Module I: Introduction to Operations Research (OR)

 

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

1. free float
2. independent float
3. interference float
4. linear float

 

To proceed with the Modified Distribution method algorithm for solving a transportation problem, the number of

dummy allocations need to be added are______________.

1. n
2. n-1
3. 2n-1
4. n-2

 

 

A feasible solution to a linear programming problem:

1. must satisfy all the constraints of the problem simultaneously.
2. need not satisfy all of the constraints, but only a few of them.
3. must be a corner point of the feasible region.
4. must optimise the value of the objective function.

 

 

Select the correct statement:

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

 

 

The objective of network analysis is to______________.

1. minimise total project duration
2. minimise total project cost
3. minimise production delays, interruption and conflicts
4. maximise total project duration

 

 

Operations research approach is ______________.

1. multi-disciplinary
2. scientific
3. intuitive
4. collect essential data

 

 

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 ______________.

1. rows or columns
2. rows and columns
3. rows + columns - 1
4. rows-columns

 

 

Service mechanism in a queuing system is characterised by ______________.

1. customer's behaviour
2. server's behaviour
3. customers in the system
4. server in the system

 

In program evaluation review technique network, each activity time assumes a beta distribution because:

1. it is a unmoral distribution that provides information regarding the uncertainty of time estimates of activities.
2. it has got finite non-negative error.
3. it need not be symmetrical about model value.
4. the project is progressing well.

 

 

For any primal problem and its dual, ______________.

1. optimal value of objective function is same
2. dual will have an optimal solution if primal does too
3. primal will have an optimal solution if dual does too
4. both primal and dual cannot be infeasible

 

 

Decision making is the process of making choices by identifying a decision, gathering information and assessing alternative resolutions.

1. True
2. False
3. Can't say
4. None of these

Quantitative methods emphasise objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires and surveys, or by manipulating pre-existing statistical data using computational techniques.

1. True
2. False
3. Can't say
4. None of these

 

 

If there is no non-negative replacement ratio in solving a Linear Programming Problem, then the solution is______________.

1. feasible
2. bounded
3. unbounded
4. infinite

Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritising and selecting alternatives for a solution; and implementing a solution.

1. True
2. False
3. Can't say
4. None of these

 

 

Analogical models are a method of representing a phenomenon of the world, often called the "target system" by another, more understandable or analysable system.

1. TRUE
2. FALSE
3. Can't say
4. None of these

 

 

Symbolic modelling is a therapeutic method that uses symbols, metaphors and modelling to facilitate positive change.

1. FALSE
2. TRUE
3. Cant say
4. None of these

 

 

Modelling is the essence of operations research. A model is an abstraction of idealised representation of a real-life problem.

1. TRUE
2. FALSE
3. Can't say
4. None of these

 

Module II Linear Programming

 

 

In graphical method, the restriction on number of decision variables is __________.

1. Two
2. Three
3. Not more than three
4. None of these

 

Linear programming is a:

1. Constrained optimisation technique
2. Technique for economic allocation of limited resources
3. Mathematical technique
4. All of this

 

Non-negativity restriction in LPP indicates that:

1. All decision variables must take on values equal to or greater than zero.
2. there is a positive coefficient of variables in objective function.
3. there is a positive coefficient of variables in any constraint.
4. there is non-negative value of resources

 

Term ‘Linear’ in LPP symbolises that:

1. Parameter's value remains constant during the planning period.
2. Value of decision variables is non-negative.
3. Relationship among all variables is linear.
4. It has single objective function and constraints.

 

 

Which of the following is assumption of an LP model?

1. Divisibility
2. Proportionality
3. Additively
4. All of these

 

The linear function of the variables which is to be maximised or minimised is called ____________.

1. Constraints
2. Objective function
3. Decision variable
4. Non-negativity constraint

 

The mathematical model of an LP problem is important because:

1. It helps in converting the verbal description and numerical data into mathematical expression.
2. Decision-makers prefer to work with formal models.
3. It captures the relevant relationship among decisions.
4. It enables the use of algebraic technique.

 

A feasible solution to an LP problem:

1. Must satisfy all of the problem's constraints simultaneously.
2. Need not satisfy all of the constraints, only some of them.
3. Must be a corner point of the feasible region.
4. Must optimise the value of the objective function.

 

The first step in formulating a linear programming problem is:

1. Plot a graph
2. Perform the sensitivity analysis
3. Identify and define the decision variables
4. Find out the redundant constraints

 

Constraints in LPP mean:

1. Limitations are expressed in mathematical equalities (or inequalities)
2. Assumption
3. Goal is to be achieved
4. A function is to be optimised

 

In graphical method, the restriction on number of constraints is __________.

