applications of assignment problem in business

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:

Nonlinear Assignment Problems

Algorithms and Applications

• © 2000
• Panos M. Pardalos   ORCID: https://orcid.org/0000-0003-2824-101X 0 ,
• Leonidas S. Pitsoulis 1

University of Florida, USA

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Princeton University, USA

Part of the book series: Combinatorial Optimization (COOP, volume 7)

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Geometric Optimization Revisited

Nonlinear Optimization: A Brief Overview

A View of Lagrangian Relaxation and Its Applications

• Operations Research
• combinatorial optimization
• communication
• mathematical programming
• optimization
• programming

Table of contents (10 chapters)

Front matter, multi index assignment problems: complexity, approximation, applications.

• Frits C. R. Spieksma

Multidimensional Assignment Problems Arising in Multitarget and Multisensor Tracking

• Aubrey B. Poore

Target-Based Weapon Target Assignment Problems

• Robert A. Murphey

The Nonlinear Assignment Problem in Experimental High Energy Physics

• Jean-Francois Pusztaszeri

Polyhedral Methods for Solving Three Index Assignment Problems

• Liqun Qi, Defeng Sun

Polyhedral Methods for the QAP

• Volker Kaibel

Semidefinite Programming Approaches to the Quadratic Assignment Problem

• Henry Wolkowicz

Heuristics for Nonlinear Assignment Problems

• Stefan Voss

Symbolic Scheduling of Parameterized Task Graphs on Parallel Machines

• Michel Cosnard, Emmanuel Jeannot, Tao Yang

Decomposition Algorithms for Communication Minimization in Parallel Computing

• Ioannis T. Christou, Robert R. Meyer

Back Matter

Editors and affiliations.

Panos M. Pardalos

Leonidas S. Pitsoulis

Bibliographic Information

Book Title : Nonlinear Assignment Problems

Book Subtitle : Algorithms and Applications

Editors : Panos M. Pardalos, Leonidas S. Pitsoulis

Series Title : Combinatorial Optimization

DOI : https://doi.org/10.1007/978-1-4757-3155-2

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer Science+Business Media Dordrecht 2000

Hardcover ISBN : 978-0-7923-6646-1 Published: 30 November 2000

Softcover ISBN : 978-1-4419-4841-0 Published: 07 December 2010

eBook ISBN : 978-1-4757-3155-2 Published: 09 March 2013

Series ISSN : 1388-3011

Edition Number : 1

Number of Pages : XXIV, 304

Topics : Processor Architectures , Computer System Implementation , Optimization , Theory of Computation , Mathematical Modeling and Industrial Mathematics , Calculus of Variations and Optimal Control; Optimization

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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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assignment problem

Learn about this topic in these articles:, treatment in operations research.

…resulting problem is one of assignment. If resources are divisible, and if both jobs and resources are expressed in units on the same scale, it is termed a transportation or distribution problem. If jobs and resources are not expressed in the same units, it is a general allocation problem.

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4 Examples of Business Analytics in Action

• 15 Jan 2019

Data is a valuable resource in today’s ever-changing marketplace. For business professionals, knowing how to interpret and communicate data is an indispensable skill that can inform sound decision-making.

“The ability to bring data-driven insights into decision-making is extremely powerful—all the more so given all the companies that can’t hire enough people who have these capabilities,” says Harvard Business School Professor Jan Hammond , who teaches the online course Business Analytics . “It’s the way the world is going.”

Before taking a look at how some companies are harnessing the power of data, it’s important to have a baseline understanding of what the term “business analytics” means.

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What Is Business Analytics?

Business analytics is the use of math and statistics to collect, analyze, and interpret data to make better business decisions.

There are four key types of business analytics: descriptive, predictive, diagnostic, and prescriptive. Descriptive analytics is the interpretation of historical data to identify trends and patterns, while predictive analytics centers on taking that information and using it to forecast future outcomes. Diagnostic analytics can be used to identify the root cause of a problem. In the case of prescriptive analytics , testing and other techniques are employed to determine which outcome will yield the best result in a given scenario.

