operations research quiz questions with answers

Operations Research

1. Operations Research approach is ______________.

• multi-disciplinary
• collect essential data

2. A feasible solution to a linear programming problem ______________.

• must satisfy all the constraints of the problem simultaneously
• need not satisfy all of the constraints, only some of them
• must be a corner point of the feasible region.
• must optimize the value of the objective function

3. If any value in XB column of final simplex table is negative, then the solution is ______________.

• no solution

4. For any primal problem and its dual______________.

• optimal value of objective function is same
• dual will have an optimal solution iff primal does too
• primal will have an optimal solution iff dual does too
• both primal and dual cannot be infeasible

5. The difference between total float and head event slack is ______________

• independent float
• interference float
• linear float

6. An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost should be equal to the number of ______________.

• rows or columns
• rows and columns.
• rows+columns- 1
• rows-columns.

7. To proceed with the Modified Distribution method algorithm for solving an transportation problem, the number of dummy allocations need to be added are______________.

8. Select the correct statement

• EOQ is that quantity at which price paid by the buyer is minimum
• If annual demand doubles with all other parameters remaining constant, the Economic Order Quantity is doubled
• Total ordering cost equals holding cost
• Stock out cost is never permitted

9. Service mechanism in a queuing system is characterized by ______________.

• customers behavior
• servers behavior
• customers in the system
• server in the system

10. The objective of network analysis is to______________.

• minimize total project duration
• minimize toal project cost
• minimize production delays, interruption and conflicts
• maximize total project duration

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• Operations Research Objective Question and Answer

Operations Research MCQs Quiz Multiple Choice Questions & Answers

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Operations Research Questions with Answers

1. Operations Research (OR), which is a very powerful tool for

• None of the above
• Decision – Making

2. Who coined the term Operations Research?

• Both A and B
• J.F. McCloskey
• F.N. Trefethen

3. An objective function which states the determinants of the quantity to be either maximized or minimized is called

• Criterion function
• Feasible function
• Optimal function

4. .........................is another method to solve a given LPP involving some artificial variable ?

• Two.phase simplex method
• Big M method
• Method of penalties

5. .........................which is a subclass of a linear programming problem (LPP)

• Computer problem
• Both are incorrect
• Programming problem
• Transportation problem

6. .................assumption means the prior knowledge of all the coefficients in the objective function, the coefficients of the constraints and the resource values.

• Finite choices
• Proportionality

7. ................are the representation of reality

8. ................models are obtained by enlarging or reducing the size of the item

• Symbolic Models
• Iconic Models
• Analogue Models

9. ...............are called mathematical models

10. ...............models assumes that the values of the variables do not change with time during a particular period

• Static Models
• Dynamic Models

11. ...............models involves the allocation of resources to activities in such a manner that some measure of effectiveness is optimized.

• Queuing Theory
• Decision Theory
• Allocation Models

12. ..............are expressed is n the form of inequities or equations

• Constraints
• Objective Functions

13. .............may be defined as a method of determining an optimum programme inter dependent activities in view of available resources

• Decision Making
• Goal Programming
• Linear Programming

14. .............refers to the combination of one or more inputs to produce a particular output.

15. ............is one of the fundamental combinatorial optimization problems.

• Optimization Problem
• Assignment problem

16. A basic solution which also satisfies the condition in which all basic variables are non.negative is called

• Optimal solution
• Basic feasible solution
• Feasible solution

17. A BFS of a LPP is said to be...............if at least one of the basic variable is zero

• Non.degenerate

18. A feasible solution is called a basic feasible solution if the number of non.negative allocations is equal to

19. A given TP is said to be unbalanced, if the total supply is not equal to the total

• Optimization

20. A minimization problem can be converted into a maximization problem by changing the sign of coefficients in the

21. A non – degenerate basic feasible solution is the basic feasible solution which has exactly m positive Xi (i=1,2,…,m), i.e., none of the basic variable is

22. A path formed by allowing horizontal and vertical lines and the entire corner cells of which are occupied is called a

• Closed path
• Occupied path

23. A set of values X1, X2,…Xn which satisfies the constraints of the LPP is called

24. A solution may be extracted from a model either by

• Diversified Techniques
• Conducting experiments on it
• Mathematical analysis

25. A...................models considers time as one of the important variable

26. A........has rows / column having non. basic cells for holding compensating (+) or (.) sign.

• Dead – end

27. According to transportation problem number of basic cells will be exactly

28. After determining every basic cell with in this cycle, adjustment is obtained as minimum value in basic cells . this is known as

• Alternatives
• Adjustment amount

29. All the constraints are expressed as equations and the right hand side of each constraint and all variables are non.negative is called

• Canonical solution
• Canonical variable
• Canonical form

30. All the parameters in the linear programming model are assumed to be

31. Allocation Models are

• Iconic models

32. Allocation problems can be solved by

• Linear Programming Technique
• Non – Linear Programming Technique

33. An assumption that implies that finite numbers of choices are available to a decision – maker and the decision variables do not assume negative values is known as

34. An objective function is maximized when it is a..........function

35. An optimal solution is the..........stage of a solution obtained by improving the initial solution

36. An optimization model

• Helps in evaluating various alternatives constantly
• All of the above
• Mathematically provides the best decision
• Provides decision within its limited context

37. An optimum solution is considered the.............among feasible solutions.

• Ineffective

38. Any column or raw of a simplex table is called a

39. Any feasible solution to a transportation problem containing m origins and n destinations is said to be

• Independent

40. Any feasible solution which optimizes (minimizes or maximizes) the objective function of the LPP is called its

• Non.basic variables

41. Any set of non.negative allocations (Xij>0) which satisfies the raw and column sum (rim requirement )is called a

• Linear programming

42. Any solution to a LPP which satisfies the non. negativity restrictions of the LPP is called its

• Unbounded solution

43. As for maximization in assignment problem, the objective is to maximize the

• optimization

44. Assignment problem helps to find a maximum weight identical in nature in a weighted

• Partite graph
• Tripartite graph
• Bipartite graph

45. Basic cells indicate positive values and non. basic cells have..........value for flow

46. Before starting to solve the problem, it should be balanced. If not then make it balanced by..........column incase demand is less than supply or by adding.........................raw incase supply is less than the demand

• Horizontal, Vertical
• Unshipped supply, Shortage

47. Currently, LPP is used in solving a wide range of practical

• Manufacturing problems
• Business problems
• Agricultural problems

48. Decision variables are

• Controllable
• Uncontrollable

49. Dual of the dual is

• Alternative

50. Every LPP is associated with another LPP is called

• Non.linear programming
• Next →

Multiple Choice Questions and Answers on Operations Research

Operations research multiple choice questions and answers, operations research trivia quiz, operations research question and answer pdf online.

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Operation Research Module 1

10 questions

Introducing new   Paper mode

No student devices needed.   Know more

Scope of Operation research :

Road Traffic management

Agriculture

Cost allocation

  t e = t 0 + 4 t m + t p 6 t_e=\frac{t_0+4t_m+t_p}{6} t e ​ = 6 t 0 ​ + 4 t m ​ + t p ​ ​   is the formula for :

Elapsed Time

Expected Time

Earliest Time

Transportation model problems are used to minimize :

Transportation Cost

Packaging Cost

Shipping Cost

Manufacturing Cost

Advantage of LPP:

Figuring out Bottlenecks

Improved Manufacturing Process

Better utilization of resources

Model based Solution

Application of Linear Programming:

Portfolio Selection problem

Queue management

Military Applications

Health Applications

________ is assumed in all liner programming models that all parameters be be constant and known.

LPP consist of three components :

Time elapsed

Objective function

Limitation of Linear Programming are :

Not fitting Real Life situations

No concrete answer

suitable for small scale problems

effect of time not measured

Problems concerned with assignment of human resource

Transportation problem

Assignment problems

Utilization problem

Minimization problems

Vogel Approximation is used to find initial solution for :

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Top 20 Operations Research Interview Questions & Answers

Master your responses to Operations Research related interview questions with our example questions and answers. Boost your chances of landing the job by learning how to effectively communicate your Operations Research capabilities.

Embarking on a career in operations research means diving into a world where analytical problem-solving is paramount. As an operations researcher, you leverage sophisticated mathematical models and statistical techniques to solve complex organizational challenges, streamline processes, and optimize efficiency. With this high level of expertise, your job interview is not merely about affirming that you have the technical know-how; it’s also about demonstrating your strategic thinking and ability to apply theoretical knowledge to real-world situations.

To assist you in preparing for what could be one of the most critical conversations of your professional life, we’ve gathered some common interview questions tailored specifically to operations research roles. These will help you articulate how your skills can translate into success for potential employers and provide insights into constructing well-thought-out responses that highlight your proficiency in this intricate field.