1. Two
2. Three
3. Not more then three
4. None of these

 

Certainty means that the problem is assumed to have no probabilistic elements whatsoever. This is technically never true in the real world; some degree of uncertainty is always present.

1. True
2. False
3. Can't say
4. None of these

 

Decision making is the process of making choices by identifying a decision, gathering information and assessing alternative resolutions.

1. True
2. False
3. Can't say
4. None of these

 

Additively is the combined effect of the decision variables in any one equation is the algebraic sum of their individual weighted effects.

1. True
2. False
3. Can't say
4. None of these

 

Model formulation is the step where our knowledge of a natural system is translated in mathematical form.

1. False
2. True
3. Cant say
4. None of these

 

Proportionality is the means that each decision variable in every equation must appear with a constant coefficient i.e., the variable is multiplied by a number and nothing else.

1. False
2. True
3. Cant say
4. None of these

 

The simplex method is a systematic procedure for testing the vertices as possible solutions.

1. True
2. False
3. Can't say
4. None of these

 

/ Module III Sensitivity Analysis

 

The report which shows the final values of the decision variables, the objective function, and the formula, slack or surplus,

status, and LHS value for each constraint is the:

1. sensitivity report
2. answer report.
3. limits report.
4. constraint report.

 

 

The case where there are alternate solutions or multiple optimal solutions is mostly identified in solver when:

1. when the Allowable Increase or Allowable Decrease column for the RHS of a variable has a zero value in the

Constraints Table.

1. when the Allowable Increase or Allowable Decrease column for the OFC of a variable has a zero value in the

Adjustable Cells Table.

1. shadow prices are all non-zero.
2. shadow prices are zero.

 

Any change in the values for the RHS (Right Hand Side) of a binding constraint of an LP problem will:

1. change the slope of the objective function.
2. not change the slope of the constraint but move it parallel to the original.
3. not change the feasibility region.
4. change the slope of that constraint.

 

 

Suppose that a MAX problem contained the following constraint: 5x + 8y ≤ 40. Then which of the following statements is true?

1. For the point (4, 2), the slack for this constraint would be zero.
2. For the point (8, 5), the slack for this constraint would have a value of 40.
3. For the point (1, 4), the slack for this constraint would have a value of 3.
4. For the point (4, 2.5), the slack for this constraint would be a positive value.

 

When there is a change in one of the coefficients of the objective function, and yet optimal point remains as the optimal point after the change, then:

1. the value of the new optimal objective function remains the same as the original one.
2. the value of the new optimal objective function changes and is generally different from the original one.
3. Both A and B
4. None of these

 

Let x = number of units of product 1 to produce, and let y = number of units of product 2 to produce. Consider the following objective function: Maximise z = x + 2y. Subject to the following constraints: x + y ≤ 12 (resource A), x ≤ 8(resource B), y ≤ 6 (resource C), x and y ≥ 0. What will be the optimal objective function value?

1. 12
2. 10
3. 16
4. 18

 

Which of the following statements is true?

1. Changes to an objective function coefficient will not affect the size of the feasible region.
2. If a constraint is non-binding, then its LHS is greater than its RHS.
3. Shadow prices can be found in the Answer Report.
4. An equality constraint is always non-binding.

 

Consider a scenario with an objective function: Minimise $14X + $17Y. Assume that the value of X in the optimal solutions zero, and the reduced cost for variable X is $3. At what objective function coefficient will X first become part of the optimal solution?

1. 17
2. 20
3. 11
4. 14

 

Sensitivity Analysis generally assumes:

1. we are considering a change in only one input data value at a time.
2. we are considering several changes in several input data values at a time.
3. we are considering a change in two input data values at a time.
4. None of these

 

If a greater than or equal to constraint is used to model a minimum requirement constraint, then:

1. it will always be a binding constraint if the objective function is a MIN.
2. it will be a binding constraint if the minimum requirement is exactly met.
3. it will always be a binding constraint if the objective function is a MAX.
4. it will be a binding constraint if the minimum requirement is exceeded.

 

Input-Output Coefficient is defined as the objective of making decisions.

1. True
2. False
3. Can't say
4. None of these

 

Objective Function is defined as the objective of making decisions.

1. True
2. False
3. Can't say
4. None of these

 

Sensitivity analysis is a financial model that determines how target variables are affected based on changes in other variables known as input variables.

1. True
2. False
3. Can't say
4. None of these

 

A variable is a quantity that may change within the context of a mathematical problem or experiment.

1. True
2. False
3. Can't say
4. None of these

 

The term ‘dual’, in general, implies two or double. The concept of duality is very useful in mathematics, physics, statistics, engineering, and managerial decision-making.

