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# Operations Research Viva Questions and Answers

## What is Operations Research (OR)?

Operations Research (OR) is a scientific approach to problem-solving that involves the use of mathematical models, statistical analysis, and optimization techniques to help organizations make better decisions.

## What are the key elements of an Operations Research model?

The key elements of an OR model are decision variables, objective function, and constraints. Decision variables are the unknown quantities that we want to determine. The objective function is the function that we want to maximize or minimize. Constraints are the limitations or restrictions that we have to satisfy.

## What are the advantages of using OR techniques in decision-making?

The advantages of using OR techniques in decision-making are: (i) OR provides a systematic approach to problem-solving, (ii) OR helps in identifying the best possible solution among the alternatives, (iii) OR helps in optimizing the use of resources, (iv) OR provides a quantitative basis for decision-making, (v) OR helps in reducing uncertainty and risk, and (vi) OR provides a structured framework for decision-making.

## What are the different types of optimization techniques used in OR?

The different types of optimization techniques used in OR are linear programming, nonlinear programming, integer programming, dynamic programming, and network optimization.

## What is the difference between sensitivity analysis and shadow prices in linear programming?

Sensitivity analysis is used to determine how changes in the objective function coefficients or the right-hand side values of the constraints affect the optimal solution. Shadow prices, on the other hand, are the marginal values of the constraints. They indicate the increase in the objective function value associated with a unit increase in the right-hand side value of the constraint.

## What is the difference between a feasible solution and an optimal solution?

A feasible solution is a solution that satisfies all the constraints of the problem. An optimal solution is a feasible solution that gives the best possible value of the objective function.

## What is the difference between a deterministic model and a stochastic model?

A deterministic model is a model where all the parameters are known with certainty. A stochastic model is a model where some of the parameters are subject to random variation.

## What is the difference between simulation and optimization?

Simulation is a technique used to model the behavior of a system under different scenarios. Optimization is a technique used to find the best possible solution among the alternatives.

## What is the difference between a single-criterion decision problem and a multi-criterion decision problem?

A single-criterion decision problem is a problem where there is only one objective function that we want to maximize or minimize. A multi-criterion decision problem is a problem where there are multiple objectives that we want to satisfy simultaneously.

## What is the importance of sensitivity analysis in decision-making?

Sensitivity analysis is important in decision-making because it helps in identifying the critical parameters of the model that have the most significant impact on the optimal solution. This information is crucial for decision-makers because it helps them to understand the risks associated with the decision and to develop contingency plans if necessary.

## What is the difference between a deterministic model and a probabilistic model?

A deterministic model is a model that assumes all input parameters are known with certainty. A probabilistic model, on the other hand, accounts for variability in input parameters by modeling them as random variables.

## What are the main steps involved in the OR modeling process?

The main steps involved in the OR modeling process are:

(i) problem formulation,

(ii) model construction,

(iii) data collection and analysis,

(iv) model validation, and

(v) solution implementation and monitoring.

## What is the difference between a decision variable and a parameter in an OR model?

A decision variable is a variable that the decision-maker can control or set to a particular value to achieve a desired outcome. A parameter, on the other hand, is a fixed value that characterizes some aspect of the problem, such as the cost of a particular resource or the capacity of a machine.

## What are the assumptions made in linear programming?

The assumptions made in linear programming are:

(i) linearity of the objective function and constraints,

(ii) certainty of the parameters,

(iv) divisibility of decision variables, and

(v) non-negativity of decision variables.

## What is the difference between a closed-form solution and a numerical solution?

A closed-form solution is an exact analytical solution to a problem expressed in a mathematical formula or equation. A numerical solution, on the other hand, is a solution that is obtained by solving the problem using computational methods such as linear programming or simulation.

## What is the difference between a model’s sensitivity and its stability?

A model’s sensitivity refers to the degree to which the optimal solution changes in response to changes in the input parameters or constraints. A model’s stability refers to the ability of the model to maintain its optimal solution over time or in different scenarios.

## What is the difference between a heuristic and an exact algorithm?

A heuristic is an algorithm that provides a good solution to a problem but does not guarantee an optimal solution. An exact algorithm, on the other hand, is an algorithm that guarantees to find the optimal solution, but may be computationally expensive or time-consuming.

