# Institute for Operations Research and Management Sciences Speaker to Visit Math Department

The S-COAM program and the Mathematics Department are pleased to announce that Adam Rosenberg will be at IUP as part of the INFORMS (Institute for Operations Research and the Management Sciences) Speakers Program on April 25, 2013.

Rosenberg will give three presentations. Verification of attendance can be provided for students.

## “Least Squares with One Constraint”

2:00–3:00 p.m., Stright 327/329

### Abstract:

We have a collection of prices that reflect brand preferences from a retail client. Think of a grocery store chain with various name brands like Kellogg’s, General Mills, or Quaker Oats and private-label store brands. Think Cheerios versus “Tasty-O’s.” We are trying to quantify the price relationships among N brands based on existing prices.

We’re going to use a least-squares fit to find N-1 brand values (if we fix one of them) based on the N*(N-1)/2 observed price ratios. We avoid the trivial solution of all the values equal to zero by imposing a single constraint on the magnitude of the values.

Starting with the derivation of the basic formula for minimizing the least sum of squared error with linear coefficients, we’ll add the single constraint and derive the formula we’re using in our own brand-value calculation.

## Operations Research Career Talk

3:30–4:20 p.m., Stright 327/329

### Abstract:

A discussion of three decades of Operations Research work.

## “Optimal Choices contour for sums”

5:00–6:00 p.m., Stright 327/329

### Abstract:

For each of N products p we have a selection of M(p) prices. Each of these prices has revenue R(P) and profit pi(P) [that’s supposed to be the Greek letter pi for profit] associated with that price. The revenue and profit value are derived from retail demand models. We want to know the best price for each product.

The concept of “best” depends on our relative weight of revenue and profit. We consider a pure-revenue objective to be lambda=zero and pure profit to be lambda=one with a continuum of revenue-profit lambda optimization weights in between. The goal of this work is to present all the optimal price possibilities for all N products over the zero-to-one range of lambda.

We’ll start by finding the optimal price for each product as a function of lambda. That involves finding the frontier, part of the convex hull of the revenue-profit values for all the prices.

Rather than enumerate M-to-the-N price-choice possibilities, we’ll find their convex hull in revenue-profit space with nothing more computationally vigorous than sorting the individual-product solutions once. While this two-objective frontier is complete and exact, extension this method to three objectives (for example, revenue, profit, and units sold) is diluted to a good approximation.

Adam Rosenberg has three decades of mathematical decision-support expertise in industries including retail science, airline optimization, financial-market analysis, hotel yield management, railroad line simulation, and telephony. He started his career at Bell Telephone Laboratories developing the emerging cellular telephone systems. He also worked in printed circuit board design and manufacture and wrote a book on CDMA, the most-recent mobile telephone technology. Many of his software solutions have remained in production for over a decade and they have earned or saved hundreds of millions of dollars for his employers and clients. Rosenberg earned his M.S. and Ph.D. degrees from Stanford University in Operations Research and his A.B. from Princeton University in Mathematics (cum laude). He holds several patents.

Department of Mathematics

Posted on 4/10/2013 11:30:48 AM

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