Common Operations Research Interview Questions

1. how would you optimize a supply chain network with multiple conflicting objectives.

Understanding the trade-offs involved in supply chain management is crucial for an operations research analyst. When optimizing a supply chain with multiple conflicting objectives, such as minimizing cost while maximizing customer service, it’s a complex balancing act that requires analytical acumen and strategic thinking. The question aims to assess a candidate’s understanding of the trade-offs involved in supply chain management and their ability to apply quantitative methods to find a compromise solution. It also evaluates a candidate’s foresight in anticipating the ripple effects of changes within the network and their skill in using optimization tools and techniques.

When responding to this question, you should outline a structured approach, starting with the identification of key objectives and constraints. Discuss the use of mathematical models such as linear programming or simulations to analyze the trade-offs and propose solutions. Demonstrate your thought process by explaining how you would prioritize objectives or employ multi-criteria decision-making techniques. Share any relevant experiences where you’ve successfully optimized a supply chain, highlighting your analytical skills and the outcomes achieved. It’s also beneficial to mention how you’d involve stakeholders in the process to ensure the chosen strategy aligns with the overall business goals.

Example: “ To optimize a supply chain network with multiple conflicting objectives, I would first conduct a thorough analysis to quantify and understand the trade-offs between these objectives. For instance, minimizing costs might conflict with maximizing service level or reducing carbon footprint. I would employ a multi-objective optimization framework, using techniques such as Pareto efficiency to identify a set of optimal solutions that do not dominate each other. This approach would allow stakeholders to visualize the trade-offs and make informed decisions based on their priorities.

In practice, I would construct a mixed-integer linear programming (MILP) model or a multi-agent system simulation to capture the complexity of the supply chain and the interactions between different objectives. By incorporating sensitivity analysis, I could determine the robustness of the solutions to changes in input parameters. This dual approach of analytical modeling and stakeholder engagement ensures that the optimization strategy is not only mathematically sound but also practically viable and aligned with the overarching business goals. My experience in applying such methodologies has resulted in supply chain configurations that successfully balance cost efficiency with service level improvements, while adhering to sustainability standards.”

2. Describe your approach to solving a stochastic inventory control problem.

Stochastic inventory control problems sit at the intersection of predictive analytics and practical application, requiring an understanding of random processes and the ability to create models that can handle uncertainty and variability in demand. These problems require an understanding of random processes and the ability to create models that can handle uncertainty and variability in demand. By asking this question, employers are looking for evidence of your technical prowess, your comfort with mathematical complexity, and your capability to translate theoretical models into actionable strategies that optimize inventory levels against a backdrop of unpredictable customer behavior.

When responding to this question, it’s crucial to outline a structured methodology. Begin by explaining how you would model the inventory system, incorporating elements such as lead times, service levels, and holding or shortage costs. Discuss the use of probability distributions to model demand uncertainty and how you would apply analytical or simulation techniques to estimate optimal order quantities or reorder points. Emphasize your proficiency with relevant software tools or programming languages that aid in solving such problems. If applicable, illustrate your approach with a real-world example from your past experience, detailing how your solution balanced cost efficiency with service quality, and how you measured the success of your inventory strategy post-implementation.

Example: “ In addressing a stochastic inventory control problem, my initial step is to accurately model the system by defining the key parameters such as demand distribution, lead times, holding costs, and service level requirements. I would use historical data to fit a probability distribution to the demand, ensuring it captures the inherent variability and seasonality. For lead times, if they are variable, I would also model them as a stochastic process.

With the model in place, I employ analytical methods such as the Newsvendor model for single-period problems or continuous review policies like (s,Q) or (r,s,S) for multi-period scenarios, depending on the nature of the inventory system. In cases where the system complexity precludes analytical solutions, I would utilize simulation techniques to evaluate different inventory policies, leveraging software like Arena or developing custom simulations in a language such as Python with libraries like NumPy and SimPy.

The key to success in stochastic inventory control lies in finding the balance between inventory costs and service levels. I would iterate on the model, using optimization techniques to converge on the most cost-effective policy that meets the desired service level. The effectiveness of the chosen strategy would be measured through key performance indicators such as fill rate, average inventory level, and total cost, comparing these post-implementation metrics to the pre-implementation baseline to quantify the improvement.”

3. What metrics do you prioritize when evaluating the performance of a queuing system?

Selecting the right metrics in a queuing system reflects the health of the process, user satisfaction, and the potential revenue impact for a business. Prioritizing the right metrics demonstrates an understanding that every aspect of the queue—from the length and wait times to service rates and queue discipline—can profoundly affect customer experience and operational efficiency.

When responding to this question, one should articulate a balanced approach, highlighting the importance of both customer-centric metrics like average wait time and service time, and business-centric metrics such as queue length, abandonment rates, and system utilization. It’s crucial to convey an understanding of how these metrics interplay to inform decisions on staffing, resource allocation, and process improvements. Demonstrating knowledge of advanced metrics, such as the probability of wait in queue or the expected number of customers in the system at a given time, can show a deeper analytical capability.

Example: “ In evaluating the performance of a queuing system, I prioritize metrics that effectively balance customer satisfaction with operational efficiency. Average wait time is critical as it directly impacts customer experience and satisfaction levels. Service time is equally important to assess the speed and efficiency of the service process itself. Together, these metrics provide insights into the customer-facing efficiency of the system.

From an operational standpoint, I monitor queue length and abandonment rates to gauge customer behavior and system performance under varying loads. These metrics are indicative of potential issues in service delivery or capacity planning. System utilization is also a key metric, as it reflects the balance between idle and busy states of the system, indicating the effectiveness of resource allocation. Advanced metrics, such as the probability of wait in queue and the expected number of customers in the system, offer a more nuanced view of the queuing dynamics and are essential for making informed decisions regarding staffing and process optimization. These metrics allow for a comprehensive analysis of the queuing system, ensuring that improvements can be targeted effectively to enhance both customer satisfaction and operational efficiency.”

4. In what ways have you used simulation models to inform decision-making in real-world scenarios?

Demonstrating practical application of simulation models to solve complex problems is a key skill for operations research analysts. Simulation models are a powerful tool for capturing the complexity of real-world systems and predicting the outcomes of various scenarios without the risk and cost of experimenting in the real world. The question seeks to explore the candidate’s experience with these models, their ability to translate theoretical knowledge into practice, and their understanding of the model’s impact on decision-making processes.

When answering this question, provide specific examples from your past work where simulation models have played a key role. Describe the context of the problem, the construction of the simulation model, the analysis of the results, and how the insights gained from the model influenced the decision-making process. Be sure to highlight your analytical skills, your ability to work with complex data, and your understanding of how the simulation outcomes align with business objectives or operational goals.

Example: “ In a recent project, we needed to optimize the inventory levels for a distribution network with multiple echelons. Given the stochastic nature of demand and supply lead times, I developed a discrete-event simulation model to capture the dynamics of the system. The model incorporated real-time data feeds for demand forecasts, historical lead times, and service level requirements. By simulating various inventory policies and replenishment strategies under different scenarios, we were able to identify a robust policy that minimized stockouts and reduced overall holding costs. The simulation results were instrumental in convincing stakeholders to adjust their inventory management approach, leading to a 15% reduction in inventory costs while maintaining service levels.

In another instance, I used agent-based modeling to simulate customer behavior in a retail environment. The goal was to understand the impact of store layout changes on customer flow and sales. The model included parameters for customer preferences, walking speed, and purchase probabilities. By running simulations, we could predict the effects of layout modifications on customer throughput and identify potential bottlenecks. This informed the store redesign process, resulting in a layout that improved customer satisfaction scores by 10% and increased sales by 5%. These examples underscore my ability to translate complex systems into actionable insights through simulation, directly impacting operational efficiency and profitability.”

5. Can you provide an example where you’ve applied linear programming to maximize efficiency?

Linear programming is a cornerstone of operations research, enabling analysts to achieve maximum efficiency in complex systems and processes. Employers ask this question to evaluate whether candidates have practical experience translating theoretical mathematical concepts into real-world applications. It is essential for them to assess a candidate’s ability to identify variables and constraints, construct objective functions, and use linear programming techniques to solve problems that improve operations, reduce costs, or increase profits.

When responding to this question, outline a specific situation where linear programming was necessary. Describe the problem you were addressing, the objective function you sought to optimize, and the constraints you faced. Walk the interviewer through your decision-making process, the linear programming model you constructed, and the solution you reached. Highlight the impact of your solution on the organization’s efficiency, demonstrating your analytical prowess and problem-solving skills.

Example: “ In a project aimed at optimizing the supply chain network for a manufacturing company, I utilized linear programming to minimize the total cost of transportation and warehousing. The objective function was designed to reflect the sum of transportation costs between factories, warehouses, and customers, along with the fixed and variable costs of storage. Constraints included the capacities of each warehouse, the demand fulfillment for each customer, and the availability of products from the factories.

