Solving Large-Scale Combinatorial Optimization Problems.

Optimization problems are concerned with the efficient use or allocation of limited resources to meet desired objectives. These problems are characterized by the large number of alternatives that satisfy the basic conditions of each problem. The selection of a particular solution as the best solution to a problem depends on some goal or overall objective. The versatility of the combinatorial model stems from the fact that in many practical problems, activities or resources, such as machines, airplanes, missile target sites, and people are indivisible. Also, many problems have only a finite number of alternative choices and consequently can appropriately be formulated as combinatorial problems. We refer the reader to the following texts and their bibliographical references for further review of some of these important engineering and managerial decision problems Combinatorial and Integer Programming Nemhauser and Wolsey, Applied Mathematieal Programming Bradley, Hax and Magnanti, Principles of Operations Research Wagner, and Model Building in Mathematical Programming Williams.