1. True
2. False
3. Can't say
4. None of these

 

The Dual Simplex Method will pivot from dual feasible dictionary to dual feasible dictionary working towards feasibility.

1. True
2. False
3. Can't say
4. None of these

 

Constraint is something that imposes a limit or restriction or that prevents something from occurring. An example of constraint is the fact that there are so many hours in a day to accomplish things.

1. True
2. False
3. Can't say
4. None of these

 

 

Module IV Transportation Model /

 

 

 

Transportation model is based on the assumption that any damage sustained while travelling has negative repercussions, it is

used to examine transportation networks and determine the most effective path for resource allocation.

1. True
2. False
3. Can't say
4. None of these

 

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

1. balance the transportation problem.
2. prevent solution from becoming degenerate.
3. ensure that total cost does not exceed a limit.
4. the solution not be degenerate

 

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

1. It is complicated to use.
2. It does not take into account cost of transportation.
3. It leads to a degenerate initial solution.
4. It may provide wrong solution.

 

In applying Vogel’s approximation method, row and column penalties are determined by:

1. finding the largest unit cost in each row or column.
2. finding the smallest unit cost in each row or column.
3. finding the sum of the unit costs in each row or column.
4. finding the difference between the two lowest unit costs in each row and column.

 

 

The maximisation type of transportation problem can be converted into minimisation type:

1. by subtracting smallest cost element from all other cost elements.
2. by adding smallest cost element to all other cost elements.
3. by subtracting all the unit costs from the highest unit cost of the table.
4. by adding smallest cost element to all other cost elements.

 

When the total demand is equal to supply, then the transportation problem is said to be ______________

1. balanced
2. unbalanced
3. maximisation
4. minimisation

 

The transportation problem deals with the transportation of:

1. single product from a source to several destinations.
2. several products from a source to a destination.
3. single product from several sources to a destination.
4. several products from several sources to several destinations.

 

In northwest corner method, first allocation is made at:

1. Lower right corner of the table.
2. Upper right corner of the table.
3. Highest costly cell of the table.
4. Upper left-hand corner of the table.

 

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

1. m + n
2. m*n
3. m+n-1
4. m+n+1

 

For finding an optimum solution in transportation problem, ____________ method is used.

1. Simplex
2. Big-M
3. MODI
4. Hungarian

 

The Vogel's Approximation Method or VAM is an iterative procedure calculated to find out the initial feasible solution of the transportation problem.

1. True
2. False
3. Can't say
4. None of these

 

The Modified Distribution Method or MODI is an efficient method of checking the optimality of the initial feasible solution

1. True
2. False
3. Can't say
4. None of these

 

The Least Cost Method is another method used to obtain the initial feasible solution for the transportation problem. Here, the allocation begins with the cell which has the minimum cost. The lower cost cells are chosen over the higher-cost cells with the objective to have the least cost of transportation.

1. True
2. False
3. Can't say
4. None of these

 

The North-West Corner Rule is a method adopted to compute the initial feasible solution of the transportation problem. The name North-West Corner is given to this method because the basic variables are selected from the extreme left corner.

1. True
2. False
3. Can't say
4. None of these

 

 

Degeneracy is a term referring to the fact that two or more stationary states of the same quantum-mechanical system may have the same energy even though their wave functions are not the same.

1. False
2. True
3. Cant say
4. None of these

 

The multiple optimal solutions arise in a linear programming problem with more than one set of basic solutions that can minimise or maximise the required objective function. The multiple optimal solutions are called the alternate basic solutions.

1. False
2. True
3. Cant say
4. None of these

 

Unbalanced transportation problem is a transportation problem where the total availability at the origins is not equal to the total requirements at the destinations.

1. True
2. False
3. Can't say
4. None of these

 

 

 

Module V Assignment Model /

 

 

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 ________.

1. one; one
2. unlimited; one
3. one; unlimited
4. unlimited; unlimited

 

 

An assignment problem is considered as a particular case of a __________________.

1. Transportation problem
2. Sequencing problem
3. Queuing problem
4. Game theory

 

Dummy row or column is added in an assignment problem:

1. To balance total activities and total resources
2. To prevent a solution from getting degenerated
3. To reduce the total cost of assignment
4. To increase the profit function

 

The method used for solving an assignment problem is called _____________.

1. Simplex method
2. Least cost method
3. Hungarian method
4. Steppingstone method

 

In marking assignments, which of the following should be preferred?

1. Only row having single zero
2. Only column having single zero
3. Only row/column having single zero
4. Column having more than one zero

 

______ is based on the principle that if a constant is added to every element of a row and/or a column of cost matrix, the optimum solution of the resulting assignment problem is the same as the original problem and vice versa.

