight is 27hrs 15min – 12hrs – 7hrs 15min = 8 hours.

With this, and bearing in mind that each stopover only takes one hour:

If Sara leaves at 2pm from Madrid then: 2pm + 8hrs – 6hrs (time difference) + 1hr (at NY airport) + 7hrs 15min + 5hrs (time difference) + 1hr + 12hrs + 8hrs (time difference) = 2:15am on day 3.

In Paul’s case: 2pm + 2hrs 30min – 1hr (time difference) + 1hr + 12hrs + 8hrs (time difference) = 12:30pm on day 2.

Miguel Barral

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Analysis of operations research methods for decision problems in the industrial symbiosis: a literature review

• Review Article
• Published: 25 August 2022
• Volume 29 , pages 70658–70673, ( 2022 )

Cite this article

• Emre Yazıcı 1 ,
• Hacı Mehmet Alakaş   ORCID: orcid.org/0000-0002-9874-7588 1 &
• Tamer Eren 1  

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Industrial symbiosis (IS) is an approach that aims to use resources efficiently by cooperating between independent enterprises in raw materials, energy, and similar sectors. As a result of cooperation, businesses gain economic, environmental, and social benefits. Especially in recent years, IS applications have become widespread due to the problems experienced in the supply of resources. The presence of more than one enterprise in cooperation creates a complex network structure in IS applications. In this complex system, many decision problems are encountered in establishing and effectively maintaining the industrial symbiosis network. Operations research techniques are at the forefront of the methods used to solve decision problems. This study examined studies using operations research techniques in industrial symbiosis. Studies were divided into four classes according to the methods they used: exact methods, heuristic methods, multi-criteria decision-making, and simulation. In the literature review, the studies in the Web of Science (WOS) database are systematically presented by scanning with the determined keywords. As a result of the study, it was analyzed which method was preferred and where the methods could be applied in industrial symbiosis.

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Analysis of factors affecting industrial symbiosis collaboration

Mathematical Optimization Models for the Design of Industrial Symbiosis Networks: Challenges and Trends

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EY is supported by the Higher Education Institution (CoHE) within the scope of 100/2000 PhD scholarship.

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Department of Industrial Engineering, Faculty of Engineering, Kırıkkale University, Ankara Yolu 7. Km, 71451, Yahşihan/Kırıkkale, Turkey

Emre Yazıcı, Hacı Mehmet Alakaş & Tamer Eren

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EY wrote the original draft of the manuscript. HMA and TE reviewed and edited the manuscript. All authors read and approved the final manuscript.

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Correspondence to Hacı Mehmet Alakaş .

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Yazıcı, E., Alakaş, H.M. & Eren, T. Analysis of operations research methods for decision problems in the industrial symbiosis: a literature review. Environ Sci Pollut Res 29 , 70658–70673 (2022). https://doi.org/10.1007/s11356-022-22507-w

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Received : 06 May 2022

Accepted : 08 August 2022

Published : 25 August 2022

Issue Date : October 2022

DOI : https://doi.org/10.1007/s11356-022-22507-w

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