Mathematics - Publications - Faculty & Research - Harvard Business School

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January 1990 (Revised February 1990)
Case

MSA: The Software Company--Planning the AMAPs Product Line

By: Robert J. Dolan

MSA has commissioned a major market research study to assess demand potential for a computer software system designed for aerospace and defense contractors. Students must evaluate the results of the study (including a conjoint analysis) to assess whether MSA should... View Details

Keywords: Product; Marketing; Mathematical Methods; Software

May 1984 (Revised September 1986)
Background Note

Basic Quantitative Analysis for Marketing

By: Robert J. Dolan

Shows how to calculate and use the break-even volume in marketing decision making. View Details

Keywords: Marketing Strategy; Mathematical Methods

01 Dec 2008
News

A U.S. Turnaround?

sad story of our slippage in mathematics and science. In fourth grade, American children are ahead of almost everyone in the world. By the eighth grade they are even, and by twelfth grade they are seriously behind. If you walk through the... View Details

Keywords: Byron Wien; Performing Arts, Spectator Sports, and Related Industries; Arts, Entertainment; Computer and Electronic Product Manufacturing; Manufacturing; Transportation Equipment Manufacturing; Manufacturing; Electric Power Generation, Transmission, Distribution; Utilities

01 Feb 1997
News

Merton Discusses Risk Management at Dean's Seminar

Merton noted that "risk management will become an essential internal process for the lending institution if it expects to remain viable and competitive." By demonstrating mathematically how to determine and hedge risk exposure for any new... View Details

Keywords: Elizabeth McNair

2011
Working Paper

The Cost of Capital for Alternative Investments

By: Jakub W. Jurek and Erik Stafford

This paper studies the cost of capital for alternative investments. We document that the risk profile of the aggregate hedge fund universe can be accurately matched by a simple index put option writing strategy that offers monthly liquidity and complete transparency... View Details

Keywords: Cost of Capital; Financial Liquidity; Investment; Investment Return; Mathematical Methods; Risk and Uncertainty

December 1988
Article

Strategic Responses to Automobile Emissions Control: A Game-Theoretic Analysis

This paper examines the dynamics of standard-setting regulation under technological uncertainty and asymmetric information about technological capability. A two-period model which allows fully strategic action is developed and applied to the regulation of automobile... View Details

Keywords: Transportation; Pollutants; Standards; Governance Controls; Technological Innovation; Research and Development; Mathematical Methods

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2023
Working Paper

An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits

By: Biyonka Liang and Iavor I. Bojinov

Typically, multi-armed bandit (MAB) experiments are analyzed at the end of the study and thus require the analyst to specify a fixed sample size in advance. However, in many online learning applications, it is advantageous to continuously produce inference on the... View Details

Keywords: Analytics and Data Science; AI and Machine Learning; Mathematical Methods

October 1, 2021
Article

An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance.

By: B.M. Balk, M.R. De Koster, Christian Kaps and J.L. Zofio

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a... View Details

Keywords: Efficiency Analysis; Performance Benchmarking; Warehousing; Analytics and Data Science; Performance Evaluation; Measurement and Metrics; Mathematical Methods

2022
Working Paper

The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective

By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju

As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how... View Details

Keywords: AI and Machine Learning; Analytics and Data Science; Mathematical Methods

2023
Article

Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse

By: Martin Pawelczyk, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci and Himabindu Lakkaraju

As machine learning models are increasingly being employed to make consequential decisions in real-world settings, it becomes critical to ensure that individuals who are adversely impacted (e.g., loan denied) by the predictions of these models are provided with a means... View Details

Keywords: AI and Machine Learning; Decision Choices and Conditions; Mathematical Methods

November–December 2018
Article

Online Network Revenue Management Using Thompson Sampling

By: Kris J. Ferreira, David Simchi-Levi and He Wang

We consider a network revenue management problem where an online retailer aims to maximize revenue from multiple products with limited inventory constraints. As common in practice, the retailer does not know the consumer's purchase probability at each price and must... View Details