I constructed a mixed-integer linear programming model to account for the discrete decision variables involved in opening or closing warehouses. The model also incorporated transportation decisions, ensuring that the flow of goods did not exceed the capacities while meeting customer demands. The solution provided a detailed plan that reduced the overall cost by 15%, significantly increasing the efficiency of the supply chain. This optimization led to a more streamlined operation, with fewer warehouses needed and reduced miles traveled by the transportation fleet.”

6. Detail a situation where non-linear optimization was critical for project success.

When relationships between variables are curved or irregular, non-linear optimization becomes essential, requiring a deep understanding of advanced mathematics and problem-solving techniques. Employers pose this question to determine if a candidate has hands-on experience tackling real-world issues where linear models fall short and to evaluate their ability to apply theoretical knowledge to achieve tangible outcomes.

When responding, outline a specific project where you faced a challenge that linear methods couldn’t address. Describe the non-linear problem, the optimization techniques you applied, and how your solution positively impacted the project. Detail your thought process, the tools and software you used, and the results of your intervention, highlighting the value you brought to the project through your expertise in non-linear optimization.

Example: “ In a project aimed at maximizing the throughput of a chemical production process, we encountered a non-linear optimization challenge due to the complex reactions and variable operating conditions that could not be accurately modeled with linear approximations. The process exhibited diminishing returns at certain reactant concentrations and temperatures, which required a non-linear model to optimize. We formulated the problem using a non-linear programming (NLP) approach, incorporating the chemical kinetics and thermodynamics into the objective function and constraints.

Utilizing a combination of gradient-based and heuristic methods, specifically Sequential Quadratic Programming (SQP) for its robustness in handling non-linearities, and Genetic Algorithms (GA) to escape local optima, we were able to determine the optimal set points for reactant feeds and temperature profiles. The solution was implemented using a commercial optimization software package integrated with our process simulation tools. The outcome was a 15% increase in yield without additional capital expenditure, demonstrating the critical role that non-linear optimization played in unlocking the full potential of the existing system.”

7. Which software tools are you most proficient in for conducting operations research analysis?

Fluency in specialized software is often a prerequisite for modeling complex problems and deriving optimal solutions in operations research. The question targets your technical toolkit, aiming to assess not only your familiarity with industry-standard software but also your ability to adapt to the specific tools that may be integral to the prospective employer’s processes. This question also serves as a litmus test for how your technical skills will translate into immediate productivity and problem-solving within their operations.

When responding, list the software tools you are proficient in and provide examples of projects or problems you’ve tackled using each one. It’s beneficial to mention any certifications or training you have received in these tools. If you have experience with the specific software used by the company, highlight this and discuss your proficiency level. Where possible, quantify the impact your work with these tools has had on previous projects, such as improvements in efficiency, cost savings, or enhanced decision-making processes.

Example: “ I am most proficient in using Gurobi, Python with its Pyomo library, and MATLAB for operations research analysis. With Gurobi, I’ve tackled complex linear and mixed-integer programming problems, optimizing logistics and supply chain networks for large-scale systems. This involved reducing transportation costs by 15% while improving service levels. In Python, leveraging the Pyomo library, I’ve developed custom optimization models for workforce scheduling, achieving a 20% increase in staff utilization across multiple shifts.

MATLAB has been instrumental for simulation and algorithm development, particularly in stochastic models and Monte Carlo simulations to assess risk in investment portfolios, which resulted in a 10% reduction in risk exposure for a financial institution. My proficiency with these tools is backed by certifications in advanced optimization techniques and Python programming. Additionally, my experience with Gurobi and Python directly aligns with the tools used by your company, ensuring a smooth integration into your current operations research framework.”

8. How do you validate and test the assumptions in your predictive models?

The validity of the underlying assumptions in mathematical models is critical for accurate predictions and optimized decision-making. This question targets the candidate’s methodological rigor and understanding that assumptions can significantly impact the model’s accuracy and applicability. It also touches on the candidate’s ability to remain objective, adapt when faced with new data, and their commitment to due diligence in ensuring their models stand up to real-world conditions.

When responding, outline a systematic approach to validation and testing. Describe the process of identifying key assumptions, using techniques such as sensitivity analysis to understand their impact, and employing data validation methods like cross-validation or bootstrapping. Discuss the importance of comparing model predictions with actual outcomes and adjusting assumptions accordingly. Highlight any experience with software tools that assist in this process and emphasize a continuous improvement mindset, demonstrating that you not only build models but also refine them over time to maintain their accuracy and reliability.

Example: “ In validating and testing assumptions in predictive models, I employ a rigorous approach that begins with the identification of key assumptions. I utilize sensitivity analysis to gauge how changes in these assumptions impact model outcomes. This helps in understanding the robustness of the model and in pinpointing which assumptions are most critical to the model’s performance.

For data validation, I often rely on techniques such as k-fold cross-validation or bootstrapping to mitigate overfitting and assess the model’s generalizability. This involves partitioning the data into training and validation sets multiple times to ensure that the model performs well across different subsets of data. Furthermore, I compare model predictions with actual outcomes to evaluate the model’s predictive power and recalibrate assumptions as necessary.

Throughout this process, software tools like R or Python libraries (e.g., scikit-learn) are instrumental in streamlining the validation and testing procedures. I maintain a continuous improvement cycle, where models are not static but evolve with new data and insights, ensuring their ongoing relevance and accuracy.”

9. Share an experience where game theory influenced organizational strategy.

Game theory offers a lens through which interactions and competitive dynamics can be analyzed to enhance decision-making. When asking about game theory in the context of organizational strategy, the interviewer is looking for evidence of your ability to apply complex theoretical concepts to real-world business challenges. They are interested in your strategic thinking process, how you anticipate competitor moves, and how you incorporate the behavior of different stakeholders into your planning to achieve optimal outcomes.

When responding to this question, recount a specific instance where you utilized game theory to inform a strategic decision. Detail the situation, the players involved, and the potential outcomes you considered. Explain the strategies you derived from the game theory analysis and how they were implemented within the organization. Discuss the results and what you learned from applying such an approach. This response not only demonstrates your analytical skills but also your practical experience in leveraging advanced theories for tangible business benefits.

Example: “ In a project focused on competitive bidding, we faced a scenario where multiple firms were vying for a high-value government contract. Utilizing game theory, specifically the concepts of Nash Equilibrium and Bayesian games, we modeled the behavior of our competitors based on historical bidding patterns, financial strength, and risk tolerance. By analyzing the payoff matrices and considering incomplete information, we predicted the range of possible bids from competitors and identified a strategy that balanced between an aggressive bid to win and a conservative bid to maintain profitability.

The strategy derived from this analysis was to place a bid slightly lower than the second-lowest competitor’s expected bid, as our intelligence suggested they were the price-setter in the market. This approach was a mix of a pure strategy, given our fixed bid, and a mixed strategy, as we prepared contingent plans for renegotiation. The outcome was successful; we secured the contract with a favorable margin, and the analysis provided a framework for future bidding strategies. This experience underscored the importance of game theory in developing competitive strategies that account for the actions and potential reactions of other market players.”

10. What strategies do you employ to manage risk in complex systems analysis?

Understanding and mitigating risk factors is a key aspect of operations research. This question targets the candidate’s foresight in identifying potential pitfalls, their analytical acumen in assessing the severity and probability of risks, and the breadth of their toolkit for managing such risks. It also subtly assesses their experience with real-world systems and their capacity to balance risk with opportunity, aligning with organizational risk tolerance levels.

When responding to this question, candidates should outline a structured approach, perhaps referencing industry-standard risk management frameworks such as ISO 31000 or the use of advanced analytical techniques like Monte Carlo simulations. They should give examples that show their ability to anticipate risks through thorough analysis, implement preventative measures, and develop contingency plans. Demonstrating a blend of qualitative and quantitative risk assessment strategies, along with clear communication of risks to stakeholders, will illustrate a comprehensive risk management capability.

Example: “ In managing risk within complex systems analysis, I adhere to a rigorous framework that mirrors the principles outlined in ISO 31000, ensuring that risk management is an integral part of the decision-making process. Initially, I conduct a thorough risk identification exercise, which involves both qualitative and quantitative assessments. This dual approach allows for a comprehensive understanding of potential uncertainties and their impacts.

For quantitative analysis, I frequently employ Monte Carlo simulations to understand the probabilistic outcomes of different scenarios and their potential variances. This technique is particularly valuable in revealing the risk profile of complex systems where multiple variables and their interactions can lead to a wide range of outcomes. In parallel, I develop robust contingency plans that are informed by both the simulation outcomes and qualitative insights. These plans are designed to be adaptable, allowing for swift response to unforeseen events. Communication is also a key aspect of my strategy; I ensure that all stakeholders are informed of the identified risks and the measures put in place to mitigate them, fostering a culture of transparency and preparedness.”

