Order of Speakers

1 – 1:30 pm

Dr. Emma Jane Riddle, College of Business Administration, Winthrop University

Two Applications of Mathematics to Business

1:35 – 2:05 pm

Dr. Andrew Yingst, Mathematics, USCL

Measure, Category, Cardinality:

Ubiquitous things that can't be found

2:10 – 2:40 pm

Allan Pangburn, Mathematics, USCL

A New Algorithm for Maximum Flow Distribution Networks: The Modified Push Algorithm

Abstracts

Two Applications of Mathematics to Business

Businesses use mathematics and statistics every day. Two applications of mathematics to business will be presented.

The first example shows how queuing theory can be used to analyze the waiting line at a drive-up teller window. The data for the problem includes the number of customers arriving per hour (arrival rate) and the number of customers the teller can serve in an hour (service rate). We will determine the average waiting time, the average length of the line, the utilization of the teller, and the idle time of the teller. Adding a second teller window would decrease waiting time but would also increase costs for the bank.

The second example involves breakeven analysis. A business obtains revenue by selling goods or services. Every business pays fixed costs, such as rent, which must be paid even if no products are sold. Businesses also pay variable costs, such as materials and labor. Variable costs increase with the number of units produced. The breakeven point is the number of units that must be produced to pay fixed and variable costs, so that the business does not lose money. We will use algebra to find the formula for the breakeven point. If time permits, "what-if" analysis will be used to show the impact of pricing assumptions on the breakeven point.

Measure, Category, Cardinality:

Ubiquitous things that can't be found

When a mathematician says that "almost everything" of a certain type has a certain property, she may be describing one of a few concepts. In this talk, aimed at the introductory level, we discuss the three most common interpretations of this phrase, we give examples of how these definitions lead to the knowledge that things may exist without the ability to construct any examples of them, and we'll touch on the surprising fact that almost every point might have some property in one sense, while almost every point does not have that same property in another.

A New Algorithm for Maximum Flow Distribution Networks: The Modified Push Algorithm

Over the years researchers and programmers have created and revised algorithms to solve maximum flow network (MFN) problems. These problems contain: source node(s), transshipment (ordinary) nodes , sink node(s), and arcs with limited capacities. The objective is to send the maximum amount of flow from the source nodes, through the ordinary nodes to reach the termination nodes. A variation of MFN is a maximum flow distribution network (MFDN) problem. These problems contain the same nodes as MFN, but with additional nodes called distribution nodes. These nodes have only one

ow entering and multiple flows leaving, but the leaving flows are proportion to the entering flow. In this presentation, we present a new method to determine an initial feasible flow by revising: Goldberg and Tarjan's algorithm of 1988, and Sheu, Ting, and Wang's algorithm of 2006. Major revisions include: defining a predetermined search order, resetting capacities on arcs, two formulas to lessen the amount of excess flow, and defining a new subgraph.

More information about Carolina Mathematics Seminar is available at http://macs.citadel.edu/florez/seminar.html