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Optimizing Job Assignments with Python: A Greedy Approach

In this article, we will learn the skill of job assignment which is a very important topic in the field of Operations Research. For this, we will utilize Python programming language and the Numpy library for the same. We will also solve a small case on a job assignment.

Job assignment involves allocating tasks to workers while minimizing overall completion time or cost. Python’s greedy algorithm, combined with NumPy, can solve such problems by iteratively assigning jobs based on worker skills and constraints, enabling efficient resource management in various industries.

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What is a Job Assignment?

Let us understand what a job assignment is with an example. In our example, three tasks have to be completed. Three workers have different sets of skills and take different amounts of time to complete the above-mentioned tasks. Now our goal is to assign the jobs to the workers to minimize the period of completing the three tasks.

Now, we solve the above problem using the concepts of Linear programming. Now there are certain constraints as well, each worker can be assigned only a single job at a time. Our objective function is the sum of all the time taken by the workers and minimize it. Let us now solve this problem using the power of the Numpy library of Python programming language.

Let us now look at the output of the problem.

From the output, we can see that The assignment is complete and optimized. Let us now look at a small case and understand the job assignment further.

A Real-World Job Assignment Scenario

Continuing with the example of assigning workers some jobs, in this case, a company is looking to get some work done with the help of some freelancers. There are 15 jobs and we have 10 freelancers. We have to assign jobs to workers in such a way, that we minimize the time as well as the cost of the whole operation. Let us now model this in the Python programming language.

This problem is solved using the greedy algorithm. In short, the greedy algorithm selects the most optimal choice available and does not consider what will happen in the future while making this choice. In the above code, we have randomly generated data on freelancer details. Let us now look at the output of the code.

Thus, we complete our agenda of job assignment while minimizing costs as evidenced by the output.

Assigning jobs optimally is crucial for maximizing productivity and minimizing costs in today’s competitive landscape. Python’s powerful libraries like NumPy make it easy to implement greedy algorithms and solve complex job assignment problems, even with larger sets of jobs and workers. How could you adapt this approach to accommodate dynamic changes in job requirements or worker availability?

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Python Job Responsibilities

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Python Practice for Beginners: 15 Hands-On Problems

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Want to put your Python skills to the test? Challenge yourself with these 15 Python practice exercises taken directly from our Python courses!

There’s no denying that solving Python exercises is one of the best ways to practice and improve your Python skills . Hands-on engagement with the language is essential for effective learning. This is exactly what this article will help you with: we've curated a diverse set of Python practice exercises tailored specifically for beginners seeking to test their programming skills.

These Python practice exercises cover a spectrum of fundamental concepts, all of which are covered in our Python Data Structures in Practice and Built-in Algorithms in Python courses. Together, both courses add up to 39 hours of content. They contain over 180 exercises for you to hone your Python skills. In fact, the exercises in this article were taken directly from these courses!

In these Python practice exercises, we will use a variety of data structures, including lists, dictionaries, and sets. We’ll also practice basic programming features like functions, loops, and conditionals. Every exercise is followed by a solution and explanation. The proposed solution is not necessarily the only possible answer, so try to find your own alternative solutions. Let’s get right into it!

Python Practice Problem 1: Average Expenses for Each Semester

John has a list of his monthly expenses from last year:

He wants to know his average expenses for each semester. Using a for loop, calculate John’s average expenses for the first semester (January to June) and the second semester (July to December).

Explanation

We initialize two variables, first_semester_total and second_semester_total , to store the total expenses for each semester. Then, we iterate through the monthly_spending list using enumerate() , which provides both the index and the corresponding value in each iteration. If you have never heard of enumerate() before – or if you are unsure about how for loops in Python work – take a look at our article How to Write a for Loop in Python .

Within the loop, we check if the index is less than 6 (January to June); if so, we add the expense to first_semester_total . If the index is greater than 6, we add the expense to second_semester_total .

After iterating through all the months, we calculate the average expenses for each semester by dividing the total expenses by 6 (the number of months in each semester). Finally, we print out the average expenses for each semester.

Python Practice Problem 2: Who Spent More?

John has a friend, Sam, who also kept a list of his expenses from last year:

They want to find out how many months John spent more money than Sam. Use a for loop to compare their expenses for each month. Keep track of the number of months where John spent more money.

We initialize the variable months_john_spent_more with the value zero. Then we use a for loop with range(len()) to iterate over the indices of the john_monthly_spending list.