Keywords: Online Marketing; Revenue Management; Revenue; Management; Marketing; Internet and the Web; Price; Mathematical Methods

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Winter 2017
Article

Why Big Data Isn't Enough

By: Sen Chai and Willy C. Shih

There is a growing belief that sophisticated algorithms can explore huge databases and find relationships independent of any preconceived hypotheses. But in businesses that involve scientific research and technological innovation, this approach is misguided and... View Details

Keywords: Big Data; Science-based; Science; Scientific Research; Data Analytics; Data Science; Data-driven Management; Data Scientists; Technological Innovation; Analytics and Data Science; Mathematical Methods; Theory

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May 2011
Teaching Note

Baria Planning Solutions, Inc.: Fixing the Sales Process (Brief Case)

By: Steven C. Wheelwright and William Schmidt

Teaching Note for 4568. View Details

Keywords: Quantitative Analysis; Technology; Operations Management; Product Lines; Manufacturing; Capacity Planning; Production Planning; Information Technology; Production; Mathematical Methods; Performance Capacity; Product Development; Planning; Manufacturing Industry

May 1993
Case

Patient Transfusion Services Lab of Central Blood Bank

By: James L. Heskett

The vice president of the Lab and Clinical Services at Central Blood Bank is faced with the challenge of convincing a hospital to use economical shared patient transfusion testing services. View Details

Keywords: Health Care and Treatment; Quality; Service Operations; Mathematical Methods; Customer Satisfaction; Health Industry

September 2018
Article

Aggregation of Consumer Ratings: An Application to Yelp.com

By: Weijia Dai, Ginger Jin, Jungmin Lee and Michael Luca

Because consumer reviews leverage the wisdom of the crowd, the way in which they are aggregated is a central decision faced by platforms. We explore this "rating aggregation problem" and offer a structural approach to solving it, allowing for (1) reviewers to vary in... View Details

Keywords: User Generated Content; Crowdsourcing; Yelp; Social and Collaborative Networks; Information; Internet and the Web; Learning; Mathematical Methods; E-commerce

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January 2008
Background Note

Index Options

By: Joshua Coval and Erik Stafford

The goal of this simulation is to understand the patterns in index option prices that are not predicted by the Black-Scholes model. In particular, the simulation focuses on two properties of options prices. First, at-the-money implied volatilities from index options... View Details

Keywords: Volatility; Stock Options; Investment; Price; Profit; Risk Management; Mathematical Methods

January 2002 (Revised October 2007)
Case

Grantham, Mayo, Van Otterloo & Co., 2001

By: Joshua Musher and Andre F. Perold

Asset manager GMO underperforms the market during the 1996-2000 stock market bubble because of the focus on absolute risk. After suffering significant client withdrawals, performance again shines when the bubble collapses. Did they win the battle only to lose the war?... View Details

Keywords: Customers; Asset Management; Stocks; Investment; Price Bubble; Mathematical Methods; Risk and Uncertainty

October 1993 (Revised August 1996)
Background Note

Forecasting with Regression Analysis

By: Arthur Schleifer Jr.

Provides an example of regression in one of its most important roles. Relating probabilistic forecasts based on past data to decision analysis. View Details

Keywords: Management Analysis, Tools, and Techniques; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods

February 2010 (Revised March 2016)
Background Note

Marketing Analysis Toolkit: Break-even Analysis

By: Thomas J. Steenburgh and Jill Avery

Marketing managers are often called upon to make recommendations for or against programs that cost money to implement. Before expenditures are made, managers want to be sure that they will be getting a return on their investment. One way of assessing this is by... View Details

Keywords: Decision Making; Investment Return; Spending; Management Analysis, Tools, and Techniques; Marketing Strategy; Strategic Planning; Mathematical Methods

22 Sep 2015
News

Turning Troubled Schools into High-Achievers

of stories of success. If I think about one of our turnaround schools, before we intervened at that school, only about 12 or 13 percent of students were demonstrating grade-level proficiency in mathematics and in reading. We were asked to... View Details

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