## What is the difference between a continuous and a discrete decision variable?

A continuous decision variable is a variable that can take on any value within a given range, such as the amount of a resource to be used. A discrete decision variable, on the other hand, is a variable that can only take on a limited number of values, such as the number of machines to be used.

## What is the difference between a static and a dynamic OR model?

A static OR model is a model that assumes that the problem parameters do not change over time. A dynamic OR model, on the other hand, is a model that accounts for changes in problem parameters over time and may require a different solution approach.

## What is the role of sensitivity analysis in OR?

The role of sensitivity analysis in OR is to provide decision-makers with insights into the robustness and reliability of the solution obtained from a model. Sensitivity analysis helps decision-makers understand the impact of changes in problem parameters or constraints on the solution, which can help them make more informed decisions.

## What is the difference between a constraint and an objective function in an OR model?

A constraint is a condition or limitation that must be satisfied in the model, such as a limited availability of resources. An objective function, on the other hand, is the measure of performance that the model is designed to optimize, such as maximizing profits or minimizing costs.

## What is the difference between a single-objective and a multi-objective optimization problem?

A single-objective optimization problem involves optimizing a single objective function, while a multi-objective optimization problem involves optimizing multiple objective functions simultaneously, often with conflicting goals.

## What is the difference between a linear and a nonlinear optimization problem?

A linear optimization problem is one in which the objective function and constraints are linear functions of the decision variables. A nonlinear optimization problem is one in which the objective function or constraints are nonlinear functions of the decision variables.

## What is the difference between a network flow problem and an assignment problem?

A network flow problem involves optimizing the flow of a commodity through a network of interconnected nodes and arcs subject to capacity constraints, while an assignment problem involves assigning a set of tasks to a set of agents subject to constraints on the assignments.

## What is the difference between a simulation and an optimization model?

A simulation model is a model that involves the creation of a mathematical or computational model of a system to understand its behavior over time, often by generating random inputs to the model. An optimization model is a model that involves finding the optimal solution to a specific problem by searching through a set of possible solutions.

## What is the difference between a discrete event simulation and a continuous simulation?

A discrete event simulation models the behavior of a system by simulating individual events or transactions, such as customer arrivals or machine breakdowns. A continuous simulation models the behavior of a system over a continuous range of time, such as a chemical process or a traffic flow.

## What is the difference between a Monte Carlo simulation and a Latin hypercube simulation?

A Monte Carlo simulation involves generating random inputs to a model to estimate the distribution of possible outcomes, while a Latin hypercube simulation involves dividing the input parameter space into equally sized intervals and generating random samples within each interval.

## What is the difference between a decision tree and a Markov chain?

A decision tree is a tool used to model decision-making under uncertainty, while a Markov chain is a tool used to model systems that exhibit a certain type of stochastic behavior, where the future state of the system depends only on its current state and not on its past history.

## What is the difference between a transportation problem and a transshipment problem?

A transportation problem involves transporting goods from a set of sources to a set of destinations subject to capacity and demand constraints, while a transshipment problem involves transporting goods through a network of intermediate nodes or facilities.

## What is the difference between a queuing model and a scheduling model?

A queuing model is used to model the behavior of a system that involves waiting in line, such as a call center or a bank, while a scheduling model is used to model the allocation of resources over time, such as the scheduling of production on a manufacturing line.

## What is the difference between sensitivity analysis and post-optimality analysis?

Sensitivity analysis involves examining how changes in the input data of a model affect the optimal solution, while post-optimality analysis involves examining the properties of the optimal solution itself, such as its uniqueness or stability.

## What is the difference between a heuristic and an exact algorithm?

A heuristic is a method or procedure that is not guaranteed to find the optimal solution but is often used to quickly find a good solution, while an exact algorithm is a method or procedure that is guaranteed to find the optimal solution.

## What is the difference between a local optimum and a global optimum?

A local optimum is a solution that is optimal within a certain region of the solution space, while a global optimum is a solution that is optimal over the entire solution space.

## What is the difference between a feasibility problem and an optimization problem?

A feasibility problem involves finding a feasible solution that satisfies a set of constraints, while an optimization problem involves finding the optimal solution that satisfies a set of constraints and maximizes or minimizes an objective function.

