explain assignment problem in detail

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

Solving the Assignment Problem

There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method.

Step 1: Set up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

• Subtract the smallest entry in each row from all the entries of the row.
• Subtract the smallest entry in each column from all the entries of the column.
• Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
• Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Next, we subtract the smallest entry in each column from all the entries of the column:

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

• Emp 1 to Task 3
• Emp 2 to Task 2
• Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

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Operations Research

1 Operations Research-An Overview

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

2 Linear Programming: Formulation and Graphical Method

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

3 Linear Programming-Simplex Method

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

4 Transportation Problem

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

5 Assignment Problem

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

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

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

• Some Integer Programming Formulation Techniques
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9 Dynamic Programming

• Dynamic Programming Methodology: An Example
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10 Non-Linear Programming

• Solution of a Non-linear Programming Problem
• Convex and Concave Functions
• Kuhn-Tucker Conditions for Constrained Optimisation
• Quadratic Programming
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11 Introduction to game theory and its Applications

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12 Monte Carlo Simulation

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13 Queueing Models

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Assignment problem

1 formulation of the problem, 2 variants of the problem, 3 algorithms for solving the problem, 4 references.

Suppose that there are [math]n[/math] agents and [math]m[/math] tasks, which can be distributed between these agents. Only one task can be assigned to each agent, and each task can be assigned to only one agent. The cost of assignment of the [math]i[/math] -th task to the [math]j[/math] -th agent is [math]c(i, j)[/math] . If [math]c(i, j) = \infty[/math] , then the [math]i[/math] -th task cannot be assigned to the [math]j[/math] -th agent.

The assignment problem : find a feasible set of assignments [math]A = \{ (i_1, j_1), \ldots, (i_k, j_k) \}[/math] , [math]k = \min \{m, n\}[/math] having the maximum total cost:

If [math]m = n[/math] , then we say of the linear assignment problem : each agent is assigned to perform exactly one task, and each task is assigned to exactly one agent.

In the case of unit weights, we have to find a maximum matching in a bipartite graph, and the problem reduces to assigning as much tasks as possible.

• The Hungarian Method [1] [2] [3] for the linear problem. The complexity is [math]O(n^4)[/math] (and can be reduced [4] to [math]O(n^3)[/math] );
• the auction algorithm [5] [6] ;
• the Hopcroft-Karp algorithm [7] for the problem with unit weights. The complexity is [math]O(m \sqrt{n})[/math] .
• ↑ Kuhn, H W. “The Hungarian Method for the Assignment Problem.” Naval Research Logistics Quarterly 2, no. 1 (March 1955): 83–97. doi:10.1002/nav.3800020109.
• ↑ Kuhn, H W. “Variants of the Hungarian Method for Assignment Problems.” Naval Research Logistics Quarterly 3, no. 4 (December 1956): 253–58. doi:10.1002/nav.3800030404.
• ↑ Munkres, James. “Algorithms for the Assignment and Transportation Problems.” Journal of the Society for Industrial and Applied Mathematics 5, no. 1 (March 1957): 32–38. doi:10.1137/0105003.
• ↑ Tomizawa, N. “On Some Techniques Useful for Solution of Transportation Network Problems.” Networks 1, no. 2 (1971): 173–94. doi:10.1002/net.3230010206.
• ↑ Bertsekas, Dimitri P. “Auction Algorithms for Network Flow Problems: a Tutorial Introduction.” Computational Optimization and Applications 1 (1992): 7–66.
• ↑ Zavlanos, Michael M, Leonid Spesivtsev, and George J Pappas. “A Distributed Auction Algorithm for the Assignment Problem,” Proceedings of IEEE CDC'08, 1212–17, IEEE, 2008. doi:10.1109/CDC.2008.4739098.
• ↑ Hopcroft, John E, and Richard M Karp. “An $N^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs.” SIAM Journal on Computing 2, no. 4 (1973): 225–31. doi:10.1137/0202019.
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Assignment Problems

Definition of the assignment problem, mathematical formulation of the assignment problem, hungarian method for solving assignment problem, flow chart of hungarian method.

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Suppose there are \(n\) jobs to be performed and \(n\) persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let \(c_{ij}\) be the cost if the \(i-th\) person is assigned to the \(j-th\) job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

An assignment problem can be mathematically formulated as follows:

Minimise the total cost

\(x_{ij} =1\), if \(i^{th}\) person is assigned to the \(j^{th}\) job \(x_{ij}=0\), if \(i^{th}\) person is that assigned to the \(j^{th}\) job

subject to the constraints

i) \(\sum_{i=1}^n x_{ij} = 1, j=1, 2, \cdots n\)

which means that only one job is done by the \(i^{th}\) person, \(i= 1, 2, \cdots, n\)

ii) \(\sum_{i=1}^n x_{ij} = 1, j=1, 2, \cdots n\)

which means that only one person should be assigned to the \(j^{th}\) person, \(j= 1, 2, \cdots, n\)

The Hungarian method of assignment provides us with an efficient method of finding the optimal solution without having to make a-direct comparison of every solution. It works on the principle of reducing the given cost matrix to a matrix of opportunity costs.

Opportunity cost show the relative penalties associated with assigning resources to an activity as opposed to making the best or least cost assignment. If we can reduce the cost matrix to the extent of having at least one zero in each row and column, it will be possible to make optimal assignment.

The Hungarian method can be summarized in the following steps:

Step 1: Develop the Cost Table from the given Problem

If the no of rows are not equal to the no of columns and vice versa, a dummy row or dummy column must be added. The assignment cost for dummy cells are always zero.

Step 2: Find the Opportunity Cost Table

(a) Locate the smallest element in each row of the given cost table and then subtract that from each element of that row, and

(b) In the reduced matrix obtained from 2 (a) locate the smallest element in each column and then subtract that from each element. Each row and column now have at least one zero value.

Step 3: Make Assignment in the Opportunity Cost Matrix

The procedure of making assignment is as follows:

(a) Examine rows successively until a row with exactly one unmarked zero is obtained. Make an assignment single zero by making a square around it.

(b) For each zero value that becomes assigned, eliminate (Strike off) all other zeros in the same row and/ or column

(c) Repeat step 3 (a) and 3 (b) for each column also with exactly single zero value all that has not been assigned.