11. Outline your process for data collection and preparation before model development.

Ensuring the accuracy, relevance, and appropriate structure of data is a fundamental part of operations research. The question targets your methodology for ensuring the data on which these decisions will be based is accurate, relevant, and structured appropriately. It also touches on your ability to identify which data is necessary, how to source it efficiently, and prepare it for analysis, which often includes cleaning, transforming, and enriching the data. This process is crucial because the quality of the data directly affects the reliability of the model’s output and, consequently, the effectiveness of operational strategies developed from that output.

When responding, outline a systematic approach that begins with defining the problem and identifying the key questions that the model needs to answer. Discuss how you determine the necessary data, the sources you might tap into, and any tools or techniques you employ for data extraction. Explain your process for cleaning the data, dealing with missing values, outliers, and any transformation steps you take to ensure it’s in the right format for your modeling tool. It’s also helpful to mention any checks you perform to validate the quality of the data and any documentation you create to track the data preparation process.

Example: “ In the initial phase of data collection, I start by clearly defining the problem at hand and identifying the key questions that the operations research model needs to answer. This involves a thorough understanding of the system’s dynamics, constraints, and objectives. Once the problem is scoped, I determine the necessary data types and sources, which could range from internal databases, process logs, to external data providers. I leverage tools such as SQL for extraction from databases and Python or R for scraping and API interactions when dealing with unstructured or semi-structured data.

The preparation stage is critical; I begin by performing exploratory data analysis to understand distributions and identify any anomalies or outliers. Data cleaning is then conducted to handle missing values, which may involve imputation techniques or data augmentation, depending on the context and the impact on the model’s robustness. I ensure that categorical data is appropriately encoded and numerical data is normalized or standardized if required by the modeling technique. Throughout this process, I maintain meticulous documentation to track transformations and decisions made, which aids in reproducibility and validation. Before proceeding to model development, I conduct a final quality check using statistical tests and visualization tools to ensure the data is clean, relevant, and accurately reflects the real-world scenario it is intended to model.”

12. When faced with multi-criteria decision-making, how do you determine weights for criteria?

Assigning weights to multiple criteria in decision-making reflects the relative importance of each factor in the context of the overall objective. This question delves into the candidate’s ability to discern what matters most in a given situation, their understanding of the business’s strategic goals, and their proficiency in employing quantitative methods to support qualitative judgments.

When responding, articulate a structured approach to multi-criteria decision-making, such as employing the Analytic Hierarchy Process (AHP) or similar methodologies. Describe how you gather relevant data, consult with key stakeholders to understand priorities, and use statistical or mathematical tools to quantify the importance of each criterion. Emphasize the adaptability of your process to different scenarios and your commitment to aligning the decision-making process with organizational goals and values.

Example: “ In multi-criteria decision-making, determining the appropriate weights for each criterion is a critical step that requires a systematic approach. I typically employ the Analytic Hierarchy Process (AHP), which allows for a comprehensive comparison of criteria based on their relative importance to the decision at hand. First, I establish a hierarchy of criteria and sub-criteria, ensuring that all relevant factors are included. Then, I gather data and insights from various sources, including empirical evidence, expert opinions, and stakeholder preferences, to inform the pairwise comparison process.

During the pairwise comparison, I quantify the subjective judgments using a scale that reflects how much more one criterion is preferred over another. This process is facilitated by statistical or mathematical tools to ensure consistency and objectivity. The resulting comparison matrices are then used to calculate the weights through eigenvalue methods, providing a set of priorities that are proportional and normalized. Throughout this process, I remain flexible and open to iterative refinement, ensuring that the weights align with the organization’s strategic objectives and the specific context of the decision. This adaptability is crucial as it allows for the incorporation of new information or changes in organizational priorities, maintaining the relevance and accuracy of the decision-making framework.”

13. Describe a time when you had to use integer programming over continuous variables.

Integer programming is a powerful tool for modeling scenarios where decisions involve discrete choices, such as assigning employees to shifts, routing delivery vehicles, or planning production schedules. The use of integer programming over continuous variables indicates a candidate’s experience with combinatorial problems where solutions must be whole numbers, reflecting real-world constraints and requirements that can’t be fractional or divided.

When responding to this question, you should recount a specific instance where the constraints of the problem necessitated the use of integer variables. Outline the context, the challenge you faced, and the rationale behind choosing integer programming. Walk the interviewer through your process of formulating the problem, implementing the integer programming model, and explain how this approach led to an optimal or satisfactory solution. Highlight your analytical thinking, problem-solving skills, and proficiency with mathematical modeling tools.

Example: “ In a project focused on optimizing the allocation of a limited number of advertising slots across various media channels, integer programming was essential due to the discrete nature of the slots. Continuous variables would not accurately represent the problem since you cannot allocate a fraction of an advertising slot. The challenge was to maximize reach while adhering to budget constraints and ensuring that each slot was used to its fullest potential.

The model I formulated used binary variables to represent the selection of each slot, with constraints to capture the budget, reach goals, and exclusivity conditions for certain products. The objective function was designed to maximize the total audience reach. By employing a branch-and-bound algorithm within an integer programming framework, the solution provided a clear, actionable schedule for ad placements that optimized reach within the given constraints.

This approach not only ensured a feasible and optimal allocation of advertising slots but also allowed for easy interpretation and implementation of the results by the marketing team. The success of this campaign was evident in the subsequent increase in audience engagement metrics, validating the effectiveness of integer programming in scenarios where decisions are binary or resources are indivisible.”

14. How do you handle dynamic and uncertain environments in operational planning?

Adaptability and the ability to apply analytical methods to make informed decisions despite incomplete information are crucial in operations research. Employers seek candidates who can demonstrate resilience and strategic thinking when faced with unexpected challenges, and who can adjust plans and strategies swiftly and effectively to maintain performance and achieve objectives.

When responding, outline specific strategies or methodologies you use to manage uncertainty, such as scenario planning, risk assessment, or decision analysis models. Discuss your experience in monitoring trends and indicators that may signal the need for plan adjustments. Provide examples of past situations where you successfully adapted to changes, emphasizing your thought process and the outcomes of your actions. It’s important to show that you can remain calm under pressure and that you have a systematic approach to problem-solving in dynamic conditions.

Example: “ In dynamic and uncertain environments, I employ a combination of stochastic modeling, robust optimization, and simulation to manage uncertainties in operational planning. Stochastic models help in understanding the probability distributions of uncertain parameters, allowing for the development of plans that can accommodate a range of possible outcomes. Robust optimization is crucial for creating solutions that are effective under various scenarios, ensuring that the plans remain viable even when conditions change unexpectedly.

When faced with real-time changes, I rely on a continuous monitoring system to track key performance indicators and external factors, enabling quick detection of trends that necessitate plan adjustments. For example, during a supply chain disruption, I utilized a Monte Carlo simulation to assess the impact of various risk factors on delivery schedules and inventory levels. This allowed for the recalibration of the supply chain strategy, minimizing the disruption’s impact on service levels. The outcome was a more resilient supply chain with a clear protocol for responding to similar incidents in the future.”

15. What is your method for determining the optimal number of facilities in a distribution network?

Determining the optimal number of facilities in a distribution network requires a balance of analytical and strategic thinking, understanding of supply chain management, and the ability to balance cost with service level requirements. They expect you to demonstrate familiarity with quantitative methods and perhaps even specific software tools used for facility location and capacity planning. Your methodology should reflect a deep understanding of not only the mathematical models but also the real-world variables such as market demand, transportation costs, and the ever-present challenge of uncertainty in forecasting.

To respond, outline a structured, step-by-step approach that starts with data collection, including market analysis and demand forecasting. Mention the use of specific mathematical models such as mixed-integer linear programming or heuristic algorithms, if applicable. Emphasize the importance of scenario analysis to test the robustness of your solution against various uncertainties. Highlight your experience with any relevant software tools and the cross-functional collaboration needed to gather inputs and validate assumptions. End with how you would monitor the performance of the distribution network post-implementation to ensure ongoing optimization.

Example: “ In determining the optimal number of facilities in a distribution network, I begin with a comprehensive data collection process, focusing on market analysis, demand forecasting, and cost considerations. This involves understanding the geographical distribution of customers, service level requirements, and transportation costs. I then apply mixed-integer linear programming to model the facility location problem, incorporating constraints such as capacity, budget, and service level agreements.

