describe test sets, Graver bases, and generating functions for proving results about integer programs with linear constraints, the role of Grobner bases in integer programming, and the solution of global optimization problems with polynomial constraints via a sequence of linear algebra or semidefinite programming.

IBM ILOG CPLEX Optimizer--High-performance mathematical programming solver for linear programming, mixed integer programming, and quadratic programming, 2012.

Some other areas discussed include forecasting the demand for emergency department services, improving fairness in nurse scheduling using auctions and integer programming optimization, and alternative emergency care settings.

THE BRANCH AND BOUND APPROACH In an effort to show the value of the LDE approach, we compare it to an equivalent integer resource allocation problem formulated as an integer programming (IP) problem.

In an integer programming case the usual interpretation requires obvious modification, because if packages to be stored come in a minimum size of, say, one cubic foot, then the addition of a cubic inch of space to that offered by the warehouse clearly is zero, meaning that the first derivative of profit with respect to the constraining warehouse space is also apt to be zero, even if more warehouse space is needed urgently.

Applying Stowe's mathematics results in the integer programming formulation for this credit investigation and credit-granting problem illustrated in Table 2 for X = $500.

We have developed an integer programming model, a modification of the traditional "location" problem model (Revelle 1987), that can be used to identify a minimum set of hospitals at which to do reviews, subject to sampling design constraints derived from an analysis of statistical power.

In this paper we develop an integer programming model, as well as a heuristic to effectively assign machines to cells.