(d) If a row and/or column has two or more unmarked zeros and one cannot be chosen by inspection, then choose the assigned zero cell arbitrarily.

(e) Continue this process until all zeros in row column are either enclosed (Assigned) or struck off (x)

Step 4: Optimality Criterion

If the member of assigned cells is equal to the numbers of rows column then it is optimal solution. The total cost associated with this solution is obtained by adding original cost figures in the occupied cells.

If a zero cell was chosen arbitrarily in step (3), there exists an alternative optimal solution. But if no optimal solution is found, then go to step (5).

Step 5: Revise the Opportunity Cost Table

Draw a set of horizontal and vertical lines to cover all the zeros in the revised cost table obtained from step (3), by using the following procedure:

(a) For each row in which no assignment was made, mark a tick (√)

(b) Examine the marked rows. If any zero occurs in those columns, tick the respective rows that contain those assigned zeros.

(c) Repeat this process until no more rows or columns can be marked.

If a no of lines drawn is equal to the no of (or columns) the current solution is the optimal solution, otherwise go to step 6.

Step 6: Develop the New Revised Opportunity Cost Table

(a) From among the cells not covered by any line, choose the smallest element, call this value K

(b) Subtract K from every element in the cell not covered by line.

(c) Add K to very element in the cell covered by the two lines, i.e., intersection of two lines.

(d) Elements in cells covered by one line remain unchanged.

Step 7: Repeat Step 3 to 6 Unlit an Optimal Solution is Obtained

The flow chart of steps in the Hungarian method for solving an assignment problem is shown in following figures:

In a factory there are five operator \(O_1\), \(O_2\), \(O_3\), \(O_4\), \(O_5\) and five machine \(M_1\), \(M_2\), \(M_3\), \(M_4\), \(M_5\). The operating costs are given when the \(O_i\) operator operates the \(M_j\) machine \((i,j=1,2,..,5)\). But there is a restriction that \(O_3\) cannot be allowed to operate the third machine \(M_3\) and \(O_2\) cannot be allowed to operate the fifth machine \(M_5\). The cost matrix is given above. Find the optional assignment and the optimal assignment cost also.

[2018, 15M]

2) Solve the following assignment problem to maximize the sales: \(\begin{array}{|c|c|c|c|c|c|} \hline {} & {I} & {II} & {III} & {IV} & {V} \\ \hline {A} & {3} & {4} & {5} & {6} & {7} \\ \hline {B} & {4} & {15} & {13} & {7} & {6} \\ \hline {C} & {6} & {13} & {12} & {5} & {11} \\ \hline {D} & {7} & {12} & {15} & {8} & {5} \\ \hline {E} & {8} & {13} & {10} & {6} & {9} \\ \hline \end{array}\)

where \(I\), \(II\), \(III\), \(IV\) and \(V\) are Territories; \(A\), \(B\), \(C\), \(D\), \(E\) are Salesmen.

[2015, 10M]

3) Solve the minimum time assignment problem: \(\begin{array}{|c|c|c|c|c|} \hline { } & {I} & {II} & {III} & {IV} \\ \hline {A} & {3} & {12} & {5} & {4} \\ \hline {B} & {7} & {9} & {8} & {12} \\ \hline {C} & {5} & {11} & {10} & {12} \\ \hline {D} & {6} & {14} & {4} & {11} \\ \hline \end{array}\)

where \(I\), \(II\), \(III\) and \(IV\) are Machines; \(A\), \(B\), \(C\) and \(D\) are Jobs.

[2013, 15M]

4) A travelling salesman has to visit 5 cities. He wishes to start from a particular city, visit each city once and then return to his starting point. Cost of going from one city to another is given below:

You are required to find the least cost route.

[2004, 15M]

5) Find the optimal solution for the assignment problem with the following cost matrix: \(\begin{bmatrix}{6} & {1} & {9} & {11} & {12} \\ {2} & {8} & {17} & {2} & {5} \\ {11} & {8} & {3} & {3} & {3} \\ {4} & {10} & {8} & {6} & {11} \\ {8} & {10} & {11} & {5} & {13}\end{bmatrix}\)

Indicate clearly the rule you apply to arrive at the complete assignment.

[2003, 15M]

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Assignment Problem

5.1  introduction.

The assignment problem is one of the special type of transportation problem for which more efficient (less-time consuming) solution method has been devised by KUHN (1956) and FLOOD (1956). The justification of the steps leading to the solution is based on theorems proved by Hungarian mathematicians KONEIG (1950) and EGERVARY (1953), hence the method is named Hungarian.

5.2  GENERAL MODEL OF THE ASSIGNMENT PROBLEM

Consider n jobs and n persons. Assume that each job can be done only by one person and the time a person required for completing the i th job (i = 1,2,...n) by the j th person (j = 1,2,...n) is denoted by a real number C ij . On the whole this model deals with the assignment of n candidates to n jobs ...

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Procedure, Example Solved Problem | Operations Research - Solution of assignment problems (Hungarian Method) | 12th Business Maths and Statistics : Chapter 10 : Operations Research

Chapter: 12th business maths and statistics : chapter 10 : operations research.

Solution of assignment problems (Hungarian Method)

First check whether the number of rows is equal to the numbers of columns, if it is so, the assignment problem is said to be balanced.

Step :1 Choose the least element in each row and subtract it from all the elements of that row.

Step :2 Choose the least element in each column and subtract it from all the elements of that column. Step 2 has to be performed from the table obtained in step 1.

Step:3 Check whether there is atleast one zero in each row and each column and make an assignment as follows.

Step :4 If each row and each column contains exactly one assignment, then the solution is optimal.

Example 10.7

Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the machines I, II, III and IV.

Here the number of rows and columns are equal.

∴ The given assignment problem is balanced. Now let us find the solution.

Step 1: Select a smallest element in each row and subtract this from all the elements in its row.

Look for atleast one zero in each row and each column.Otherwise go to step 2.

Step 2: Select the smallest element in each column and subtract this from all the elements in its column.

Since each row and column contains atleast one zero, assignments can be made.

Step 3 (Assignment):

Thus all the four assignments have been made. The optimal assignment schedule and total cost is

The optimal assignment (minimum) cost

Example 10.8

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

∴ The given assignment problem is balanced.