Within the loop, we compare John's expenses with Sam's expenses for the corresponding month using the index i . If John's expenses are greater than Sam's for a particular month, we increment the months_john_spent_more variable. Finally, we print out the total number of months where John spent more money than Sam.

Python Practice Problem 3: All of Our Friends

Paul and Tina each have a list of their respective friends:

Combine both lists into a single list that contains all of their friends. Don’t include duplicate entries in the resulting list.

There are a few different ways to solve this problem. One option is to use the + operator to concatenate Paul and Tina's friend lists ( paul_friends and tina_friends ). Afterwards, we convert the combined list to a set using set() , and then convert it back to a list using list() . Since sets cannot have duplicate entries, this process guarantees that the resulting list does not hold any duplicates. Finally, we print the resulting combined list of friends.

If you need a refresher on Python sets, check out our in-depth guide to working with sets in Python or find out the difference between Python sets, lists, and tuples .

Python Practice Problem 4: Find the Common Friends

Now, let’s try a different operation. We will start from the same lists of Paul’s and Tina’s friends:

In this exercise, we’ll use a for loop to get a list of their common friends.

For this problem, we use a for loop to iterate through each friend in Paul's list ( paul_friends ). Inside the loop, we check if the current friend is also present in Tina's list ( tina_friends ). If it is, it is added to the common_friends list. This approach guarantees that we test each one of Paul’s friends against each one of Tina’s friends. Finally, we print the resulting list of friends that are common to both Paul and Tina.

Python Practice Problem 5: Find the Basketball Players

You work at a sports club. The following sets contain the names of players registered to play different sports:

How can you obtain a set that includes the players that are only registered to play basketball (i.e. not registered for football or volleyball)?

This type of scenario is exactly where set operations shine. Don’t worry if you never heard about them: we have an article on Python set operations with examples to help get you up to speed.

First, we use the | (union) operator to combine the sets of football and volleyball players into a single set. In the same line, we use the - (difference) operator to subtract this combined set from the set of basketball players. The result is a set containing only the players registered for basketball and not for football or volleyball.

If you prefer, you can also reach the same answer using set methods instead of the operators:

It’s essentially the same operation, so use whichever you think is more readable.

Python Practice Problem 6: Count the Votes

Let’s try counting the number of occurrences in a list. The list below represent the results of a poll where students were asked for their favorite programming language:

Use a dictionary to tally up the votes in the poll.

In this exercise, we utilize a dictionary ( vote_tally ) to count the occurrences of each programming language in the poll results. We iterate through the poll_results list using a for loop; for each language, we check if it already is in the dictionary. If it is, we increment the count; otherwise, we add the language to the dictionary with a starting count of 1. This approach effectively tallies up the votes for each programming language.

If you want to learn more about other ways to work with dictionaries in Python, check out our article on 13 dictionary examples for beginners .

Python Practice Problem 7: Sum the Scores

Three friends are playing a game, where each player has three rounds to score. At the end, the player whose total score (i.e. the sum of each round) is the highest wins. Consider the scores below (formatted as a list of tuples):

Create a dictionary where each player is represented by the dictionary key and the corresponding total score is the dictionary value.

This solution is similar to the previous one. We use a dictionary ( total_scores ) to store the total scores for each player in the game. We iterate through the list of scores using a for loop, extracting the player's name and score from each tuple. For each player, we check if they already exist as a key in the dictionary. If they do, we add the current score to the existing total; otherwise, we create a new key in the dictionary with the initial score. At the end of the for loop, the total score of each player will be stored in the total_scores dictionary, which we at last print.

Python Practice Problem 8: Calculate the Statistics

Given any list of numbers in Python, such as …

 … write a function that returns a tuple containing the list’s maximum value, sum of values, and mean value.

We create a function called calculate_statistics to calculate the required statistics from a list of numbers. This function utilizes a combination of max() , sum() , and len() to obtain these statistics. The results are then returned as a tuple containing the maximum value, the sum of values, and the mean value.

The function is called with the provided list and the results are printed individually.

Python Practice Problem 9: Longest and Shortest Words

Given the list of words below ..

… find the longest and the shortest word in the list.

To find the longest and shortest word in the list, we initialize the variables longest_word and shortest_word as the first word in the list. Then we use a for loop to iterate through the word list. Within the loop, we compare the length of each word with the length of the current longest and shortest words. If a word is longer than the current longest word, it becomes the new longest word; on the other hand, if it's shorter than the current shortest word, it becomes the new shortest word. After iterating through the entire list, the variables longest_word and shortest_word will hold the corresponding words.