Related : 4 Types of Data Analytics to Improve Decision-Making

Across industries, these data-driven approaches have been employed by professionals to make informed business decisions and attain organizational success.

Check out the video below to learn more about business analytics, and subscribe to our YouTube channel for more explainer content!

Business Analytics vs. Data Science

It’s important to highlight the difference between business analytics and data science . While both processes use big data to solve business problems they’re separate fields.

The main goal of business analytics is to extract meaningful insights from data to guide organizational decisions, while data science is focused on turning raw data into meaningful conclusions through using algorithms and statistical models. Business analysts participate in tasks such as budgeting, forecasting, and product development, while data scientists focus on data wrangling , programming, and statistical modeling.

While they consist of different functions and processes, business analytics and data science are both vital to today’s organizations. Here are four examples of how organizations are using business analytics to their benefit.

Business Analytics Examples

According to a recent survey by McKinsey , an increasing share of organizations report using analytics to generate growth. Here’s a look at how four companies are aligning with that trend and applying data insights to their decision-making processes.

1. Improving Productivity and Collaboration at Microsoft

At technology giant Microsoft , collaboration is key to a productive, innovative work environment. Following a 2015 move of its engineering group's offices, the company sought to understand how fostering face-to-face interactions among staff could boost employee performance and save money.

Microsoft’s Workplace Analytics team hypothesized that moving the 1,200-person group from five buildings to four could improve collaboration by increasing the number of employees per building and reducing the distance that staff needed to travel for meetings. This assumption was partially based on an earlier study by Microsoft , which found that people are more likely to collaborate when they’re more closely located to one another.

In an article for the Harvard Business Review , the company’s analytics team shared the outcomes they observed as a result of the relocation. Through looking at metadata attached to employee calendars, the team found that the move resulted in a 46 percent decrease in meeting travel time. This translated into a combined 100 hours saved per week across all relocated staff members and an estimated savings of $520,000 per year in employee time.

The results also showed that teams were meeting more often due to being in closer proximity, with the average number of weekly meetings per person increasing from 14 to 18. In addition, the average duration of meetings slightly declined, from 0.85 hours to 0.77 hours. These findings signaled that the relocation both improved collaboration among employees and increased operational efficiency.

For Microsoft, the insights gleaned from this analysis underscored the importance of in-person interactions and helped the company understand how thoughtful planning of employee workspaces could lead to significant time and cost savings.

2. Enhancing Customer Support at Uber

Ensuring a quality user experience is a top priority for ride-hailing company Uber. To streamline its customer service capabilities, the company developed a Customer Obsession Ticket Assistant (COTA) in early 2018—a tool that uses machine learning and natural language processing to help agents improve their speed and accuracy when responding to support tickets.

COTA’s implementation delivered positive results. The tool reduced ticket resolution time by 10 percent, and its success prompted the Uber Engineering team to explore how it could be improved.

For the second iteration of the product, COTA v2, the team focused on integrating a deep learning architecture that could scale as the company grew. Before rolling out the update, Uber turned to A/B testing —a method of comparing the outcomes of two different choices (in this case, COTA v1 and COTA v2)—to validate the upgraded tool’s performance.

Preceding the A/B test was an A/A test, during which both a control group and a treatment group used the first version of COTA for one week. The treatment group was then given access to COTA v2 to kick off the A/B testing phase, which lasted for one month.

At the conclusion of testing, it was found that there was a nearly seven percent relative reduction in average handle time per ticket for the treatment group during the A/B phase, indicating that the use of COTA v2 led to faster service and more accurate resolution recommendations. The results also showed that customer satisfaction scores slightly improved as a result of using COTA v2.

With the use of A/B testing, Uber determined that implementing COTA v2 would not only improve customer service, but save millions of dollars by streamlining its ticket resolution process.

Related : How to Analyze a Dataset: 6 Steps

3. Forecasting Orders and Recipes at Blue Apron

For meal kit delivery service Blue Apron, understanding customer behavior and preferences is vitally important to its success. Each week, the company presents subscribers with a fixed menu of meals available for purchase and employs predictive analytics to forecast demand , with the aim of using data to avoid product spoilage and fulfill orders.