Now let us find the solution.

The cost matrix of the given assignment problem is

Column 3 contains no zero. Go to Step 2.

Thus all the five assignments have been made. The Optimal assignment schedule and total cost is

The optimal assignment (minimum) cost = ` 9

Example 10.9

Solve the following assignment problem.

Since the number of columns is less than the number of rows, given assignment problem is unbalanced one. To balance it , introduce a dummy column with all the entries zero. The revised assignment problem is

Here only 3 tasks can be assigned to 3 men.

Step 1: is not necessary, since each row contains zero entry. Go to Step 2.

Step 3 (Assignment) :

Since each row and each columncontains exactly one assignment,all the three men have been assigned a task. But task S is not assigned to any Man. The optimal assignment schedule and total cost is

The optimal assignment (minimum) cost = ₹ 35

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Quadratic Assignment Problem (QAP)

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• IBM Placement Paper | Quantitative Analysis Set - 5

The Quadratic Assignment Problem (QAP) is an optimization problem that deals with assigning a set of facilities to a set of locations, considering the pairwise distances and flows between them.

The problem is to find the assignment that minimizes the total cost or distance, taking into account both the distances and the flows.

The distance matrix and flow matrix, as well as restrictions to ensure each facility is assigned to exactly one location and each location is assigned to exactly one facility, can be used to formulate the QAP as a quadratic objective function.

The QAP is a well-known example of an NP-hard problem , which means that for larger cases, computing the best solution might be difficult. As a result, many algorithms and heuristics have been created to quickly identify approximations of answers.

There are various types of algorithms for different problem structures, such as:

• Precise algorithms
• Approximation algorithms
• Metaheuristics like genetic algorithms and simulated annealing
• Specialized algorithms

Example: Given four facilities (F1, F2, F3, F4) and four locations (L1, L2, L3, L4). We have a cost matrix that represents the pairwise distances or costs between facilities. Additionally, we have a flow matrix that represents the interaction or flow between locations. Find the assignment that minimizes the total cost based on the interactions between facilities and locations. Each facility must be assigned to exactly one location, and each location can only accommodate one facility.

Facilities cost matrix:

Flow matrix:

To solve the QAP, various optimization techniques can be used, such as mathematical programming, heuristics, or metaheuristics. These techniques aim to explore the search space and find the optimal or near-optimal solution.

The solution to the QAP will provide an assignment of facilities to locations that minimizes the overall cost.

The solution generates all possible permutations of the assignment and calculates the total cost for each assignment. The optimal assignment is the one that results in the minimum total cost.

To calculate the total cost, we look at each pair of facilities in (i, j) and their respective locations (location1, location2). We then multiply the cost of assigning facility1 to facility2 (facilities[facility1][facility2]) with the flow from location1 to location2 (locations[location1][location2]). This process is done for all pairs of facilities in the assignment, and the costs are summed up.

Overall, the output tells us that assigning facilities to locations as F1->L1, F3->L2, F2->L3, and F4->L4 results in the minimum total cost of 44. This means that Facility 1 is assigned to Location 1, Facility 3 is assigned to Location 2, Facility 2 is assigned to Location 3, and Facility 4 is assigned to Location 4, yielding the lowest cost based on the given cost and flow matrices.This example demonstrates the process of finding the optimal assignment by considering the costs and flows associated with each facility and location. The objective is to find the assignment that minimizes the total cost, taking into account the interactions between facilities and locations.

Applications of the QAP include facility location, logistics, scheduling, and network architecture, all of which require effective resource allocation and arrangement.

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Understanding Assignments

What this handout is about.

The first step in any successful college writing venture is reading the assignment. While this sounds like a simple task, it can be a tough one. This handout will help you unravel your assignment and begin to craft an effective response. Much of the following advice will involve translating typical assignment terms and practices into meaningful clues to the type of writing your instructor expects. See our short video for more tips.

Basic beginnings

Regardless of the assignment, department, or instructor, adopting these two habits will serve you well :

• Read the assignment carefully as soon as you receive it. Do not put this task off—reading the assignment at the beginning will save you time, stress, and problems later. An assignment can look pretty straightforward at first, particularly if the instructor has provided lots of information. That does not mean it will not take time and effort to complete; you may even have to learn a new skill to complete the assignment.
• Ask the instructor about anything you do not understand. Do not hesitate to approach your instructor. Instructors would prefer to set you straight before you hand the paper in. That’s also when you will find their feedback most useful.

Assignment formats

Many assignments follow a basic format. Assignments often begin with an overview of the topic, include a central verb or verbs that describe the task, and offer some additional suggestions, questions, or prompts to get you started.

An Overview of Some Kind

The instructor might set the stage with some general discussion of the subject of the assignment, introduce the topic, or remind you of something pertinent that you have discussed in class. For example:

“Throughout history, gerbils have played a key role in politics,” or “In the last few weeks of class, we have focused on the evening wear of the housefly …”

The Task of the Assignment

Pay attention; this part tells you what to do when you write the paper. Look for the key verb or verbs in the sentence. Words like analyze, summarize, or compare direct you to think about your topic in a certain way. Also pay attention to words such as how, what, when, where, and why; these words guide your attention toward specific information. (See the section in this handout titled “Key Terms” for more information.)

“Analyze the effect that gerbils had on the Russian Revolution”, or “Suggest an interpretation of housefly undergarments that differs from Darwin’s.”

Additional Material to Think about

Here you will find some questions to use as springboards as you begin to think about the topic. Instructors usually include these questions as suggestions rather than requirements. Do not feel compelled to answer every question unless the instructor asks you to do so. Pay attention to the order of the questions. Sometimes they suggest the thinking process your instructor imagines you will need to follow to begin thinking about the topic.

“You may wish to consider the differing views held by Communist gerbils vs. Monarchist gerbils, or Can there be such a thing as ‘the housefly garment industry’ or is it just a home-based craft?”

These are the instructor’s comments about writing expectations:

“Be concise”, “Write effectively”, or “Argue furiously.”

Technical Details

These instructions usually indicate format rules or guidelines.

“Your paper must be typed in Palatino font on gray paper and must not exceed 600 pages. It is due on the anniversary of Mao Tse-tung’s death.”