To ensure the robustness of the solution, I conduct scenario analysis, varying key parameters like demand, costs, and transportation scenarios to evaluate the impact on the network design. This is complemented by sensitivity analysis to identify critical variables that significantly influence the outcome. I leverage software tools like CPLEX or Gurobi for solving the optimization models and employ visualization tools for presenting the results to stakeholders. Post-implementation, I monitor key performance indicators such as delivery times, costs, and service levels to ensure the network remains optimal over time, making adjustments as necessary based on real-world performance data and changing market conditions.”

16. How have you incorporated sustainability considerations into operations research projects?

Sustainability adds an essential layer of complexity to operations research—requiring a balance between efficiency, cost, and environmental impact. Employers are increasingly aware of their corporate social responsibility and the long-term viability of their operations. They seek professionals who can integrate eco-friendly practices while maintaining or improving operational performance. This question delves into a candidate’s ability to innovate within constraints and their commitment to future-proofing business practices by reducing carbon footprints, conserving resources, and adhering to regulations, which is becoming a competitive advantage in many industries.

When responding to this question, articulate specific examples where you’ve evaluated the environmental aspects of operational decisions. Describe the methodologies you employed to assess the sustainability impact, such as life cycle analysis or carbon accounting, and how these considerations influenced the final recommendations. Highlight any successful outcomes, like reductions in waste, energy savings, or improved supply chain sustainability. Your answer should demonstrate a strategic mindset that values long-term ecological and economic benefits and showcases your ability to be a forward-thinking problem-solver in operations research.

Example: “ In a recent project focused on supply chain optimization, sustainability was a core consideration. We employed a multi-objective optimization framework that balanced cost efficiency with environmental impact. By integrating life cycle analysis, we quantified the carbon footprint of various supply chain configurations. This allowed us to identify strategies that not only reduced logistics costs but also minimized greenhouse gas emissions. For instance, we optimized routing and load consolidation, which led to a significant reduction in the number of truck deliveries and, consequently, a notable decrease in carbon emissions.

In another project, we addressed the issue of waste production in manufacturing processes. Using a combination of predictive analytics and simulation, we developed a model to forecast waste generation under different production scenarios. This model informed the design of a closed-loop system where waste was repurposed within the production cycle, leading to both material savings and a reduction in the environmental burden. These projects underscored the value of incorporating sustainability into operations research, not only to comply with regulations and corporate social responsibility policies but also to drive innovation and long-term cost savings.”

17. Provide an instance where heuristic methods outperformed exact algorithms in your work.

Heuristic methods can provide sufficiently good solutions much more rapidly than theoretical and exact algorithms in many real-world scenarios, especially when dealing with uncertainty or incomplete information. Interviewers are looking for evidence that you can balance the need for precision with the need for timeliness and efficiency. They want to know if you can make sound judgments about when it’s appropriate to trade off accuracy for speed, demonstrating flexibility and practical problem-solving skills.

When responding, it’s crucial to describe a specific situation where the time-sensitive nature of a problem necessitated a heuristic approach. Explain the context briefly, the constraints you were under, and the rationale behind choosing a heuristic method. Discuss the outcome and why it was successful, highlighting how the speed or simplicity of the heuristic provided a significant advantage. If possible, quantify the benefits in terms of time saved, costs reduced, or increased efficiency. This will show your ability to think critically and apply theoretical knowledge pragmatically.

Example: “ In a project focused on optimizing the routing of a fleet of delivery vehicles under tight operational deadlines, the use of exact algorithms like the branch-and-cut approach to solve the vehicle routing problem (VRP) proved to be computationally infeasible due to the size of the fleet and the dynamic nature of the delivery requirements. The time-sensitive nature of the deliveries meant that solutions needed to be generated within minutes, not hours.

To address this, a heuristic method based on the Clarke-Wright Savings algorithm was implemented, which provided good quality solutions in a fraction of the time required by exact methods. By prioritizing the most significant savings in distance first and allowing for some flexibility in route construction, the heuristic was able to quickly generate feasible routes that were within 10% of the cost identified by the best-known solutions for static instances of the problem.

The heuristic’s performance was particularly notable during peak operational hours when delivery orders were continuously coming in, requiring real-time adjustments to the routes. The adaptability and speed of the heuristic method allowed for an increase in on-time deliveries by 15% and a reduction in overall operational costs by 8%, demonstrating its effectiveness over exact algorithms in a real-world, time-constrained environment.”

18. In what scenario did you apply Markov Decision Processes, and what were the outcomes?

Markov Decision Processes (MDPs) are a mathematical framework used to model decision-making where outcomes are partly random and partly under the control of a decision maker. They are particularly useful in operations research for formulating sequential decision problems under uncertainty. By asking about your experience with MDPs, interviewers are looking for evidence that you can apply theoretical models to real-world situations, handle randomness in process outcomes, and possess the analytical skills to optimize these scenarios for the best possible results.

When responding to this question, you should outline a specific situation where you utilized MDPs, perhaps in inventory management, supply chain optimization, or another area relevant to operations research. Describe the context briefly, the complexity of the decisions to be made, and how you modeled the problem using MDPs. Highlight the steps you took to define states, actions, and rewards, and how you determined the optimal policy. Conclude with the outcomes, focusing on the success of your solution in achieving the desired objectives and any lessons learned through the process.

Example: “ In a project aimed at optimizing inventory management for a retail chain, I applied Markov Decision Processes to model the restocking policies for high-turnover products. The challenge was to balance the costs associated with holding inventory against the potential lost sales due to stockouts. I defined the states based on inventory levels, actions as reorder quantities, and rewards as the profit minus holding and stockout costs.

Using dynamic programming, I computed the value function for each state and determined the optimal policy that maximized long-term expected rewards. This policy provided clear restocking guidelines that adapted to varying demand patterns. The implementation of this MDP-based policy resulted in a 15% reduction in inventory costs while maintaining customer service levels. The success of the project highlighted the importance of accurately modeling the environment and reward structure to capture the nuances of inventory dynamics.”

19. How do you ensure stakeholder buy-in when presenting complex analytical findings?

Translating complex findings into actionable insights that stakeholders can understand and support is a critical skill for operations research analysts. Stakeholders often come from diverse backgrounds and may not have the technical proficiency to grasp intricate data models or statistical jargon. Therefore, the question digs into the candidate’s competency in communication, persuasion, and their approach to making data-driven recommendations accessible and compelling to a non-technical audience. It also touches on the candidate’s understanding of the organization’s culture and decision-making processes, and their ability to foster collaboration and consensus among key players.

When responding to this question, it’s crucial to emphasize your communication strategy. Outline how you tailor your presentation to the audience’s level of expertise, focusing on the implications of the findings rather than the technical details. Discuss how you use visual aids and storytelling to make your points clearer and more persuasive. Mention any experience you have in facilitating workshops or discussions that help stakeholders understand the analysis and its benefits. It’s also beneficial to share examples of how you’ve previously secured buy-in by linking analytical findings to strategic objectives or by demonstrating potential ROI, thus aligning your work with the stakeholders’ goals and interests.

Example: “ To ensure stakeholder buy-in when presenting complex analytical findings, I prioritize translating technical details into strategic implications. Recognizing that stakeholders are often more interested in the ‘what’ and ‘why’ rather than the ‘how’, I focus on how the findings align with our overarching strategic goals. By presenting data through visual aids and narratives, I make the results accessible and relevant to their interests. For instance, I might use a combination of charts, graphs, and infographics to depict trends and patterns that directly impact decision-making processes.

I also actively engage stakeholders in discussions to facilitate a deeper understanding of the analysis. This involves framing the findings within the context of potential ROI or cost-saving measures, which directly speaks to the interests of the audience. By demonstrating the tangible benefits, I help stakeholders see the value of the analytical work. In previous experiences, I’ve found that interactive sessions, where stakeholders can ask questions and explore the data with guided support, have been particularly effective in securing their buy-in. This approach not only builds confidence in the analytical process but also fosters a collaborative environment where stakeholders feel invested in the outcomes.”

20. What has been your biggest challenge in aligning operations research recommendations with business goals?

Navigating the complex interplay between theoretical models and the practical realities of business objectives is a challenge for operations research analysts. Employers ask this question to understand how candidates navigate the often complex interplay between theoretical models and the practical, sometimes messy, realities of business objectives. They want to ensure that candidates can translate data-driven insights into actionable strategies that resonate with stakeholders and support the overarching mission of the company.

To respond effectively, draw upon a specific instance where you faced such a challenge. Detail the operations research methods you employed and how the initial recommendations did not fully align with business objectives. Then, demonstrate your problem-solving skills and adaptability by explaining the steps you took to bridge the gap. This might include revisiting the analysis with different parameters, seeking cross-departmental input, or even refining the business goals themselves in light of new insights. Your answer should underscore your ability to balance analytical rigor with business acumen and your commitment to collaborative problem-solving.