To arrive at these predictions, Blue Apron uses algorithms that take several variables into account, which typically fall into three categories: customer-related features, recipe-related features, and seasonality features. Customer-related features describe historical data that depicts a given user’s order frequency, while recipe-related features focus on a subscriber’s past recipe preferences, allowing the company to infer which upcoming meals they’re likely to order. In the case of seasonality features, purchasing patterns are examined to determine when order rates may be higher or lower, depending on the time of year.

Through regression analysis—a statistical method used to examine the relationship between variables—Blue Apron’s engineering team has successfully measured the precision of its forecasting models. The team reports that, overall, the root-mean-square error—the difference between predicted and observed values—of their projection of future orders is consistently less than six percent, indicating a high level of forecasting accuracy.

By employing predictive analytics to better understand customers, Blue Apron has improved its user experience, identified how subscriber tastes change over time, and recognized how shifting preferences are impacted by recipe offerings.

Related : 5 Business Analytics Skills for Professionals

4. Targeting Consumers at PepsiCo

Consumers are crucial to the success of multinational food and beverage company PepsiCo. The company supplies retailers in more than 200 countries worldwide , serving a billion customers every day. To ensure the right quantities and types of products are available to consumers in certain locations, PepsiCo uses big data and predictive analytics.

PepsiCo created a cloud-based data and analytics platform called Pep Worx to make more informed decisions regarding product merchandising. With Pep Worx, the company identifies shoppers in the United States who are likely to be highly interested in a specific PepsiCo brand or product.

For example, Pep Worx enabled PepsiCo to distinguish 24 million households from its dataset of 110 million US households that would be most likely to be interested in Quaker Overnight Oats. The company then identified specific retailers that these households might shop at and targeted their unique audiences. Ultimately, these customers drove 80 percent of the product’s sales growth in its first 12 months after launch.

PepsiCo’s analysis of consumer data is a prime example of how data-driven decision-making can help today’s organizations maximize profits.

Developing a Data Mindset

As these companies illustrate, analytics can be a powerful tool for organizations seeking to grow and improve their services and operations. At the individual level, a deep understanding of data can not only lead to better decision-making, but career advancement and recognition in the workplace.

“Using data analytics is a very effective way to have influence in an organization,” Hammond says . “If you’re able to go into a meeting, and other people have opinions, but you have data to support your arguments and your recommendations, you’re going to be influential.”

Do you want to leverage the power of data within your organization? Explore Business Analytics —one of our online business essentials courses —to learn how to use data analysis to solve business problems.

This post was updated on March 24, 2023. It was originally published on January 15, 2019.

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Property Owners and the Hazard Mitigation Grant Program

This web page provides information for property owners—both residential (homeowners) and business who seek to use Hazard Mitigation Grant Program funding.

Resources for Homeowners

Resources for Businesses

Resources for homeowners (residential properties), eligibility.

The president can declare a major disaster for any natural event such as a hurricane, tornado, or earthquake. When a major disaster is declared, Hazard Mitigation Grant Program (HMGP) funding may be available to help homeowners rebuild their homes stronger than they were before the disaster. Mitigation activities help a community to build back better, safer, and stronger in order to reduce the risk of future damage from natural hazards.

To be considered for HMGP funding, your home must be located in a state that received a Presidential Disaster Declaration .

Your state and community must have an approved hazard mitigation plan.  

For projects located within a Special Flood Hazard Area, the local community must be a member of the National Flood Insurance Program in good standing (not on probation, suspended, or withdrawn).

Your home rebuilding project must be cost-effective, technically feasible, environmentally sound, comply with all relevant regulations, and approved by FEMA.

Working with the community to apply

As an individual, you cannot apply directly for Hazard Mitigation Grant Program (HMGP) funding. Rather, you will need to work with your local community as they develop an HMGP grant proposal. Discuss the hazards impacting your property and plans to mitigate with your local community leaders, planners, and engineers. If the community has not already made contact, you should meet with them and request that your property be included as part of a hazard mitigation application. The community will develop a scope of work, work schedule and detailed cost estimate for an HMGP grant application, but your interaction will help inform that process.