The assignment’s parts may not appear in exactly this order, and each part may be very long or really short. Nonetheless, being aware of this standard pattern can help you understand what your instructor wants you to do.

Interpreting the assignment

Ask yourself a few basic questions as you read and jot down the answers on the assignment sheet:

Why did your instructor ask you to do this particular task?

Who is your audience.

• What kind of evidence do you need to support your ideas?

What kind of writing style is acceptable?

• What are the absolute rules of the paper?

Try to look at the question from the point of view of the instructor. Recognize that your instructor has a reason for giving you this assignment and for giving it to you at a particular point in the semester. In every assignment, the instructor has a challenge for you. This challenge could be anything from demonstrating an ability to think clearly to demonstrating an ability to use the library. See the assignment not as a vague suggestion of what to do but as an opportunity to show that you can handle the course material as directed. Paper assignments give you more than a topic to discuss—they ask you to do something with the topic. Keep reminding yourself of that. Be careful to avoid the other extreme as well: do not read more into the assignment than what is there.

Of course, your instructor has given you an assignment so that they will be able to assess your understanding of the course material and give you an appropriate grade. But there is more to it than that. Your instructor has tried to design a learning experience of some kind. Your instructor wants you to think about something in a particular way for a particular reason. If you read the course description at the beginning of your syllabus, review the assigned readings, and consider the assignment itself, you may begin to see the plan, purpose, or approach to the subject matter that your instructor has created for you. If you still aren’t sure of the assignment’s goals, try asking the instructor. For help with this, see our handout on getting feedback .

Given your instructor’s efforts, it helps to answer the question: What is my purpose in completing this assignment? Is it to gather research from a variety of outside sources and present a coherent picture? Is it to take material I have been learning in class and apply it to a new situation? Is it to prove a point one way or another? Key words from the assignment can help you figure this out. Look for key terms in the form of active verbs that tell you what to do.

Key Terms: Finding Those Active Verbs

Here are some common key words and definitions to help you think about assignment terms:

Information words Ask you to demonstrate what you know about the subject, such as who, what, when, where, how, and why.

• define —give the subject’s meaning (according to someone or something). Sometimes you have to give more than one view on the subject’s meaning
• describe —provide details about the subject by answering question words (such as who, what, when, where, how, and why); you might also give details related to the five senses (what you see, hear, feel, taste, and smell)
• explain —give reasons why or examples of how something happened
• illustrate —give descriptive examples of the subject and show how each is connected with the subject
• summarize —briefly list the important ideas you learned about the subject
• trace —outline how something has changed or developed from an earlier time to its current form
• research —gather material from outside sources about the subject, often with the implication or requirement that you will analyze what you have found

Relation words Ask you to demonstrate how things are connected.

• compare —show how two or more things are similar (and, sometimes, different)
• contrast —show how two or more things are dissimilar
• apply—use details that you’ve been given to demonstrate how an idea, theory, or concept works in a particular situation
• cause —show how one event or series of events made something else happen
• relate —show or describe the connections between things

Interpretation words Ask you to defend ideas of your own about the subject. Do not see these words as requesting opinion alone (unless the assignment specifically says so), but as requiring opinion that is supported by concrete evidence. Remember examples, principles, definitions, or concepts from class or research and use them in your interpretation.

• assess —summarize your opinion of the subject and measure it against something
• prove, justify —give reasons or examples to demonstrate how or why something is the truth
• evaluate, respond —state your opinion of the subject as good, bad, or some combination of the two, with examples and reasons
• support —give reasons or evidence for something you believe (be sure to state clearly what it is that you believe)
• synthesize —put two or more things together that have not been put together in class or in your readings before; do not just summarize one and then the other and say that they are similar or different—you must provide a reason for putting them together that runs all the way through the paper
• analyze —determine how individual parts create or relate to the whole, figure out how something works, what it might mean, or why it is important
• argue —take a side and defend it with evidence against the other side

More Clues to Your Purpose As you read the assignment, think about what the teacher does in class:

• What kinds of textbooks or coursepack did your instructor choose for the course—ones that provide background information, explain theories or perspectives, or argue a point of view?
• In lecture, does your instructor ask your opinion, try to prove their point of view, or use keywords that show up again in the assignment?
• What kinds of assignments are typical in this discipline? Social science classes often expect more research. Humanities classes thrive on interpretation and analysis.
• How do the assignments, readings, and lectures work together in the course? Instructors spend time designing courses, sometimes even arguing with their peers about the most effective course materials. Figuring out the overall design to the course will help you understand what each assignment is meant to achieve.

Now, what about your reader? Most undergraduates think of their audience as the instructor. True, your instructor is a good person to keep in mind as you write. But for the purposes of a good paper, think of your audience as someone like your roommate: smart enough to understand a clear, logical argument, but not someone who already knows exactly what is going on in your particular paper. Remember, even if the instructor knows everything there is to know about your paper topic, they still have to read your paper and assess your understanding. In other words, teach the material to your reader.

Aiming a paper at your audience happens in two ways: you make decisions about the tone and the level of information you want to convey.

• Tone means the “voice” of your paper. Should you be chatty, formal, or objective? Usually you will find some happy medium—you do not want to alienate your reader by sounding condescending or superior, but you do not want to, um, like, totally wig on the man, you know? Eschew ostentatious erudition: some students think the way to sound academic is to use big words. Be careful—you can sound ridiculous, especially if you use the wrong big words.
• The level of information you use depends on who you think your audience is. If you imagine your audience as your instructor and they already know everything you have to say, you may find yourself leaving out key information that can cause your argument to be unconvincing and illogical. But you do not have to explain every single word or issue. If you are telling your roommate what happened on your favorite science fiction TV show last night, you do not say, “First a dark-haired white man of average height, wearing a suit and carrying a flashlight, walked into the room. Then a purple alien with fifteen arms and at least three eyes turned around. Then the man smiled slightly. In the background, you could hear a clock ticking. The room was fairly dark and had at least two windows that I saw.” You also do not say, “This guy found some aliens. The end.” Find some balance of useful details that support your main point.

You’ll find a much more detailed discussion of these concepts in our handout on audience .