There’s a catch, though: what happens if two or more words are the shortest? In that case, since the logic used is to overwrite the shortest_word only if the current word is shorter – but not of equal length – then shortest_word is set to whichever shortest word appears first. The same logic applies to longest_word , too. If you want to set these variables to the shortest/longest word that appears last in the list, you only need to change the comparisons to <= (less or equal than) and >= (greater or equal than), respectively.

If you want to learn more about Python strings and what you can do with them, be sure to check out this overview on Python string methods .

Python Practice Problem 10: Filter a List by Frequency

Given a list of numbers …

… create a new list containing only the numbers that occur at least three times in the list.

Here, we use a for loop to iterate through the number_list . In the loop, we use the count() method to check if the current number occurs at least three times in the number_list . If the condition is met, the number is appended to the filtered_list .

After the loop, the filtered_list contains only numbers that appear three or more times in the original list.

Python Practice Problem 11: The Second-Best Score

You’re given a list of students’ scores in no particular order:

Find the second-highest score in the list.

This one is a breeze if we know about the sort() method for Python lists – we use it here to sort the list of exam results in ascending order. This way, the highest scores come last. Then we only need to access the second to last element in the list (using the index -2 ) to get the second-highest score.

Python Practice Problem 12: Check If a List Is Symmetrical

Given the lists of numbers below …

… create a function that returns whether a list is symmetrical. In this case, a symmetrical list is a list that remains the same after it is reversed – i.e. it’s the same backwards and forwards.

Reversing a list can be achieved by using the reverse() method. In this solution, this is done inside the is_symmetrical function.

To avoid modifying the original list, a copy is created using the copy() method before using reverse() . The reversed list is then compared with the original list to determine if it’s symmetrical.

The remaining code is responsible for passing each list to the is_symmetrical function and printing out the result.

Python Practice Problem 13: Sort By Number of Vowels

Given this list of strings …

… sort the list by the number of vowels in each word. Words with fewer vowels should come first.

Whenever we need to sort values in a custom order, the easiest approach is to create a helper function. In this approach, we pass the helper function to Python’s sorted() function using the key parameter. The sorting logic is defined in the helper function.

In the solution above, the custom function count_vowels uses a for loop to iterate through each character in the word, checking if it is a vowel in a case-insensitive manner. The loop increments the count variable for each vowel found and then returns it. We then simply pass the list of fruits to sorted() , along with the key=count_vowels argument.

Python Practice Problem 14: Sorting a Mixed List

Imagine you have a list with mixed data types: strings, integers, and floats:

Typically, you wouldn’t be able to sort this list, since Python cannot compare strings to numbers. However, writing a custom sorting function can help you sort this list.

Create a function that sorts the mixed list above using the following logic:

• If the element is a string, the length of the string is used for sorting.
• If the element is a number, the number itself is used.

As proposed in the exercise, a custom sorting function named custom_sort is defined to handle the sorting logic. The function checks whether each element is a string or a number using the isinstance() function. If the element is a string, it returns the length of the string for sorting; if it's a number (integer or float), it returns the number itself.

The sorted() function is then used to sort the mixed_list using the logic defined in the custom sorting function.

If you’re having a hard time wrapping your head around custom sort functions, check out this article that details how to write a custom sort function in Python .

Python Practice Problem 15: Filter and Reorder

Given another list of strings, such as the one below ..

.. create a function that does two things: filters out any words with three or fewer characters and sorts the resulting list alphabetically.

Here, we define filter_and_sort , a function that does both proposed tasks.

First, it uses a for loop to filter out words with three or fewer characters, creating a filtered_list . Then, it sorts the filtered list alphabetically using the sorted() function, producing the final sorted_list .

The function returns this sorted list, which we print out.

Want Even More Python Practice Problems?

We hope these exercises have given you a bit of a coding workout. If you’re after more Python practice content, head straight for our courses on Python Data Structures in Practice and Built-in Algorithms in Python , where you can work on exciting practice exercises similar to the ones in this article.

Additionally, you can check out our articles on Python loop practice exercises , Python list exercises , and Python dictionary exercises . Much like this article, they are all targeted towards beginners, so you should feel right at home!

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Python Coding Assignments on CodeSubmit

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Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

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Solving Assignment Problem using Linear Programming in Python

Learn how to use Python PuLP to solve Assignment problems using Linear Programming.

In earlier articles, we have seen various applications of Linear programming such as transportation, transshipment problem, Cargo Loading problem, and shift-scheduling problem. Now In this tutorial, we will focus on another model that comes under the class of linear programming model known as the Assignment problem. Its objective function is similar to transportation problems. Here we minimize the objective function time or cost of manufacturing the products by allocating one job to one machine.