## What is the difference between a dual problem and a primal problem in linear programming?

The primal problem in linear programming involves maximizing or minimizing a linear objective function subject to linear constraints, while the dual problem involves finding the optimal values of a set of dual variables that satisfy a set of constraints derived from the primal problem.

## What is the difference between a mixed integer linear programming problem and a pure integer linear programming problem?

A mixed integer linear programming problem involves optimizing a linear objective function subject to linear constraints where some of the decision variables are restricted to be integers, while a pure integer linear programming problem involves optimizing a linear objective function subject to linear constraints where all decision variables are restricted to be integers.

## What is the difference between a binary variable and a continuous variable in linear programming?

A binary variable is a decision variable that can only take on the values of 0 or 1, while a continuous variable is a decision variable that can take on any value within a certain range.

## What is the difference between a dynamic programming problem and a linear programming problem?

A dynamic programming problem involves optimizing a sequence of decisions over time, while a linear programming problem involves optimizing a set of decisions at a single point in time.

## What is the difference between a genetic algorithm and a simulated annealing algorithm?

A genetic algorithm is a search algorithm inspired by the process of natural selection that uses techniques such as crossover and mutation to generate new candidate solutions, while a simulated annealing algorithm is a search algorithm that uses a probabilistic approach to accept or reject new candidate solutions based on their objective function value and a cooling schedule.

## What is the difference between a heuristic and an exact method in solving an optimization problem?

A heuristic is a method that provides a good, but not necessarily optimal, solution to a problem. An exact method, on the other hand, is a method that guarantees to find the optimal solution, but may require more computation time and resources.

## What is the difference between a primal and a dual linear program?

A primal linear program is a linear programming problem that seeks to maximize or minimize a linear objective function subject to linear constraints, while a dual linear program is a related linear programming problem that seeks to find the optimal value of a dual objective function subject to linear constraints.

## What is the difference between a constraint programming and a mathematical programming approach to solving optimization problems?

A constraint programming approach involves modeling the problem as a set of constraints, and then finding a feasible solution that satisfies all the constraints. A mathematical programming approach involves formulating the problem as an optimization problem, and then finding the optimal solution.

## What is the difference between a sensitivity analysis and a post-optimality analysis in linear programming?

A sensitivity analysis involves determining how changes to the parameters of a linear programming model affect the optimal solution, while a post-optimality analysis involves evaluating the impact of changing the objective function or constraints on the optimal solution.

## What is the difference between an open-loop and a closed-loop control system?

An open-loop control system is a system in which the control input is determined in advance and does not depend on the system’s current state. A closed-loop control system is a system in which the control input depends on the system’s current state, and is adjusted in response to feedback from the system.

## What is the difference between a static and a dynamic optimization problem?

A static optimization problem involves finding the optimal solution at a single point in time, while a dynamic optimization problem involves finding the optimal solution over a range of time periods.

## What is the difference between a combinatorial optimization problem and a continuous optimization problem?

A combinatorial optimization problem involves finding the optimal solution from a finite set of discrete options, while a continuous optimization problem involves finding the optimal solution from an infinite set of continuous options.

## What is the difference between a non-linear programming problem and a quadratic programming problem?

A non-linear programming problem is a generalization of linear programming in which the objective function or constraints are non-linear functions of the decision variables. A quadratic programming problem is a special case of non-linear programming in which the objective function is a quadratic function of the decision variables.

## What is the difference between a constraint and an equation in a mathematical model?

A constraint is a condition or limitation that must be satisfied in the model, while an equation is a mathematical statement that must be true in the model.

## What is the difference between a decision variable and a parameter in an optimization model?

A decision variable is a variable that is under the control of the decision maker and that is used to optimize the model. A parameter is a fixed value that is determined by the problem and is not under the control of the decision maker.

## What is a mixed-integer programming problem?

A mixed-integer programming problem is a type of optimization problem in which some or all of the decision variables are required to be integer valued, while others can take on continuous values.

## What is a metaheuristic optimization algorithm?

A metaheuristic optimization algorithm is a general-purpose optimization algorithm that can be applied to a wide variety of optimization problems. Metaheuristics are often inspired by natural or biological processes, and can be used to find good, but not necessarily optimal, solutions to complex problems.