The Grim Truth

With a few exceptions (including some lab and ethnography reports), you are probably being asked to make an argument. You must convince your audience. It is easy to forget this aim when you are researching and writing; as you become involved in your subject matter, you may become enmeshed in the details and focus on learning or simply telling the information you have found. You need to do more than just repeat what you have read. Your writing should have a point, and you should be able to say it in a sentence. Sometimes instructors call this sentence a “thesis” or a “claim.”

So, if your instructor tells you to write about some aspect of oral hygiene, you do not want to just list: “First, you brush your teeth with a soft brush and some peanut butter. Then, you floss with unwaxed, bologna-flavored string. Finally, gargle with bourbon.” Instead, you could say, “Of all the oral cleaning methods, sandblasting removes the most plaque. Therefore it should be recommended by the American Dental Association.” Or, “From an aesthetic perspective, moldy teeth can be quite charming. However, their joys are short-lived.”

Convincing the reader of your argument is the goal of academic writing. It doesn’t have to say “argument” anywhere in the assignment for you to need one. Look at the assignment and think about what kind of argument you could make about it instead of just seeing it as a checklist of information you have to present. For help with understanding the role of argument in academic writing, see our handout on argument .

What kind of evidence do you need?

There are many kinds of evidence, and what type of evidence will work for your assignment can depend on several factors–the discipline, the parameters of the assignment, and your instructor’s preference. Should you use statistics? Historical examples? Do you need to conduct your own experiment? Can you rely on personal experience? See our handout on evidence for suggestions on how to use evidence appropriately.

Make sure you are clear about this part of the assignment, because your use of evidence will be crucial in writing a successful paper. You are not just learning how to argue; you are learning how to argue with specific types of materials and ideas. Ask your instructor what counts as acceptable evidence. You can also ask a librarian for help. No matter what kind of evidence you use, be sure to cite it correctly—see the UNC Libraries citation tutorial .

You cannot always tell from the assignment just what sort of writing style your instructor expects. The instructor may be really laid back in class but still expect you to sound formal in writing. Or the instructor may be fairly formal in class and ask you to write a reflection paper where you need to use “I” and speak from your own experience.

Try to avoid false associations of a particular field with a style (“art historians like wacky creativity,” or “political scientists are boring and just give facts”) and look instead to the types of readings you have been given in class. No one expects you to write like Plato—just use the readings as a guide for what is standard or preferable to your instructor. When in doubt, ask your instructor about the level of formality they expect.

No matter what field you are writing for or what facts you are including, if you do not write so that your reader can understand your main idea, you have wasted your time. So make clarity your main goal. For specific help with style, see our handout on style .

Technical details about the assignment

The technical information you are given in an assignment always seems like the easy part. This section can actually give you lots of little hints about approaching the task. Find out if elements such as page length and citation format (see the UNC Libraries citation tutorial ) are negotiable. Some professors do not have strong preferences as long as you are consistent and fully answer the assignment. Some professors are very specific and will deduct big points for deviations.

Usually, the page length tells you something important: The instructor thinks the size of the paper is appropriate to the assignment’s parameters. In plain English, your instructor is telling you how many pages it should take for you to answer the question as fully as you are expected to. So if an assignment is two pages long, you cannot pad your paper with examples or reword your main idea several times. Hit your one point early, defend it with the clearest example, and finish quickly. If an assignment is ten pages long, you can be more complex in your main points and examples—and if you can only produce five pages for that assignment, you need to see someone for help—as soon as possible.

Tricks that don’t work

Your instructors are not fooled when you:

• spend more time on the cover page than the essay —graphics, cool binders, and cute titles are no replacement for a well-written paper.
• use huge fonts, wide margins, or extra spacing to pad the page length —these tricks are immediately obvious to the eye. Most instructors use the same word processor you do. They know what’s possible. Such tactics are especially damning when the instructor has a stack of 60 papers to grade and yours is the only one that low-flying airplane pilots could read.
• use a paper from another class that covered “sort of similar” material . Again, the instructor has a particular task for you to fulfill in the assignment that usually relates to course material and lectures. Your other paper may not cover this material, and turning in the same paper for more than one course may constitute an Honor Code violation . Ask the instructor—it can’t hurt.
• get all wacky and “creative” before you answer the question . Showing that you are able to think beyond the boundaries of a simple assignment can be good, but you must do what the assignment calls for first. Again, check with your instructor. A humorous tone can be refreshing for someone grading a stack of papers, but it will not get you a good grade if you have not fulfilled the task.

Critical reading of assignments leads to skills in other types of reading and writing. If you get good at figuring out what the real goals of assignments are, you are going to be better at understanding the goals of all of your classes and fields of study.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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How MSNBC’s Leftward Tilt Delivers Ratings, and Complications

NBC’s leaders have been forced to grapple with how to square its cable news network’s embrace of progressive politics with the company’s straight-news operation.

By Jim Rutenberg and Michael M. Grynbaum

MSNBC placed a big bet on becoming comfort TV for liberals. Then it doubled down.

Time slots on the cable network once devoted to news programming are now occupied by Trump-bashing opinion hosts. The channel has become a landing spot for high-profile alumni of President Biden’s administration like Jen Psaki, who went from hosting White House press briefings to hosting her own show. On Super Tuesday, when producers aired a portion of a live speech by former President Donald J. Trump, Rachel Maddow chastised her bosses on the air.

The moves have been a hit with viewers. MSNBC has leapfrogged past its erstwhile rival CNN in the ratings and has seen viewership rise over the past year, securing second place in cable news behind the perennial leader, Fox News.

But MSNBC’s success has had unintended consequences for its parent company, NBC, an original Big Three broadcaster that still strives to appeal to a mass American audience.

NBC’s traditional political journalists have cycled between rancor and resignation that the cable network’s partisanship — a regular target of Mr. Trump — will color perceptions of their straight news reporting. Local NBC stations between the coasts have demanded, again and again, that executives in New York do more to preserve NBC’s nonpartisan brand, lest MSNBC’s blue-state bent alienate their red-state viewers.

Even Comcast, NBC’s corporate owner, which is loath to intervene in news coverage, took the rare step of conveying its concern to MSNBC’s leaders when some hosts and guests criticized Israel as the Hamas attack was unfolding on Oct. 7, according to three people with knowledge of the discussions. An abrupt course correction to that coverage followed.