If we want to solve the maximization problem assignment problem then we subtract all the elements of the matrix from the highest element in the matrix or multiply the entire matrix by –1 and continue with the procedure. For solving the assignment problem, we use the Assignment technique or Hungarian method, or Flood’s technique.

The transportation problem is a special case of the linear programming model and the assignment problem is a special case of transportation problem, therefore it is also a special case of the linear programming problem.

In this tutorial, we are going to cover the following topics:

Assignment Problem

A problem that requires pairing two sets of items given a set of paired costs or profit in such a way that the total cost of the pairings is minimized or maximized. The assignment problem is a special case of linear programming.

For example, an operation manager needs to assign four jobs to four machines. The project manager needs to assign four projects to four staff members. Similarly, the marketing manager needs to assign the 4 salespersons to 4 territories. The manager’s goal is to minimize the total time or cost.

Problem Formulation

A manager has prepared a table that shows the cost of performing each of four jobs by each of four employees. The manager has stated his goal is to develop a set of job assignments that will minimize the total cost of getting all 4 jobs.  

Initialize LP Model

In this step, we will import all the classes and functions of pulp module and create a Minimization LP problem using LpProblem class.

Define Decision Variable

In this step, we will define the decision variables. In our problem, we have two variable lists: workers and jobs. Let’s create them using  LpVariable.dicts()  class.  LpVariable.dicts()  used with Python’s list comprehension.  LpVariable.dicts()  will take the following four values:

• First, prefix name of what this variable represents.
• Second is the list of all the variables.
• Third is the lower bound on this variable.
• Fourth variable is the upper bound.
• Fourth is essentially the type of data (discrete or continuous). The options for the fourth parameter are  LpContinuous  or  LpInteger .

Let’s first create a list route for the route between warehouse and project site and create the decision variables using LpVariable.dicts() the method.

Define Objective Function

In this step, we will define the minimum objective function by adding it to the LpProblem  object. lpSum(vector)is used here to define multiple linear expressions. It also used list comprehension to add multiple variables.

Define the Constraints

Here, we are adding two types of constraints: Each job can be assigned to only one employee constraint and Each employee can be assigned to only one job. We have added the 2 constraints defined in the problem by adding them to the LpProblem  object.

Solve Model

In this step, we will solve the LP problem by calling solve() method. We can print the final value by using the following for loop.

From the above results, we can infer that Worker-1 will be assigned to Job-1, Worker-2 will be assigned to job-3, Worker-3 will be assigned to Job-2, and Worker-4 will assign with job-4.

In this article, we have learned about Assignment problems, Problem Formulation, and implementation using the python PuLp library. We have solved the Assignment problem using a Linear programming problem in Python. Of course, this is just a simple case study, we can add more constraints to it and make it more complicated. You can also run other case studies on Cargo Loading problems , Staff scheduling problems . In upcoming articles, we will write more on different optimization problems such as transshipment problem, balanced diet problem. You can revise the basics of mathematical concepts in  this article  and learn about Linear Programming  in this article .

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File handling, python modules, python numpy, python pandas, python matplotlib, python scipy, machine learning, python mysql, python mongodb, python reference, module reference, python how to, python examples, python assignment operators.

Assignment operators are used to assign values to variables:

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Job Assignment Problem using Branch And Bound

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• Traveling Salesman Problem using Branch And Bound

Let there be N workers and N jobs. Any worker can be assigned to perform any job, incurring some cost that may vary depending on the work-job assignment. It is required to perform all jobs by assigning exactly one worker to each job and exactly one job to each agent in such a way that the total cost of the assignment is minimized.

Let us explore all approaches for this problem.

Solution 1: Brute Force  

We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O(n!).

Solution 2: Hungarian Algorithm  

The optimal assignment can be found using the Hungarian algorithm. The Hungarian algorithm has worst case run-time complexity of O(n^3).

Solution 3: DFS/BFS on state space tree  

A state space tree is a N-ary tree with property that any path from root to leaf node holds one of many solutions to given problem. We can perform depth-first search on state space tree and but successive moves can take us away from the goal rather than bringing closer. The search of state space tree follows leftmost path from the root regardless of initial state. An answer node may never be found in this approach. We can also perform a Breadth-first search on state space tree. But no matter what the initial state is, the algorithm attempts the same sequence of moves like DFS.