If your local jurisdiction is eligible for a grant, you can learn more through local sources, like your local jurisdiction’s website, local media outlets, flyers at the local library or public forums (such as town hall hosted by your local officials where they explain the application process and how to work together), or announcements in newspapers, or on the radio, television and online.

Benefits of Mitigation

• Reduces losses from natural disasters in the future.
• Increases the strength of your home to withstand severe weather, flooding, wind, seismic, wildfire, and other natural hazard events .
• Lowers the cost of your homeowner’s insurance premiums.
• Increases the value of your property.
• Reduces the amount of money you spend. Federal funding generally pays up to 75% of mitigation costs, the applicant is responsible for the remaining 25%.

Application Review

Your local government develops and submits Hazard Mitigation Grant Program (HMGP) project applications to the state based on mitigation strategies identified in their hazard mitigation plan. Completed applications are sent to the respective state office that manages the process for HMGP grants. Based on the FEMA-approved Hazard Mitigation Plan and funding priorities, the state, tribe, or territory will forward completed applications to FEMA for funding.

FEMA will review applications for cost-effectiveness, technical feasibility and environmental planning, and historic preservation compliance. When projects have been approved for funding, FEMA will notify the state, tribe or territory, which will notify local governments. Once funding is approved, the local community is responsible for managing the sub-grant to ensure the scope of work, work schedule, and budget are consistent with the approved application.

Funding for Hazard Mitigation Grant Programs are submitted based on the priorities listed in a community’s FEMA-approved Hazard Mitigation Plan. Government officials at the state, local, tribal and territorial levels prioritize which project plans they will submit.

Work Begins Only After Approval

HMGP funded projects must not begin until the local community has been notified that the project has been approved. Work done prior to FEMA’s review and approval will not be reimbursed by FEMA, except basic repair work necessary to make your home habitable.

After approval, FEMA will work with the state, which will work with the local community to complete the project. Depending upon the nature and complexity of a given proposal, the local community may oversee the entire project; or they may allow the property owner to implement some of the project.

Reimbursement

To meet FEMA’s requirements for reimbursement, you must keep detailed records of payments to contractors. Your local officials will ask you to provide compliance documentation so they can finalize the project and approve reimbursement requests. FEMA will reimburse you only after the approved work has been completed.

The process for inclusion in an HMGP grant application from a local community is the same for business entities as it is for individual homeowners as described above. Additional resources for both homeowners and businesses can be found below.

Additional Resources

Reduce Wildfire Risk to your Home or Business

Before the next wildfire comes, you can make changes to reduce the likelihood that your home or business will be damaged or destroyed.

Homeowner's Guide to the Hazard Mitigation Grant Program

This brochure answers some common questions homeowners have about implementing post-disaster projects that reduce future damage to their homes.

Increased Cost of Compliance Coverage Fact Sheet

This document provides information on Increased Cost of Compliance (ICC) coverage. ICC coverage is one of several resources available for flood insurance policyholders who need additional help rebuilding after a flood.

Assignment of Coverage D Increased Cost of Compliance Coverage

This job aid is a form that can be used by a National Flood Insurance Program (NFIP) policyholder to assign their Increased Cost Compliance (ICC) payment to their community. Some communities use ICC payments assigned to them by NFIP policyholders to cover their fund match requirements for Hazard Mitigation Assistance grants.

Homeowners Guide to Retrofitting

The Federal Emergency Management Agency (FEMA) has prepared this guide specifically for homeowners who want to protect their homes from flooding. It provides clear information about the options available to you and straightforward guidance that will help you make decisions.

Residential Safe Rooms (Fact Sheet)

Having a safe room built for your home can help provide near-absolute protection for you and your family.

Taking Shelter from the Storm Building a Safe Room for your Home or Small Business

This publication is primarily intended for homeowners, builders, and contractors, but can also be used by design professionals and local officials for decision-making guidance on tornado and hurricane safe rooms. Design professionals and other readers seeking more technical guidance should refer to the Federal Emergency Management Agency’s (FEMA’s) FEMA P-361, Safe Rooms for Tornadoes and Hurricanes: Guidance for Community and Residential Safe Rooms (2015).