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Over the past few years, the Midwest Independent Transmission System Operator, Inc. (MISO) has transformed the electric utility industry in 13 Midwestern US states through the development and implementation of energy and ancillary services markets. MISO uses mixed-integer programming to determine when each power plant should be on or off. Operations research methods set energy output levels and establish the prices at which energy trades. These new markets increased the efficiency of the existing electric infrastructure (power plants and transmission lines) in the Midwest, improved the reliability of the grid, and reduced the need for future infrastructure investments. These advances enabled the MISO region to realize between $2.1 billion and $3.0 billion in cumulative savings from 2007 through 2010. We expect additional savings of $6.1 billion to $8.1 billion through 2020.

Skiving is the process of joining smaller rolls to form larger rolls. When this process is combined with traditional roll-cutting technology, profitable solutions to once "hopeless" one-dimensional cutting stock problems can be found. A generalization of the classic cutting stock problem models the combined skiving and cutting stock problem. The commercial software package MAJIQTRIM solves this combined problem using both heuristic and linear programming (LP) methods. AMS subject classifications. 90B90, 90C90PII. S003614459531004X 1. Background. The one-dimensional cutting stock problem (CSP), or trim problem, is one of the most fascinating problems in operations research [6]. Nearly 60 years have passed since Nobel prize winner Kantorovich in 1939 gave a linear programming (LP) formulation of the CSP [10]. Although the CSP is truly an integer programming problem, a combined approach involving an LP relaxation of the CSP at the first stage and a rounding procedure at the second works quite well for many classes of the CSP. It is interesting to note that an auxiliary problem is needed to generate the columns of the LP matrix. This auxiliary problem is a special case of the knapsack problem known as the value independent knapsack problem [13].The "real world" problems occurring in the paper, steel, and other industries may involve billions of potential cutting patterns. Therefore, it is not always practical to generate the whole LP matrix in advance. An impressive "dynamic" column generation technique built into the framework of the simplex was proposed by Gilmore and Gomory in 1961 [1, 2]. On every iteration of the simplex algorithm, an auxiliary problem-the knapsack problem in its general form-must be solved to create a new column (pattern) to be entered into the basis.Although the LP approach was proven to be the most sophisticated method, yielding trim solutions that significantly outperformed manual methods in terms of trim efficiency, it had a drawback as well. The number of patterns in the LP solutions (nonzero variables) normally equals the number of sizes to be cut (number of rows). So if the trim problem has 50 sizes then the LP solution tends to have 50 patterns. Every pattern implies additional labor cost. The next milestone in the history of the CSP was in 1971 when Haessler [5], after studying attentively how schedulers tackle real world problems at paper mills, proposed an elegant heuristic procedure. That procedure may yield efficiency to the LP approach but uses fewer patterns (sometimes less than half).In 1985 the theoretical result of Marcotte [12] shed light on the relationship between solutions of the LP relaxation and the CSP itself. She proved that for some practical instances of the problem a so-called round-up property is valid. It means that to find the optimal value of the CSP, it is sufficient just to solve the LP relaxation *

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