## What is the difference between a single-objective and a multi-objective optimization problem?

A single-objective optimization problem seeks to find the optimal value of a single objective function, while a multi-objective optimization problem seeks to find the optimal values of multiple objective functions simultaneously.

## What is the difference between a constraint and a bound in an optimization problem?

A constraint is a condition or limitation that must be satisfied in the optimization problem, while a bound is a limit on the values that a decision variable can take.

## What is the difference between a local optimum and a global optimum in an optimization problem?

A local optimum is a solution that is optimal within a particular region of the solution space, while a global optimum is a solution that is optimal over the entire solution space.

## What is a linear programming relaxation?

A linear programming relaxation is a technique for solving an optimization problem in which a non-linear or mixed-integer objective function or constraints are linearized or relaxed to obtain a linear programming problem that can be solved using standard linear programming techniques.

## What is the difference between a non-parametric and a parametric optimization model?

A non-parametric optimization model does not require any assumptions about the distribution or characteristics of the input data, while a parametric optimization model assumes that the input data follows a particular distribution or has certain characteristics.

## What is a network flow problem?

A network flow problem is a type of optimization problem that involves determining the flow of goods or resources through a network of interconnected nodes and edges, subject to capacity constraints and other limitations.

## What is a stochastic optimization problem?

A stochastic optimization problem is a type of optimization problem in which some of the input data or parameters are subject to random or uncertain variations, and the goal is to find a solution that is robust or resilient to these variations.

## What is the difference between an objective function and a decision rule in an optimization problem?

An objective function is a mathematical expression that measures the quality or desirability of a particular solution, while a decision rule is a set of guidelines or rules that determine how to make decisions based on the solution of the optimization problem.

## What is the transportation problem?

The transportation problem is a type of linear programming problem that involves determining the optimal way to transport goods from several sources to several destinations while minimizing the total transportation cost.

## What is the assignment problem?

The assignment problem is a type of linear programming problem that involves assigning a number of tasks to a number of agents in such a way that the total cost or time required to complete all tasks is minimized.

## What is the difference between a decision variable and a parameter in an optimization problem?

A decision variable is a variable that can be controlled or adjusted in order to optimize the objective function, while a parameter is a fixed value that is used in the objective function or constraints.

## What is the difference between a deterministic and a stochastic model?

A deterministic model is a model in which the input data or parameters are known with certainty and the model produces a single, deterministic output, while a stochastic model is a model in which the input data or parameters are subject to random or uncertain variations and the model produces a range of possible outputs.

## What is the difference between a heuristic and an exact optimization algorithm?

A heuristic optimization algorithm is a general-purpose algorithm that is designed to find good, but not necessarily optimal, solutions to optimization problems, while an exact optimization algorithm is a specialized algorithm that is designed to find the exact optimal solution to a specific type of optimization problem.

## What is the difference between a convex and a non-convex optimization problem?

A convex optimization problem is a type of optimization problem in which the objective function and constraints are all convex functions, while a non-convex optimization problem is a type of optimization problem in which the objective function or constraints are non-convex.

## What is the difference between a linear and a non-linear optimization problem?

A linear optimization problem is a type of optimization problem in which the objective function and constraints are all linear functions, while a non-linear optimization problem is a type of optimization problem in which the objective function or constraints are non-linear.

## What is the difference between an interior point and a simplex algorithm for linear programming?

The interior point algorithm is a type of algorithm for solving linear programming problems that moves through the interior of the feasible region to reach the optimal solution, while the simplex algorithm is a type of algorithm for solving linear programming problems that moves along the edges of the feasible region to reach the optimal solution.

## What is a Lagrange multiplier?

A Lagrange multiplier is a scalar value that is used to incorporate constraints into the objective function of an optimization problem, in order to solve constrained optimization problems.

## What is sensitivity analysis in optimization?

Sensitivity analysis in optimization is the process of determining how the optimal solution to an optimization problem changes when the input data or parameters are varied or perturbed. It is used to assess the robustness or sensitivity of the optimal solution to changes in the input data or parameters.