This account of the tensions roiling NBC and its corporate overseers is based on interviews with more than two dozen people with knowledge of the company’s inner workings, almost all of whom insisted on anonymity to share details of internal discussions.

NBC declined to make its top executives available for interviews. The chairman of the NBCUniversal News Group, Cesar Conde, has said he wants his division — which encompasses MSNBC, CNBC, a digital streaming service, Telemundo and journalistic stalwarts like “Nightly News,” “Meet the Press” and “Today” — to be a big tent.

Yet his recent efforts to include more conservative voices on the airwaves generated newsroom suspicion and ultimately led to an embarrassing rebellion over the hiring of Ronna McDaniel, a former Republican Party chair who aided Mr. Trump’s attempt to overturn his 2020 election loss.

MSNBC hosts, for their part, view their role in the political debate as more important than ever. They dismiss the accusation that MSNBC is a “Fox News for Democrats” and say their message — that Mr. Trump’s candidacy represents a unique and clear threat to democracy — is an urgent one for the electorate to hear.

And executives inside NBC’s corporate suites at Rockefeller Center say they are confident that viewers know the differences between the company’s various news brands. Any related challenges, they argue, are of a high-class sort — because their cable channels give NBC an advantage in relevance and revenue over its original Big Three competitors, ABC and CBS, which have no cable presence.

“Our strategy is built on our distinct, complementary brands including NBC News, CNBC, NBC News Now, MSNBC and Telemundo,” the NBCUniversal News Group said in a statement. “That has driven our performance as the nation’s leading news organization with the largest reach.” (Comcast does not disclose the news division’s earnings in its reports to Wall Street.)

The tensions inside NBC are, in some ways, a microcosm of the challenges facing many traditional news organizations as the country hurtles toward a tense presidential election: how to maintain trust and present neutral, fact-based reporting in a fractionalized era when partisanship carries vast financial and cultural rewards.

But the company’s challenge is also unique. It must juggle a broadcast news operation bound by traditional standards of impartiality and a cable channel increasingly bound by the partisan preferences of an intensely loyal viewership. How NBC navigates these dueling imperatives will have important implications for Comcast, a Philadelphia-based conglomerate known for its aversion to the political spotlight.

It will also have consequences for coverage of the presidential campaign. Where MSNBC’s cable news opinion-makers sustain and galvanize the Democratic faithful, the NBC broadcast network reaches millions of the potentially persuadable voters critical to both parties, which have sought to turn NBC’s internal tensions to their own advantage.

Left, Right, Left

MSNBC has caused corporate headaches since its inception.

NBC formed the channel as a joint venture with Microsoft in 1996 with the hope that it would thrust “all the value of NBC News into the cable world,” as Tom Rogers, a former NBC executive who helped found the cable network, described it in an interview.

But critics mocked the new 24-hour channel for its informal approach to news, mixing NBC’s biggest stars with younger personalities on a set reminiscent of Central Perk on “Friends.” It was almost immediately outflanked by Fox News, which followed MSNBC to market that same year and rose to the top of the cable news ratings as the first 24-hour TV channel with an overt political appeal.

MSNBC struggled with its identity. It moved to the left ahead of the Iraq war — and later moved right by hiring new hosts like the former Republican congressman Joe Scarborough. Soon it shifted leftward again, as the host Keith Olbermann hit a nerve with his strident anti-Bush — and often anti-Fox — commentary.

But when Andrew Lack, a veteran producer, took over NBC’s news division in 2015, he decided the channel needed to tone down its partisan image. Under Mr. Lack — who oversaw MSNBC’s creation in an earlier NBC stint — the cable network bumped the Rev. Al Sharpton from the weekday schedule, hired the former Fox anchor Greta Van Susteren and added more straightforward news programs, including a daily version of “Meet the Press,” NBC’s flagship political show, with Chuck Todd.

Mr. Todd was game — but would come to believe that his MSNBC duties ultimately hurt the “Meet the Press” franchise, several people at NBC said in interviews. The daily version of the show fell increasingly out of step with MSNBC’s partisan slant even as Republicans used its association with the liberal cable network to deny interview requests from the flagship Sunday edition of “Meet the Press.”

Then, Mr. Trump’s ascent shocked the Democratic base and spiked viewership of Ms. Maddow and other left-leaning hosts, whose programs became a kind of televised safe space. MSNBC’s ratings surged .

Conde Faces the Messiness

Mr. Conde succeeded Mr. Lack in spring 2020. A Wharton-trained business executive who sits on the boards of Walmart and PepsiCo, he came up through the corporate side of news, having led a turnaround at Telemundo after serving as the president of Univision Networks. Accordingly, Mr. Conde was expected to impose a more disciplined and neater corporate sensibility to the division.

He was almost immediately confronted by the messiness he had inherited.

Within a few weeks of Mr. Conde’s ascension, Mr. Trump attacked NBC when it announced the hiring of a new contributor: Lisa Page, a former F.B.I. lawyer who became a lightning rod on the right for her role in the investigation into his campaign ties to Russia. After an initial MSNBC appearance she did not show up again.

A few months later, NBC faced criticism from the other direction when it booked Mr. Trump for a prime-time interview on the night of a presidential debate that he had boycotted. (Mr. Biden was appearing at the same time on ABC.) Ms. Maddow chastised her bosses about it on the air.

That sort of partisan tumult has often riled another important constituency for Mr. Conde: NBC’s affiliated regional stations, which the company relies on to carry its major news programs to markets throughout the country.

The stations tend to be deeply embedded — and deeply trusted — in their communities. Many of them operate in red states or counties and chafed whenever MSNBC, which Mr. Trump regularly calls “MSDNC,” drew conservative ire.

Over the years the affiliates, many of which would have been thrilled to see MSNBC’s leftward tilt abandoned entirely, increasingly urged NBC executives to better distinguish its content from the NBC journalism like “Today” and “Nightly News” that they carried on their stations.

At one point after Mr. Conde took over, executives talked about the possibility of doubling down on partisanship and stripping MSNBC of news altogether, defining it as a pure opinion channel. The company would use the new NBC News Now streaming service, started under Noah Oppenheim when he was NBC News president, for 24-hour news, according to two people with knowledge of the conversations.