Example: “ One of the most significant challenges I encountered was during a project aimed at optimizing the supply chain network of a manufacturing company. The initial operations research analysis suggested a radical restructuring of the supply chain to minimize costs, including the closure of several regional distribution centers. While this was optimal from a purely mathematical standpoint, it did not take into account the strategic importance of market presence and the potential impact on customer service levels, which were core to the business’s value proposition.

To address this, I conducted a sensitivity analysis to understand the trade-offs between cost optimization and service level objectives. I also facilitated workshops with stakeholders from sales, marketing, and customer service to incorporate their insights into the operational models. By adjusting the parameters to reflect the qualitative aspects of the business strategy and running multi-objective optimization scenarios, I was able to propose a revised solution. This new approach balanced cost savings with the need for market responsiveness, ultimately aligning the operations research recommendations with the broader business goals. It underscored the importance of integrating domain expertise and stakeholder perspectives into the analytical process to ensure that recommendations are both practically viable and strategically sound.”

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300+ top operations research mcqs and answers quiz, operations research multiple choice questions.

1. The main objective of OR is to provide a ___, ___ to the decision-makers. Answer: Scientific basis

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2. OR employs a team of ___ from ___ ___. Answer: Scientists, different disciplines

3. Mention two applications of OR. Answer: Industry Planning

4. How can a hospital benefit from the application of OR methods? Answer: To solve waiting for problems

5. OR ___ inter-disciplinary approach. Answer: Imbibes

6. OR increases the effectiveness of ___ ability. Answer: Decision making

7. OR gives a qualitative solution Answer: True

8. One of the OR phases is the Action phase Answer: True

9. Diagram belongs to the physical model Answer: True

10. Allocation problems are represented by the iconic model Answer: False

11. OR methodology consists of definition, solution and validation only. Answer: False

12. The interaction between the OR team and Management reaches peak level in the implementation phase. Answer: False

13. OR imbibes ___ team approach. Answer: Inter-disciplinary

14. Linear programming is the tool of ___. Answer: OR

15. The three phases of OR are ___. Answer: Judgement phase, Research phase & Action phase

16. To solve any problem through the OR approach the first step is ___. Answer: Define the problem

17. ___ represents a real-life system. Answer: Model

18. ___ represents the controlled variables of the system Answer: Parameters

19. Both the objective function and constraints are expressed in ___ forms. Answer: Linear

20. LPP requires existence of ___, ___, ___ and ___. Answer: An alternate course of action

21. Solution of decision variables can also be ____. Answer: Fractious

22. One of the characteristics of canonical form in the objective function must be of maximisation. Answer: True

23. 2x – 3y ≤ 10 can be written as -2x + 3y ≥-10 Answer: True

24. The collection of all feasible solutions is known as the ___ region. Answer: Feasible

25. A linear inequality in two variables is known as a ___. Answer: Half-plan

26. The feasible region is a convex set Answer: True

27. The optimum value occurs the anywhere infeasible region Answer: False

28. We add a surplus variable for “≤” of constraint. Answer: False

29. The right-hand side element of each constraint is non-negative. Answer: True

30. A basic solution is said to be a feasible solution if it satisfies all constraints. Answer: True

31. If one or more values of the basic variable are zero then the solution is said to be degenerate. Answer: True

32. The right-hand side element of each constraint is non-negative. Answer: Yes

33. The key column is determined by Zj – Cj row. Answer: Yes

34. Pivotal element lies on the crossing of the key column and key row. Answer: No

35. The negative and infinite ratios are considered for determining key row. Answer: Yes

36. The value of artificial value is “M”. Answer: Yes

37. Artificial variables enter as basic variables. Answer: Yes

38. Dual LPP always reduces the amount of computation. Answer: No

39. It is possible to reverse the dual LPP to primal LPP Answer: Yes

40. The coefficients of decision variables in the objective function become quantities on the right-hand side of ___. Answer: Dual

41. “≤” constraints changes to ___ type in dual LP. Answer: ≥

42. For every LPP, there exists a unique ___ problem. Answer: Dual

43. Dual variables represent the worth or unit of a resource. Answer: True

44. Optimality is reached when the resources are not fully utilised. Answer: False

45. At the optimum level the relationship holds as a strict equation Answer: True

46. Sensitivity analysis is carried out on ___ simplex table. Answer: Final

47. It helps us to study the effect of changes in ___ ___ in the objective function. Answer: Resource, levels

48. The results of sensitive analysis establish ___ and ___ ___ for input parameters value. Answer: Upper, lower, bounce

49. Transportation problems are a special type of ___. Answer: LPP

50. The number of rows and columns need not always be ___. Answer: Equal

51. Transportation problem develops a schedule at ___ and ___. Answer: Minimum cost

52. In transportation problems, ∑ai = ∑bj is a sufficient and necessary condition for getting a feasible solution. Answer: Yes

53. Transportation problems can also be solved by the simplex method. Answer: Yes

54. Matrix-minima method gives the optimum solution. Answer: No

55. In matrix-minima method, you start allocating from the left-top cell of the table. Answer: False

56. In Vogel‟s approximation method, you first construct penalty and then start allocating. Answer: True

57. North-west corner rule gives the optimum solution. Answer: False

58. Vogel‟s approximation method gives a solution near to the optimum solution. Answer: True

59. All the values of ΔCij – ui – vj should be ___ or ___ for the solution to be optimum. Answer: zero

60. In unbalanced transportation problem ∑ai is ___ ___ to ∑bj. Answer: Not equal to

61. If the number of allocation is less than ___ then it is said to be a degenerate transportation problem. Answer: m + n – 1

62. In an AP, the constraints are of equality type. Answer: True

63. The number of facilities should be equal to the number of resources. Answer: True

64. The decision variables can take on any value. Answer: False

65. In the Hungarian method, you prepare the row-reduced matrix. Answer: True

66. The number of assignments should be equal to the number of rows for an optimum solution. Answer: True

67. There can be more than one allocation in a row. Answer: False

68. In unbalanced AP, the number of rows ___ to the number of columns. Answer: ≠

69. Hungarian method cannot be applied directly to ___ problem. Answer: Maximisation problem

70. If some jobs cannot be assigned to some machines, then it is called ___ assignment problem. Answer: Infeasible

71. In the travelling salesman problem, the objective is to visit each city ___ ___. Answer: Only once

72. Salesman has ___ different sequences if n is the number of cities to be visited. Salesman Answer: (n-1)

73. Integer programming is applied to problems that involve discrete variables. Answer: True

74. If some variables take on non-negative values, then it is known as pure IPP. Answer: False

75. An optimum solution to IPP is first obtained by using ___. Answer: Simplex method

Operations Research MCQs

1. Operations research is the application of ____________methods to arrive at the optimal Solutions to the problems.

• a and b both

2.    In operations research, the ——————————are prepared for situations.

• mathematical models
• physical models diagrammatic
• diagrammatic models

3.    Operations management can be defined as the application of ————-to a problem within a system to yield the optimal solution.

• Suitable manpower
• mathematical techniques, models, and tools
• Financial operations

4.   Operations research is based upon collected information, knowledge and advanced study of various factors impacting a particular operation. This leads to more informed —-

• Management processes
• Decision making

5.    OR can evaluate only the effects of ————————————————–.

• Personnel factors.
• Financial factors
• Numeric and quantifiable factors.

6 Which of the following is not the phase of OR methodology?

• Formulating a problem
• Constructing a model
• Establishing controls
• Controlling the environment

7 – The  objective  function  and  constraints  are  functions  of  two  types  of  variables,

_______________ variables and ____________ variables.

• Positive and negative
• Controllable and uncontrollable
• Strong and weak
• None of the above

8 – Operations research was known as an ability to win a war without really going in to ____

• Battle field
• The opponent
• Both A and B

9 – Who defined OR as scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control?

• Morse and Kimball (1946)
• P.M.S. Blackett (1948)
• E.L. Arnoff and M.J. Netzorg

10 – OR has a characteristics that it is done by a team of

• Mathematicians
• All of the above

MCQ on Operations Research

11 – A solution can be extracted from a model either by

• Conducting experiments on it
• Mathematical analysis
• Diversified Techniques

12 OR uses models to help the management to determine its _____________

13 What have been constructed from OR problems an methods for solving the models that are available in many cases?

• Scientific Models
• Mathematical Models

14 -Which technique is used in finding a solution for optimizing a given objective, such as profit maximization or cost reduction under certain constraints?

• Quailing Theory
• Waiting Line
• Linear Programming

15 -What enables us to determine the earliest and latest times for each of the events and activities and thereby helps in the identification of the critical path?