## What is the goal of multi-objective optimization?

The goal of multi-objective optimization is to optimize multiple conflicting objectives simultaneously, in order to find a set of solutions that represents the trade-offs between the different objectives.

## What is the difference between a mixed-integer linear programming (MILP) and a mixed-integer nonlinear programming (MINLP) problem?

A mixed-integer linear programming problem is a type of optimization problem in which some of the decision variables are required to take integer values, while the objective function and constraints are all linear functions. A mixed-integer nonlinear programming problem is a type of optimization problem in which some of the decision variables are required to take integer values, and the objective function or constraints are non-linear.

## What is the purpose of a branch and bound algorithm in optimization?

The purpose of a branch and bound algorithm is to solve mixed-integer optimization problems by systematically exploring the search space of possible solutions, dividing the problem into sub-problems and solving each sub-problem to find the optimal solution.

## What is the difference between a local and a global optimization algorithm?

A local optimization algorithm is a type of algorithm that finds the best solution within a small, local region of the search space, while a global optimization algorithm is a type of algorithm that attempts to find the best solution across the entire search space.

## What is the difference between a continuous and a discrete optimization problem?

A continuous optimization problem is a type of optimization problem in which the decision variables can take on any real-valued value within a specified range, while a discrete optimization problem is a type of optimization problem in which the decision variables can only take on discrete or integer values.

## What is a surrogate model in optimization?

A surrogate model is a simplified mathematical model that is used to approximate the behavior of a more complex, computationally expensive model in order to make optimization more efficient.

## What is the difference between a single-level and a multi-level optimization problem?

A single-level optimization problem is a type of optimization problem in which there is only one objective function and one set of decision variables, while a multi-level optimization problem is a type of optimization problem in which there are multiple objectives and multiple levels of decision-making.

## What is the difference between a combinatorial and a non-combinatorial optimization problem?

A combinatorial optimization problem is a type of optimization problem in which the set of feasible solutions is discrete and finite, while a non-combinatorial optimization problem is a type of optimization problem in which the set of feasible solutions is continuous and infinite.

## What is the purpose of simulation in operations research?

The purpose of simulation in operations research is to model complex systems or processes in order to study their behavior and performance under different scenarios and to evaluate different strategies or policies.

## What is the difference between a deterministic and a stochastic simulation?

A deterministic simulation is a type of simulation that uses fixed input data or parameters and produces a single, deterministic output, while a stochastic simulation is a type of simulation that incorporates random or uncertain input data or parameters and produces a range of possible outputs.

## What is the difference between sensitivity analysis and parametric analysis?

Sensitivity analysis is a method used to assess how changes in the input parameters of a model affect the output, while parametric analysis is a method used to study how the optimal solution changes as a function of a parameter, typically the coefficients of the objective function.

## What is the difference between a feasibility and an optimality condition?

A feasibility condition is a constraint that must be satisfied in order for a solution to be feasible, while an optimality condition is a condition that must be satisfied in order for a solution to be optimal.

## What is a constraint programming problem?

A constraint programming problem is a type of optimization problem in which the constraints that must be satisfied are specified as logical or mathematical relationships between the decision variables.

## What is a metaheuristic optimization algorithm?

A metaheuristic optimization algorithm is a type of optimization algorithm that uses a general problem-solving strategy that is not specific to any particular optimization problem, but can be adapted to a wide range of problems.

## What is a heuristic optimization algorithm?

A heuristic optimization algorithm is a type of optimization algorithm that uses rules of thumb, intuition, and experience to find solutions that are good, but not necessarily optimal.

## What is the difference between a linear and a nonlinear optimization problem?

A linear optimization problem is a type of optimization problem in which the objective function and constraints are all linear functions, while a nonlinear optimization problem is a type of optimization problem in which the objective function or constraints are nonlinear functions.

## What is the difference between an exact and an approximate optimization algorithm?

An exact optimization algorithm is a type of optimization algorithm that guarantees to find the optimal solution, while an approximate optimization algorithm is a type of optimization algorithm that may not find the optimal solution, but is designed to find a good solution efficiently.

## What is a goal programming problem?

A goal programming problem is a type of multi-objective optimization problem in which the objectives are specified as goals or targets, and the goal achievement is prioritized in order to achieve the best possible compromise among the conflicting goals.

