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Mathematical Experiences in Business, Industry and Government

Mathematical Experiences in Business, Industry and Government

By Phil Gustafson

Applications of mathematics to projects in business, industry and government (BIG) offer a wealth of exciting problems for mathematicians. Examples of BIG topics were presented at the MAA Contributed paper session entitled ?Mathematics Experiences in Business, Industry and Government,? during the Joint MAA-AMS meetings in San Antonio. This article discusses highlights of the BIG projects presented at the session. The paper session was sponsored by the Business, Industry and Government Special Interest Group of the MAA (BIG SIGMAA), and was organized by Phil Gustafson of Mesa State College and Michael Monticino of the University of North Texas.

Omayra Ortega, a graduate student at the University of Iowa, described her work in Cairo, Egypt, performing a cost analysis of treating infant rotavirus. This project was conducted in cooperation with Mark Riddle and John Sanders of the U.S. Navy Medical Research Unit 3. Rotavirus is a significant cause of morbidity and mortality in Egyptian children aged 0-5 years. The Egyptian Ministry of Health and Population (MoHP) is the main payer of health care and responsible for administering the Expanded Program on Immunization within the country. The cost-benefit analysis was conducted to evaluate the economic impact of introducing a rotavirus vaccine to the current national immunization schedule. In the base-case model, it is estimated that a vaccination program would prevent 1,074,799 episodes of diarrhea, 413,133 outpatient visits, 44,770 hospitalizations and save 2,707 lives, resulting in direct medical costs savings to the MoHP of over 13.5 million dollars. The analysis predicted that the vaccine would cost the MoHP close to 32.5 million dollars. This equates to a benefit-cost ratio of 0.0726:1 and an incremental cost of $30.22 per infection prevented.

Michael Monticino of the University of North Texas spoke on a consulting project modeling teller staffing in retail banks. This project was conducted in cooperation with Travis Cogdill, a graduate student at the University of North Texas. Approximately seventy-four percent of retail bank employees are tellers, and their salaries are a bank?s chief source of labor costs. Overstaffing tellers unnecessarily increases labor costs, while understaffing affects customer service and employee morale. Thus getting the right number of tellers in a branch at the right times is essential to controlling costs, retaining customers and employees, and growing a bank?s revenue. This talk discussed the development of a Teller Staffing product for retail banks by ARGO Data Resources, Inc.

ARGO specializes in data delivery and integration technology for the financial services industry. ARGO currently has a fifty percent market share of the top ranking 30 U.S. banks where over five million financial transactions every hour are processed with ARGO systems. The Teller Staffing product combines mathematical methods with state of the art information technology, allowing banks to capture minute-by-minute transaction and service time data to make branch level staffing recommendations based on individual branch transaction volume patterns and teller service time statistics. This talk outlined the mathematical and practical challenges, as well as the collaboration between academics and business in developing the product.

Greg Coxson of Technology Service Corporation discussed ionospheric dispersion of linear frequency modulation (LFM) pulses in radar applications. Most radars are active sensors, transmitting energy in order to see targets. Radars typically have an advantage in enhancing the detectability of the often weak return signals, since the form of the transmitted signal is known. Radar receiver matched filters exploit this to optimize signal-to-noise ratio. However, the process does not always go smoothly. For example, detection of some especially demanding radar targets involve both the need for wide bandwidth and propagation through the ionosphere. The ionosphere exacts a penalty on wide-bandwidth signals in the form of a frequency-dependent time delay. The result is that the return signal may look very different from what was transmitted. A commonly used wide-bandwidth signal involves trains of LFM pulses. This talk examined two ways of dealing with ionospheric dispersion of LFM pulses, the first being to form the transmit pulse so that the return pulse is in a LFM format, and the second being to send out an LFM pulse and anticipate the form it will have on return.

Ellina Grigorieva of Texas Woman?s University spoke on optimal control theory applied to the interaction between a manufacturer and a retailer. She and Evgenii Khailov (Moscow State University) modeled the process of production, storage and sales of a perishable consumer good as a cooperative game between a manufacturer and a retailer. The model consisted of a pair of differential equations that incorporated many variables, including the quantity of the product in the market, the retailer?s inventory of the product, the rates of production and purchasing of the product, and the rate of reselling of the product. Also incorporated were parameters such as the coefficient of spoilage, the cost of storage of unsold product units, the price at which the retailer buys the product from the manufacturer and the price at which the retailer resells it. In this model, both parties seek to maximize their cumulative profits. The problem was solved with the use of Pontryagin?s Maximum Principle.

In this article we have seen several different applications of mathematics to problems in business, industry and government. In a variety of settings, mathematics is a key component to many important projects in the world around us. Who uses math? The answer includes many of the BIG mathematicians whose contributions help improve the quality of our everyday lives.

Contact Information:

Omayra Ortega
(omayra-ortega@uiowa.edu)
Michael Monticino
(monticino@unt.edu)
Greg Coxson
(GCoxson@tscwo.com)
Ellina Grigorieva
(EGrigorieva@mail.twu.edu)
Evgenii Khailov
(Khailov@cs.msu.su)
Phil Gustafson
(pgustafs@mesastate.edu)

Phil Gustafson is Associate Professor of Mathematics at Mesa State College in Grand Junction, CO, and is Vice Chair for Programs for BIG SIGMAA. He gratefully appreciates the input provided by the speakers for the content appearing in this article, and thanks them for their participation in the paper session.

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