• Programme Evaluation
• Review Technique (PERT)
• Deployment of resources

16 – OR techniques help the directing authority in optimum allocation of various limited resources like_____

• Man and machine
• all of the above

17 -The Operations research technique which helps in minimizing total waiting and service costs is

• ueuing Theory
• Decision Theory

18 .What is the objective function in linear programming problems?

• A constraint for available resource
• An objective for research and development of a company
• A linear function in an optimization problem
• A set of non-negativity conditions

19 – .Which statement characterizes standard form of a linear programming problem?

• Constraints are given by inequalities of any type
• Constraints are given by a set of linear equations
• Constraints are given only by inequalities of >= type
• Constraints are given only by inequalities of <= type

20 – Feasible solution satisfies __________

• Only constraints
• only non-negative restriction
• [a] and [b] both
• [a],[b] and Optimum solution

21 – In Degenerate solution value of objective function _____________.

• increases infinitely
• basic variables are nonzero
• decreases infinitely
• One or more basic variables are zero

22 – Minimize Z = ______________

• maximize(Z)
• maximize(-Z)
• none of the above

23 -In graphical method the restriction on number of constraint is _________

• not more than 3

24 -In graphical representation the bounded region is known as _________ region.

• basic solution
• feasible solution

25 -Graphical optimal value for Z can be obtained from

• Corner points of feasible region
• Both a and c
• corner points of the solution region

26 -In LPP the condition to be satisfied is

• Constraints have to be linear
• Objective function has to be linear
• both a and b

27 – Identify the type of the feasible region given by the set of inequalities

x – y <= 1

x – y >= 2

where both x and y are positive.

• A rectangle
• An unbounded region
• An empty region

28 -Consider the given vectors: a(2,0), b(0,2), c(1,1), and d(0,3). Which of the following vectors are linearly independent?

• a)  b, and c are independent
• a, b, and d are independent
• a and c are independent
• b and d are independent

Q29 – Consider the linear equation

x1 + 3 x2 – 4 x3 + 5 x4 = 10

How many basic and non-basic variables are defined by this equation?

• One variable is basic, three variables are non-basic
• Two variables are basic, two variables are non-basic
• Three variables are basic, one variable is non-basic
• All four variables are basic

30 – The objective function for a minimization problem is given by

z = 2 x1 – 5 x2 + 3 x3

The hyperplane for the objective function cuts a bounded feasible region in the space (x1,x2,x3). Find the direction vector d, where a finite optimal solution can be reached.

• d(-2,-5,-3)

31 – In game theory, the outcome or consequence of a strategy is referred to as the

• end-game strategy.

32-  Operations Research approach is?

• multi-disciplinary
•  collect essential data

33 – Operation research approach is typically based on the use of _____

• physical model
•  mathematical model
•  iconic model
•  descriptive model

34 – Mathematical model of linear programming problem is important because ________

• it helps in converting the verbal description and numerical data into mathematical expression
• decision makers prefer to work with formal models
•  it captures the relevant relationship among decision factors
•  it enables the use of algebraic technique

35 –  In Program Evaluation Review Technique for an activity, the optimistic time 2, the pessimistic time is 12 and most-likely time is 4. What is the expected time?

36 – Graphical method of linear programming is useful when the number of decision variable are __________.

37 – A feasible solution to a linear programming problem _______________.

• must satisfy all the constraints of the problem simultaneously
•  need not satisfy all of the constraints, only some of them
•  must be a corner point of the feasible region.
•  must optimize the value of the objective function

38 – Utilization factor is also known as ___________.

• Traffic intensity
• Kendals notation
• Row minima method
• Unbalanced assignment problem

39 –  While solving a linear programming problem in feasibility may be removed by _________.

• adding another constraint
•  adding another variable
•  removing a constraint
• removing a variable

40 –  In the optimal simplex table, Zj-Cj=0 value indicates _____________.

• alternative solution
•  bounded solution
•  infeasible solution
•  unbounded solution

41 –  If all aij values in the entering variable column of the simplex table are negative, then ___________.

• there are multiple solutions
•  there exist no solution
•  solution is degenerate
•  solution is unbounded

42 –  If an artificial variable is present in the basic variable column of optimal simplex table, then the solution is ___________.

• alternative
• no solution

43 – For any primal problem and its dual ______________.

• optimal value of objective function is same
• primal will have an optimal solution iff dual does too
•  both primal and dual cannot be infeasible
•  dual will have an optimal solution iff primal does too

44 – Principle of complementary slackness states that ____________.

• primal slack*dual main=0
•  primal main+dual slack=0
• primal main+dual surplus=0
•  dual slack*primal main not equal to zero

45 – If primal linear programming problem has a finite solution, then dual linear programming problem should have ____________.

• finite solution
•  infinite solution
• bounded solution
•  alternative solution

46 – The initial solution of a transportation problem can be obtained by applying any known method. How-ever, the only condition is that __________.

• the solution be optimal
•  the rim conditions are satisfied
•  the solution not be degenerate
• the few allocations become negative

47 -The dummy source or destination in a transportation problem is added to ______.

• satisfy rim conditions
• prevent solution from becoming degenerate
• ensure that total cost does not exceed a limit

48 – Which of the following methods is used to verify the optimality of the current solution of the transportation problem ____________.

• Modified Distribution Method
• Least Cost Method
•  Vogels Approximation Method
•  North West Corner Rule

49 – An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost be equal to the number of ________.

• rows or coloumns
• rows and coloumns
• rows+columns- 1
• rows-columns

50 –  Maximization assignment problem is transformed into a minimization problem by ________.

• adding each entry in a column from the maximum value in that column
•  subtracting each entry in a column from the maximum value in that column
• subtracting each entry in the table from the maximum value in that table
•  adding each entry in the table from the maximum value in that table

51 –  To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are ___________.

52 – An artificial variable leaves the basis means, there is no chance for the ________ variable to enter once again.

53 –  Simplex method was designed by ___________.

54 – Dual Simplex Method was introduced by ____________.

55 – The cell with allocation can be called ___________ .

•  Empty cell
•  Basic cell
• Non-basic cell

56 – The cell without allocation is called __________.

•  Non-basic cell
• Basic solution

57 – Service mechanism in a queuing system is characterized by ___

• customers behavior
•  servers behavior
•  customers in the system
•  server in the system

58 – The problem of replacement is felt when job performing units fail ____

• suddenly and gradually
•  neither gradually nor suddenly

59 – Least Cost Method is also known as __________.

• North West Corner Method
•  Matrix Minima Method
•  Row Minima method
• Coloumn Minima method

60 – The objective of network analysis is to ___________.

• minimize total project duration
•  minimize total project cost
•  minimize production delays, interruption and conflicts
•  maximize total project duration

61 – A activity in a network diagram is said to be __________ if the delay in its start will further delay the project completion time.

• forward pass
• backward pass
• non critical

62 – A strategy that is best regardless of what rival players do is called

• first-mover advantage.
• a Nash equilibrium strategy.
• tit-for-tat.
• a dominant strategy.

63 – A game that involves interrelated decisions that are made over time is a

• sequential game .
• repeated game.
• zero-sum game.
• nonzero-sum game.

64 – A game that involves multiple moves in a series of identical situations is called a

• sequential game.
• repeated game .

65 – Sequential games can be solved using

• dominated strategies.
• backward induction
• risk averaging.

66 – A firm that is threatened by the potential entry of competitors into a market builds excess production capacity. This is an example of

• a prisoners’ dilemma.
• a credible threat.

67 – What is the fundamental purpose of game theory?

• To analyse decision-making
• To analyse strategic interactions
• To predict decision outcome
• To predict firm behaviour

68 – An assignment problem is considered as a particular case of a transportation problem because

• The number of rows equals columns
• All xij= 0 or 1
• All rim conditions are 1

69 – An optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of

• Rows or columns
• Rows & columns
• Rows + columns –1 d.

70 – While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to

• Minimize total cost of assignment
• Reduce the cost of assignment to zero
• Reduce the cost of that particular assignment to zero

71 – The method used for solving an assignment problem is called

• Reduced matrix method
• MODI method
• Hungarian method

72 – The purpose of a dummy row or column in an assignment problem is to

• Obtain balance between total activities &total resources
• Prevent a solution from becoming degenerate
• Provide a means of representing a dummy problem

73 – Maximization assignment problem is transformed into a minimization problem by

• Adding each entry in a column from the maximization value in that column
• Subtracting each entry in a column from the maximum value in that column
• Subtracting each entry in the table from the maximum value in that table
• Any one of the above

74 – If there were n workers & n jobs there would be

• n! solutions
• (n-1)! solutions
• (n!)nsolutions
• n solutions

75 -An assignment problem can be solved by

• Simplex method
• Transportation method
• Both a & b
• none of above

76 – The assignment problem

• Requires that only one activity be assigned to each resource
• Is a special case of transportation problem
• Can be used to maximize resources

Q77 – An assignment problem is a special case of transportation problem, where

• Number of rows equals number of columns
• Values of each decision variable is either 0 or 1

78 – Every basic feasible solution of a general assignment problem, having a square pay-off matrix of order, n should have assignments equal t

79 – To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are

80 – The Hungarian method for solving an assignment problem can also be used to solve

• A transportation problem
• A travelling salesman problem
• A LP problem

MCQ on Operations Research 

81  An optimal solution of an assignment problem can be obtained only if

• Each row & column has only one zero element
• Each row & column has at least one zero element
• The data is arrangement in a square matrix

82 – Which method usually gives a very good solution to the assignment problem?