That idea fizzled. Mr. Conde was not prepared to entirely abandon news, but he began to better distinguish the various parts of his news division — which effectively moved MSNBC and NBC News further apart.

In the Lack era, Mr. Oppenheim of NBC News and Phil Griffin, the longtime chief of MSNBC, often worked closely as they managed a collection of stars who worked for both networks, like Mr. Todd, Craig Melvin and Hallie Jackson.

Creating more distance between the cable and broadcast outlets, Mr. Conde and Mr. Griffin’s successor, Rashida Jones, moved Mr. Todd, Ms. Jackson and Mr. Melvin off MSNBC to work exclusively at NBC News and NBC News Now. MSNBC’s daytime block of hard news shrank to six hours from eight, as the cable network extended by an hour each two opinion shows with loyal followings: “Morning Joe” featuring Mr. Scarborough and his wife Mika Brzezinski, and “Deadline: White House” with Nicolle Wallace as host.

Nothing did more to signal that MSNBC was more tightly embracing its partisan direction than Ms. Jones’s decision to hire Ms. Psaki and another Biden aide, Symone D. Sanders, straight from the White House.

It was the kind of revolving-door hiring that liberal pundits used to criticize when it happened with Fox News and the Trump administration.

It also created an awkward situation for the NBC News White House team, which was caught off guard when word that Ms. Psaki was in talks for the job leaked while she was still serving as White House press secretary.

A tense, televised confrontation followed in the White House briefing room when Kristen Welker, then NBC News’s co-chief White House correspondent, asked her future colleague: “How is it ethical to have these conversations with media outlets while you continue to have a job standing behind that podium?”

Chasing a Broad Appeal

At the same time, NBC News was going through its own changes.

Early last year, Mr. Oppenheim left his post running NBC News, and Mr. Conde split his job in three. In a jigsaw-like structure, one executive now oversaw “Today,” another “Nightly News” and NBC News Now, and a third “Meet the Press,” “Dateline” and news coverage across numerous shows and platforms.

Mr. Conde said the new setup would provide “growth opportunities,” with each show acting like its own megafranchise. “Today,” for instance, includes an e-commerce business and online sites dedicated to cooking, wellness and books.

He gave his deputies another brief: making additional efforts to ensure that news coverage reflected a wider range of political viewpoints.

Mr. Conde wanted to get Republicans back onto shows.

That was in line with an industrywide recalibration. After four years of combat between the press and Mr. Trump, media companies have sought better ways to reach Trump supporters who feel alienated from mainstream news. Television executives were also concerned that Republican elected officials were shunning their shows in favor of the congenial confines of right-wing media.

It was especially thorny for NBC, as Mr. Trump continued to yoke NBC News to MSNBC while accusing them, along with Comcast, of committing “Country Threatening Treason.”

A chance for a fresh start seemed to come last September when Ms. Welker succeeded Mr. Todd as the moderator of “Meet the Press.”

According to several people with knowledge of the internal discussions, Mr. Conde and Ms. Welker agreed that she should make booking both Mr. Trump and Mr. Biden for interviews a priority. Mr. Biden declined; Mr. Trump accepted.

But when Mr. Conde said she should schedule the Trump interview for her debut episode, Ms. Welker disagreed. Questioning the mendacious former president can be a high-wire act for even the most experienced TV interviewers, and Ms. Welker did not think it was a wise way to introduce herself to viewers. She acquiesced only after coaxing from Mr. Conde and several of his deputies.

Ms. Welker worked to fact-check Mr. Trump in real time while also eliciting an admission that he ignored his own campaign lawyers when they told him there was no evidence the 2020 presidential election results were rigged. Mr. Trump steamrolled ahead with a litany of lies nonetheless. The interview was panned on social media — complete with a “#boycottmeetthepress” campaign — but was deemed a success by Mr. Conde.

Mr. Conde and Rebecca Blumenstein, a former editor at The New York Times whom Mr. Conde hired as one of his top deputies, also worked aggressively to secure a Republican primary debate in fall 2023, pitching Ms. McDaniel and other Republican officials in person.

They succeeded, but only after accepting terms that unsettled some journalists within the company. NBC agreed to include a moderator from a right-wing media company, Salem Radio, and stream the debate live on Rumble, a video site that frequently hosts pro-Nazi and other extremist content. (NBC executives have defended the decision, noting that Rumble was already the party’s official streamer and had no editorial input.)

The debate received good marks in the press. And in general, red-state affiliates felt that Mr. Conde was doing a better job of bringing balance to NBC News, according to an executive at one company that owns affiliates.

Reverberations Continue

Each network was now set on its own distinct course: MSNBC toward more partisan and progressive opinion, and NBC News toward Mr. Conde’s commitment to “presenting our audiences with a widely diverse set of viewpoints and experiences,” as he put it.

But each tripped over the limits of its approach in an election landscape already littered with ideological tripwires.

When Hamas staged its terror attack against Israel on Oct. 7, MSNBC mixed breaking news of the attacks with discussions about the historical backdrop of Israel’s treatment of Palestinians. The coverage reflected views on the left — and presaged the pro-Palestinian demonstrations that would soon grow in number — but it struck many others as discordant, or even offensive, given that the violence was still coming into view.

“I love this network, but I’ve got to ask: Who’s writing your scripts? Hamas?” Jonathan Greenblatt, the Anti-Defamation League chief executive, asked two days later on “Morning Joe.”

Some of the blowback came from within.

In a call with Mr. Conde, Michael Cavanagh, the president of Comcast, who oversees NBC, shared concerns about that initial coverage, according to three people with knowledge of the discussions. Mr. Conde harbored the same concerns, according to a person briefed on their conversation, and he directed MSNBC to be more circumspect and to focus on facts, not opinions, in those initial days.

Five months later, Mr. Conde thought he had achieved a milestone at NBC News in his efforts to integrate right-wing perspectives into its programming. At the recommendation of Ms. Blumenstein and Carrie Budoff Brown, who oversees political coverage, Mr. Conde hired Ms. McDaniel, the former Republican Party chair, as a contributor who could offer on-air commentary.

