Excelsior Statistics and Optimization


Large or small, statistical or deterministic, we can help you formulate the optimization problem your business needs to solve, and then help you solve it. Contact us for a free consultation, or read about problems we’ve solved before in these areas:

What is optimization?

Optimization problems, in their most general form, involve finding the values of variables which maximize the value of some objective function, subject to a set of constraints.

Problems are classed as either continuous or discrete, according to the type of variables they contain. The former are often solved by calculus; the latter often require enumeration of possible cases.

Many optimization problems include no random component: find the shortest path through a network; find the smallest set of coins necessary to make any needed amount of change (the answer is 10, incidentally: 3 quarters, 2 dimes, 1 nickel, and 4 pennies), or find the set of set of U.S. states with the smallest population that still add up to 270 electoral votes.

When a problem includes a random component, there may be more than one reasonable choice of objective function: maximize a mean or median value; minimize variability, while holding the mean fixed; ensure that some threshold will be exceeded only a fixed percentage of the time. An airline that wishes to overbook a particular flight, for instance, might seek to minimize (expected number of empty seats) x (airfare) + (expected number of bumped passengers) x (cost of a hotel room).

This page last edited 10.09.17