• northwest corner rule
• Vogel’s approximation method

d) stepping-stone method

83 – The northwest corner rule requires that we start allocating units to shipping routes in the: middle cell.

• Lower right corner of the table.
• Upper right corner of the table.
• Highest costly cell of the table.
• Upper left-hand corner of the table.

84 – The table represents a solution that is:

• an initial solution
• degenerate.

85 – Which of the following is used to come up with a solution to the assignment problem?

• northwest corner method
• stepping-stone method

86 – What is wrong with the following table?

• The solution is infeasible.
• The solution is degenerate.
• The solution is unbounded.
• The solution is inefficient in that it is possible to use fewer routes.

87 –  The solution presented in the following table is

• infeasible.

88 – The solution shown was obtained by Vogel’s approximation. The difference between the objective function for this solution and that for the optimal is

89 – Optimal solution of an assignment problem can be obtained only if

90 – In assignment problem of maximization, the objective is to maximise

• optimization

91 – What is the difference between minimal cost network flows and transportation problems?

• The minimal cost network flows are special cases of transportation problems
• The transportation problems are special cases of the minimal cost network flows
• There is no difference
• The transportation problems are formulated in terms of tableaus, while the minimal cost network flows are formulated in terms of graphs

92 – With the transportation technique, the initial solution can be generated in any fashion one chooses. The only restriction is that

• the edge constraints for supply and demand are satisfied.
• the solution is not degenerate.
• the solution must be optimal.
• one must use the northwest-corner method

93 – The purpose of the stepping-stone method is to

• develop the initial solution to the transportation problem.
• assist one in moving from an initial feasible solution to the optimal solution.
• determine whether a given solution is feasible or not.
• identify the relevant costs in a transportation problem.

94 – The purpose of a dummy source or dummy destination in a transportation problem is to

• prevent the solution from becoming degenerate.
• obtain a balance between total supply and total demand.
• make certain that the total cost does not exceed some specified figure.
• provide a means of representing a dummy problem.

94 – Which of the following is NOT needed to use the transportation model?

• the cost of shipping one unit from each origin to each destination
• the destination points and the demand per period at each
• the origin points and the capacity or supply per period at each

95 – Which of the following is a method for improving an initial solution in a transportation problem?

• northwest-corner
• intuitive lowest-cost
• southeast-corner rule
• stepping-stone

96 – The transportation method assumes that

• there are no economies of scale if large quantities are shipped from one source to one destination
• the number of occupied squares in any solution must be equal to the number of rows in the table plus the number of columns in the table plus 1.
• there is only one optimal solution for each problem.
• the number of dummy sources equals the number of dummy destinations.

97 – An initial transportation solution appears in the table.

• Yes, this solution can be improved by $50.
• Yes, this solution can be improved by $100.
• No, this solution is optimal.
• Yes, the initial solution can be improved by $10.

98 – What is the cost of the transportation solution shown in the table?

99 – Which statement regarding this transportation table is best?

• This solution can be improved by shipping from C to X.
• This solution would be improved by shipping from B to W.
• This solution was developed using the northwest corner rule.

100 – Which of these statements about the stepping-stone method is best?

• A dummy source and destination must be added if the number of rows plus columns minus 1 is not equal to the number of filled squares.
• Only squares containing assigned shipments can be used to trace a path back to an empty square.
• An improvement index that is a net positive means that the initial solution can be improved.
• Only empty squares can be used to trace a path back to a square containing an assigned shipment

101 – In  a  transportation  problem,  we  must  make  the  number  of  _______  and______ equal.

• destinations; sources
• units supplied; units demanded
• columns; rows
• positive cost coefficients; negative cost coefficients

102 – _________ or __________ are used to “balance” an assignment or transportation problem.

• Destinations; sources
• Units supplied; units demanded
• Dummy rows; dummy columns
• Large cost coefficients; small cost coefficients

103 – The net cost of shipping one unit on a route not used in the current transportation problem solution is called the __________.

• change index
• Improvement index

104 – The procedure used to solve assignment problems wherein one reduces the original assignment costs to a table of opportunity costs is called __________.

• matrix reduction
• northwest reduction

105 – The method of finding an initial solution based upon opportunity costs is called__________.

• the northwest corner rule
• Vogel’s approximation
• Johanson’s theorem
• Flood’s technique

106 – An assignment problem can be viewed as a special case of transportation problem in which the capacity from each source is _______ and the demand at each destination is________.

• Infinity; infinity

107 – _______ occurs when the number of occupied squares is less than the number of rows plus

• Infeasibility
• Unboundedness

108 – Both transportation and assignment problems are members of a category of LP problems called ______.

• shipping problems
• logistics problems
• generalized flow problems
• network flow problem

109 – The equation Ri + Kj = Cij is used to calculate __________.

• an improvement index for the stepping-stone method
• the opportunity costs for using a particular route
• the MODI cost values (Ri, Kj)
• the degeneracy index

110 – In case of an unbalanced problem, shipping cost coefficients of ______ are assigned to each created dummy factory or warehouse.

• very high positive costs
• very high negative costs

111 – The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that

• The solution be optimal
• The rim conditions are satisfied
• The solution not be degenerate

112 – The dummy source or destination in a transportation problem is added to

• Satisfy rim conditions
• Prevent solution from becoming degenerate
• Ensure that total cost does not exceed a limit

113 – The occurrence of degeneracy while solving a transportation problem means that

• Total supply equals total demand
• The solution so obtained is not feasible
• The few allocations become negative

114 – An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is:

• Positive & greater than zero
• Positive with at least one equal to zero
• Negative with at least one equal to zero

115 – One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that

• It is complicated to use
• It does not take into account cost of transportation
• It leads to a degenerate initial solution

116 – The solution to a transportation problem with ‘m’ rows (supplies) & ‘n’ columns (destination) is feasible if number of positive allocations are

117 – If an opportunity cost value is used for an unused cell to test optimality, it should be

• Equal to zero
• Most negative number
• Most positive number

118 – During an iteration while moving from one solution to the next, degeneracy may occur when

• The closed path indicates a diagonal move
• Two or more occupied cells are on the closed path but neither of them represents a corner of the path.
• Two or more occupied cells on the closed path with minus sign are tied for lowest circled value
• Either of the above

119 – The large negative opportunity cost value in an unused cell in a transportation table is chosen to improve the current solution because

• It represents per unit cost reduction
• It represents per unit cost improvement
• It ensure no rim requirement violation

120 – The smallest quantity is chosen at the corners of the closed path with negative sign to be assigned at unused cell because

• It improve the total cost
• It does not disturb rim conditions
• It ensure feasible solution

121 – When total supply is equal to total demand in a transportation problem, the problem is said to be

122 – Which of the following methods is used to verify the optimality of the current solution of the transportation problem

• Least cost method
• Modified distribution method

123 – The degeneracy in the transportation problem indicates that

• Dummy allocation(s) needs to be added
• The problem has no feasible solution
• The multiple optimal solution exist
• a & b but not c

124 – In a transportation problem, when the number of occupied routes is less than the number of rows plus the number of columns -1, we say that the solution is:

• Unbalanced.
• Infeasible.
• Degenerate.

125 – The only restriction we place on the initial solution of a transportation problem is that: we must have nonzero quantities in a majority of the boxes.

• all constraints must be satisfied.
• demand must equal supply.
• we must have a number (equal to the number of rows plus the number of columns minus one) of boxes which contain nonzero quantities.

126 – The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that

• the rim condition are satisfied
• the solution not be degenerate

127 – The dummy source or destination in a transportation problem is added to

• satisfy rim condition

128 – The occurrence of degeneracy while solving a transportation problem means that

• total supply equals total demand
• the solution so obtained is not feasible

129 – An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused routes of transportation is:

• positive and greater than zero
• positive with at least one equal to zero
• negative with at least one equal to zero

130 – One disadvantage of using North-West Corner Rule to find initial solution to the transportation problem is that

• it is complicated to use
• it does not take into account cost of transportation
• it leads to degenerate initial solution

Operations Research Objective Questions with Answers Pdf Download

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