## What is the difference between a hard and a soft constraint?

A hard constraint is a constraint that must be satisfied in order for a solution to be feasible, while a soft constraint is a constraint that is desirable to satisfy, but is not required.

## What is a network flow optimization problem?

A network flow optimization problem is a type of optimization problem in which the objective is to determine the optimal flow of goods or services through a network, subject to capacity constraints, flow conservation constraints, and other constraints that are specific to the problem.

## What is a mixed-integer programming problem?

A mixed-integer programming problem is a type of optimization problem in which some or all of the decision variables are required to be integer values, while others can take on continuous values.

## What is the difference between a binary and an integer decision variable?

A binary decision variable is a decision variable that can only take on the values 0 or 1, while an integer decision variable can take on any integer value.

## What is the difference between a deterministic and a stochastic optimization problem?

A deterministic optimization problem is a type of optimization problem in which all of the input parameters are known with certainty, while a stochastic optimization problem is a type of optimization problem in which some or all of the input parameters are random variables.

## What is the difference between a local and a global optimum?

A local optimum is a solution that is optimal within a specific region of the search space, while a global optimum is a solution that is optimal over the entire search space.

## What is the difference between a primal and a dual problem?

A primal problem is the original optimization problem that is being solved, while a dual problem is a related optimization problem that can be used to provide bounds on the optimal value of the primal problem.

## What is the difference between a feasible and an infeasible solution?

A feasible solution is a solution that satisfies all of the constraints of the optimization problem, while an infeasible solution is a solution that violates one or more of the constraints.

## What is a constraint violation?

A constraint violation occurs when a solution violates one or more of the constraints of the optimization problem.

## What is a branch-and-bound algorithm?

A branch-and-bound algorithm is a type of optimization algorithm that is used to solve mixed-integer programming problems by systematically exploring the search space, dividing it into smaller regions or “branches,” and using bounds to prune the search tree.

## What is a cutting plane algorithm?

A cutting plane algorithm is a type of optimization algorithm that is used to solve linear programming problems by iteratively adding constraints that are violated by the current solution until a feasible solution is found.

## What is a genetic algorithm?

A genetic algorithm is a type of metaheuristic optimization algorithm that is inspired by the process of natural selection and uses a population-based approach to search for optimal solutions. It involves creating a population of potential solutions, evaluating their fitness, and using crossover and mutation operators to create new offspring.

## What is a linear programming relaxation?

A linear programming relaxation is the process of removing the integer constraints from a mixed-integer programming problem to create a linear programming problem. The optimal solution to the linear programming relaxation provides an upper bound on the optimal solution to the mixed-integer programming problem.

## What is a Lagrangian relaxation?

A Lagrangian relaxation is a method used to solve optimization problems with constraints by adding a penalty term to the objective function that reflects the degree of constraint violation. The Lagrangian relaxation involves relaxing the constraints and solving a series of unconstrained optimization problems.

## What is the difference between a continuous and a discrete search space?

A continuous search space is a search space in which the decision variables can take on any real value, while a discrete search space is a search space in which the decision variables can only take on a finite set of discrete values.

## What is a local search algorithm?

A local search algorithm is a type of optimization algorithm that iteratively improves a solution by making small changes to it in the hopes of finding a better solution in the local neighborhood.

## What is a simulated annealing algorithm?

A simulated annealing algorithm is a type of metaheuristic optimization algorithm that is inspired by the process of annealing in metallurgy. It involves iteratively changing a solution to a nearby solution, and accepting worse solutions with a decreasing probability over time.

## What is a tabu search algorithm?

A tabu search algorithm is a type of metaheuristic optimization algorithm that uses a memory structure to store previous search moves and avoid repeating them. It involves making small changes to the current solution and avoiding moves that have been previously made.

## What is a particle swarm optimization algorithm?

A particle swarm optimization algorithm is a type of metaheuristic optimization algorithm that is inspired by the behavior of swarms of birds or fish. It involves creating a population of particles that move through the search space, and adjusting their positions and velocities based on the best solution found so far.

## What is a constraint satisfaction problem?

A constraint satisfaction problem is a type of optimization problem in which the goal is to find a solution that satisfies a set of constraints. The constraints can be expressed as logical or mathematical relationships between the decision variables.