Solution 4: Finding Optimal Solution using Branch and Bound  

The selection rule for the next node in BFS and DFS is “blind”. i.e. the selection rule does not give any preference to a node that has a very good chance of getting the search to an answer node quickly. The search for an optimal solution can often be speeded by using an “intelligent” ranking function, also called an approximate cost function to avoid searching in sub-trees that do not contain an optimal solution. It is similar to BFS-like search but with one major optimization. Instead of following FIFO order, we choose a live node with least cost. We may not get optimal solution by following node with least promising cost, but it will provide very good chance of getting the search to an answer node quickly.

There are two approaches to calculate the cost function:  

• For each worker, we choose job with minimum cost from list of unassigned jobs (take minimum entry from each row).
• For each job, we choose a worker with lowest cost for that job from list of unassigned workers (take minimum entry from each column).

In this article, the first approach is followed.

Let’s take below example and try to calculate promising cost when Job 2 is assigned to worker A. 

Since Job 2 is assigned to worker A (marked in green), cost becomes 2 and Job 2 and worker A becomes unavailable (marked in red). 

Now we assign job 3 to worker B as it has minimum cost from list of unassigned jobs. Cost becomes 2 + 3 = 5 and Job 3 and worker B also becomes unavailable. 

Finally, job 1 gets assigned to worker C as it has minimum cost among unassigned jobs and job 4 gets assigned to worker D as it is only Job left. Total cost becomes 2 + 3 + 5 + 4 = 14. 

Below diagram shows complete search space diagram showing optimal solution path in green. 

Complete Algorithm:  

Below is the implementation of the above approach:

Time Complexity: O(M*N). This is because the algorithm uses a double for loop to iterate through the M x N matrix.  Auxiliary Space: O(M+N). This is because it uses two arrays of size M and N to track the applicants and jobs.

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Should you give job applicants an assignment during the interview process? Be thoughtful about the ask

Hiring is a time-consuming and expensive endeavor. Companies need candidates who offer the right skills and experience for a given role, and who align with their organization’s vision and mission.

To find the best fit, many companies still lean on a strategy that continues to generate debate : the assignment. Some candidates believe their experience and interviews should give prospective employers enough information to determine whether they will fit the role. Employers have to ask themselves whether they are willing to turn off a strong candidate by asking them to do additional work.

Is the assignment valuable enough to the evaluation process that they cannot move someone forward without it? Sometimes it is—sometimes they help an employer decide between two strong candidates. And if they are necessary, how can employers make assignments fair and equitable for the candidate or candidates?

When done right, assignments help assess practical skills and problem-solving abilities, giving a clearer picture of a candidate beyond what their resume or interview reveals. But employers should be thoughtful about the ask. While it may make sense for roles that require specific technical expertise or creative thinking, it isn’t appropriate for all roles—so assignments should always be given with a clear reason for why they are needed.

Plus, they don’t just benefit the employer. For job seekers, an assignment during the interview process might also help them stand out from the competition. It can also offer a window into what their day-to-day in the new role might entail. Remember that the candidate should be interviewing the company, too. Having a test run of the work they’d be asked to do is a great way to see whether they believe the role is a fit.

However, there is a rift in how people perceive the assignment as part of the interview process. Workers today span many generations, each with unique values and expectations. Whereas older workers often prioritize stability and loyalty, younger millennials and Gen Zers are more focused on flexibility and work well-being, Indeed data shows .

This mindset impacts the amount of time and energy a candidate is willing to devote to each application. After multiple rounds of interviews and prep, taking on an in-depth assignment may feel like a bridge too far—especially if the expectations for the assignment are not clearly communicated ahead of time.

Some candidates are wary of providing free labor to a company that may use their work and not hire them. Hiring managers should be clear about how the work will be used. They may also consider offering compensation if the assignment requires more than a couple hours of someone’s time, or if they plan to use the work without hiring the candidate.

The key for early career candidates in particular is to ensure their time and efforts are respected. This is a win-win for employers: By providing clarity and transparency, they not only elicit the additional information they want from candidates, but they demonstrate that the organization is transparent and fair.

Equity is also imperative: Which candidates are being asked to complete assignments? Is the hiring team consistent in giving out assignments across ages, experience levels, and roles? There should always be a process and clear evaluation criteria in place to ensure fairness.

As we adapt to the rapidly evolving world of work, we must continue to think critically about each step in the hiring process. Candidate assignments can be a valuable tool, but only with appropriate respect for job seekers’ time and contributions.

With the right strategy, we can bridge the gap between generations in the workplace and build a hiring culture that values efficiency, talent, and integrity.

Eoin Driver is the global vice president of talent at Indeed.

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