1. The Hungarian Method
2. Opportunity cost
3. Transportation problem
4. None of these

 

While solving an assignment problem, an activity is assigned to a resource with zero opportunity cost because the objective is to ______

1. minimise total cost of assignment.
2. reduce total cost of assignment to zero.
3. reduce cost of that assignment to zero.
4. maximise total cost of assignment.

 

The assignment problem will have alternate solutions when:

1. there is at least one zero in each row and column.
2. all rows have two zeros.
3. there is a tie between zero opportunity cost cells.
4. two diagonal elements are zeros.

 

The assignment problem is always a ______________matrix

1. circle
2. square
3. rectangle
4. triangle

 

Maximisation assignment problem is transformed into a minimisation problem by:

1. adding each entry in a column from the maximum value in that column.
2. subtracting each entry in a column from the maximum value in that column.
3. subtracting each entry in the table from the maximum value in that table.
4. adding each entry in the table from the maximum value in that table.

 

______ is one of the topics of operations research. It consists of assigning a specific task or job to a specific person or worker assuming that there are the number of persons equal to the number of tasks available.

1. Assignment models
2. Opportunity cost
3. Transportation problem
4. None of these

 

______ problem is an assignment problem where the number of facilities is not equal to the number of jobs.

1. Balanced Assignment Problem
2. Opportunity Cost
3. Unbalanced Assignment Problem
4. None of these

 

_____ is the forgone benefit that would have been derived from an option not chosen. To properly evaluate opportunity costs ,the costs and benefits of every option available must be considered and weighed against the others.

1. The Hungarian Method
2. Opportunity Cost
3. Transportation problem
4. None of these

 

_____ is standard technique in linear programming for solving an optimisation problem, typically one involving a function and several constraints expressed as inequalities.

1. The Hungarian Method
2. Opportunity cost
3. Simplex method
4. None of these

 

A travelling salesman problem differs from an assignment problem in that distinct destinations are assigned to different sources in an assignment problem, whereas a destination is assigned to a source in a travelling salesman problem.

1. True
2. False
3. Can't say
4. None of these

 

An unbalanced assignment can be transformed into a balanced one.

1. True
2. False
3. Can't say
4. None of these

 

 

An assignment problem is a type of transportation problem in which the resources (such as facilities) are assignees, and the destinations (such as activities) are destinations (say jobs).

1. True
2. False
3. Can't say
4. None of these

 

Assignment 2

 

 

CASE STUDY

Case on the Central Post Office Bandung

1. Introduction

The transportation problem is a subset of the people assignment problem. It appears in a wide range of decision-making

scenarios. The personnel assignment problem is distinguished by the fact that each worker is assigned to only one task. In

general, the assignment problem entails assigning n jobs to n workers, each of whom has varying levels of competency in

executing each task. The goal of the assignment problem is to assign each task to the most appropriate worker such that the

total resource expenditure to complete all the tasks is minimised. An assignment price, time spent completing tasks, travel,

and other factors can all be used to optimise a resource.

Many researchers have used assignment problems to help them address decision-making problems. Sasaki devised a novel

technique to one-sided assignment challenges. Macon and Bradbury proposed a problem with repetitive work and attempted

to include a human factor in the research. Bogomolnaia and Moulin developed a simple random assignment issue with a

unique solution. For tackling assignment problems, Naas described a specific branch-and-bound technique. Soured looked

into the continuous assignment problem in order to solve scheduling issues involving irregular cost functions. Odour et al.

tackled the issue of the efficacy of plausible solutions to assignment difficulties.

This case looks at how to solve a personnel assignment problem using the Hungarian technique. This optimisation process

was applied to a case study of the central post office in Bandung in assigning employees to deliver packets to destination

locations based on several criteria owned by each employee, as well as conducting a sensitivity analysis of data changes that

may occur in order to avoid changing the optimal assignment from the original problem.

2. Supplies and Procedures

The concept of an assignment problem based on journey time was used to address a problem for a case study on the central

Post Office in Bandung using Hungarian methodologies.

 

The transportation problem is a subset of the people assignment problem.

1. True
2. False
3. Can't say
4. None of these

 

The personnel assignment problem is distinguished by the fact that each worker is assigned to only one task.

1. True
2. False
3. Can't say
4. None of these

 

Researchers have used assignment problems to help them address decision-making problems.

1. True
2. False
3. Can't say
4. None of these

 

 

The goal of the assignment problem is to assign each task to the most appropriate worker such that the total resource expenditure to complete all tasks is minimised.

1. True
2. False
3. Can't say
4. None of these

 

An assignment price, time spent completing tasks, travel, and other factors can all be used to optimise a resource.

1. True
2. False
3. Can't say
4. None of these

 

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