## What is the difference between an objective function and a utility function?

An objective function is a mathematical expression that measures the quality of a solution to an optimization problem, while a utility function is a mathematical expression that measures the satisfaction or happiness of an individual or agent.

## What is a multi-objective optimization problem?

A multi-objective optimization problem is a type of optimization problem in which there are multiple conflicting objectives that must be optimized simultaneously. The goal is to find a set of solutions that represent a trade-off between the conflicting objectives.

## What is the difference between a heuristic and an exact algorithm?

A heuristic algorithm is a problem-solving method that uses a rule of thumb or educated guess to quickly find a near-optimal solution, while an exact algorithm is a problem-solving method that guarantees finding the optimal solution to a problem.

## What is the branch and bound method?

The branch and bound method is a technique used in integer programming to find the optimal solution of a problem by branching on the integer variables and bounding the solution space of the problem.

## What is the cutting plane method?

The cutting plane method is a technique used in linear programming to iteratively add constraints to a linear program to reduce the feasible region until an optimal solution is found.

## What is the difference between sensitivity analysis and post-optimality analysis?

Sensitivity analysis is the process of analyzing how changes in the parameters of an optimization problem affect the optimal solution, while post-optimality analysis is the process of analyzing the optimal solution after it has been found to gain insights into the problem.

## What is a transportation problem?

A transportation problem is a type of linear programming problem in which the goal is to find the optimal way to transport a given quantity of goods from a set of sources to a set of destinations while minimizing the total transportation cost.

## What is a network flow problem?

A network flow problem is a type of linear programming problem in which the goal is to find the optimal way to flow a given quantity of goods through a network of nodes and arcs subject to capacity constraints and other constraints.

## What is a shortest path problem?

A shortest path problem is a type of optimization problem in which the goal is to find the shortest path between two nodes in a network.

## What is a critical path in project management?

The critical path in project management is the sequence of tasks that must be completed in order to finish a project in the shortest amount of time possible. Any delay in the critical path will delay the overall project completion time.

## What is a resource-constrained project scheduling problem?

A resource-constrained project scheduling problem is a type of optimization problem in which the goal is to schedule a set of tasks subject to resource constraints such as limited availability of workers or machinery.

## What is a queueing theory?

Queueing theory is the study of the behavior of waiting lines and the mathematics of queuing systems. It is used to analyze and optimize the performance of systems that involve waiting, such as call centers, traffic networks, and manufacturing lines.

## What is integer programming?

Integer programming is a branch of mathematical optimization that deals with optimizing a linear objective function subject to integer constraints on the decision variables.

## What is mixed-integer programming?

Mixed-integer programming is a type of optimization problem in which some of the decision variables are restricted to take on integer values, while others can take on continuous values.

## What is the simplex algorithm?

The simplex algorithm is a method for solving linear programming problems that involves starting at a feasible solution and iteratively moving towards an optimal solution by pivoting on the variables in the objective function.

## What is the interior point method?

The interior point method is an optimization algorithm that solves linear and nonlinear programming problems by solving a sequence of barrier problems, which are problems that add a term to the objective function that penalizes solutions that violate the constraints.

## What is the difference between linear programming and nonlinear programming?

Linear programming is a type of optimization problem in which the objective function and constraints are linear functions of the decision variables, while nonlinear programming is a type of optimization problem in which the objective function and/or constraints are nonlinear functions of the decision variables.

## What is the goal programming method?

The goal programming method is a technique used to solve multi-objective optimization problems by defining a set of goals or objectives and then assigning priorities to them to find a solution that best satisfies all the goals.

## What is simulation modeling?

Simulation modeling is the process of creating and analyzing computer models of real-world systems or processes to gain insights into their behavior and performance under different scenarios.

## What is stochastic programming?

Stochastic programming is a branch of mathematical optimization that deals with optimization problems that involve uncertainty or randomness, such as random demand or uncertain input parameters.

## What is the Monte Carlo method?

The Monte Carlo method is a simulation technique used to estimate the probability distribution of an uncertain variable by repeatedly generating random samples of the variable and computing the corresponding outcomes of the system being modeled.