If the hiring was in service of Mr. Conde’s goal of adding balance, it came as an unwelcome surprise to NBC’s ranks of correspondents, hosts and anchors. Ms. Welker had booked Ms. McDaniel for her next episode of “Meet the Press” — as a guest, not as a colleague. In the interview, she grilled Ms. McDaniel about her role in Mr. Trump’s effort to overturn the 2020 election result, actions that many at NBC and MSNBC viewed as disqualifying for a job there.

Mr. Todd, appearing as a guest on that day’s episode, unleashed a live, on-air denunciation of his bosses after the interview that left the control room in stunned silence. His rebellion carried over the next day on MSNBC, from “Morning Joe” up through “The Rachel Maddow Show.” Under pressure, Mr. Conde broke the deal with Ms. McDaniel, a move that only served to upset the Republicans he was trying to attract.

In the aftermath, NBC’s public stumble turned into a point of contention on the presidential campaign trail. The Republican Party said it was weighing an attempt to restrict NBC News at this summer’s convention, while Mr. Trump yet again bashed “Fake News NBC.”

Aides to Mr. Biden were also perturbed about the McDaniel hire, viewing it as part of a broader attempt by NBC News to overcompensate for MSNBC’s decidedly pro-Biden stance. In private conversations with NBC correspondents, Biden aides have argued that “Nightly News,” whose huge audience is of critical political importance to the campaign, was taking it easy on Mr. Trump and treating Mr. Biden too harshly.

Executives at NBC dismissed these complaints, saying the partisan brickbats simply come with the territory. They believe that each campaign will use anything at its disposal to pressure news organizations for more favorable coverage.

The company pointed to comments made by Mr. Conde after the McDaniel imbroglio: “We will redouble our efforts to seek voices that represent different parts of the political spectrum.” It also shared data intended to show strong performance across its cable, broadcast and online operations.

The message was clear. Regardless of any turbulence, NBC has no plans to change course.

Jim Rutenberg is a writer at large for The Times and The New York Times Magazine and writes most often about media and politics. More about Jim Rutenberg

Michael M. Grynbaum writes about the intersection of media, politics and culture. He has been a media correspondent at The Times since 2016. More about Michael M. Grynbaum

A new theory of quantum gravity could explain the biggest puzzle in cosmology, study suggests

A new theory of quantum gravity, which attempts to unite quantum physics with Einstein's relativity, could help solve the puzzle of the universe's expansion, a theoretical paper suggests.

A variation on the theory of quantum gravity — the unification of quantum mechanics and Einstein's general relativity — could help solve one of the biggest puzzles in cosmology, new research suggests.

For nearly a century, scientists have known that the universe is expanding. But in recent decades, physicists have found that different types of measurements of the expansion rate — called the Hubble parameter — produce puzzling inconsistencies.

To resolve this paradox, a new study suggests incorporating quantum effects into one prominent theory used to determine the expansion rate.

"We tried to resolve and explain the mismatch between the values of the Hubble parameter from two different prominent types of observations," study co-author P.K. Suresh , a professor of physics at the University of Hyderabad in India, told Live Science via email.

An expanding problem

The universe's expansion was first identified by Edwin Hubble in 1929. His observations with the largest telescope of that time revealed that galaxies farther from us appear to move away at faster speeds. Although Hubble initially overestimated the expansion rate, subsequent measurements have refined our understanding, establishing the current Hubble parameter as highly reliable.

Later in the 20th century, astrophysicists introduced a novel technique to gauge the expansion rate by examining the cosmic microwave background, the pervasive "afterglow" of the Big Bang .

However, a serious problem arose with these two types of measurements. Specifically, the newer method produced a Hubble parameter value almost 10% lower than the one deduced from the astronomical observations of distant cosmic objects. Such discrepancies between different measurements, called the Hubble tension, signal potential flaws in our understanding of the universe's evolution.

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In a study published in the journal Classical and Quantum Gravity , Suresh and his colleague from the University of Hyderabad, B. Anupama, proposed a solution to align these disparate results. They underscored that physicists infer the Hubble parameter indirectly, employing our universe's evolutionary model based on Einstein's theory of general relativity.

The team argued for revising this theory to incorporate quantum effects. These effects, intrinsic to fundamental interactions, encompass random field fluctuations and the spontaneous creation of particles from the vacuum of space.

Despite scientists' ability to integrate quantum effects into theories of other fields, quantum gravity remains elusive, making detailed calculations extremely difficult or even impossible. To make matters worse, experimental studies of these effects require reaching temperatures or energies many orders of magnitude higher than those achievable in a lab.

Acknowledging these challenges, Suresh and Anupama focused on broad quantum-gravity effects common to many proposed theories.

"Our equation doesn't need to account for everything, but that does not prevent us from testing quantum gravity or its effects experimentally," Suresh said.

Their theoretical exploration revealed that accounting for quantum effects when describing the gravitational interactions in the earliest stage of the universe's expansion, called cosmic inflation, could indeed alter the theory's predictions regarding the properties of the microwave background at present, making the two types of Hubble parameter measurements consistent.

Of course, final conclusions can be drawn only when a full-fledged theory of quantum gravity is known, but even the preliminary findings are encouraging. Moreover, the link between the cosmic microwave background and quantum gravitational effects opens the way to experimentally studying these effects in the near future, the team said.

"Quantum gravity is supposed to play a role in the dynamics of the early universe; thus its effect can be observed through measurements of the properties of the cosmic microwave background," Suresh said.

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"Some of the future missions devoted to studying this electromagnetic background are highly probable and promising to test quantum gravity. … It provides a promising suggestion to resolve and validate the inflationary models of cosmology in conjunction with quantum gravity."

Additionally, the authors posit that quantum gravitational phenomena in the early universe might have shaped the properties of gravitational waves emitted during that period. Detecting these waves with future gravitational-wave observatories could further illuminate quantum gravitational characteristics.

"Gravitational waves from various astrophysical sources have only been observed so far, but gravitational waves from the early universe have not yet been detected," Suresh said. "Hopefully, our work will help in identifying the correct inflationary model and detecting the primordial gravitational waves with quantum gravity features."

Andrey got his B.Sc. and M.Sc. degrees in elementary particle physics from Novosibirsk State University in Russia, and a Ph.D. in string theory from the Weizmann Institute of Science in Israel. He works as a science writer, specializing in physics, space, and technology. His articles have been published in  Elements ,  N+1 , and  AdvancedScienceNews .

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