Linear Bi-level Programming

Abstract

As has been pointed out in Chapter 1, most of the developments on multiple-level programming problem (MLPP) start with this structurally simplest bi-level programming problem (BLPP). Another reason is that many decision problems encountered in practice can be formulated as the duo-ploy type decision problem. Thus, various algorithms have been developed for solving these practical problems. Obviously, it is impossible to cover all the algorithms. Only several typical algorithms to illustrate the approaches will be discussed in this chapter. We shall restrict our discussions to the various numerical solution algorithms and avoid any theoretical treatments. Only linear and non-fuzzy approaches or Categories I and II in Table 1.1 will be discussed in this chapter and fuzzy interactive approaches, which form the main aim of this book, will be discussed in detail in later chapters. There are no linear BLPPs in Category III and Category IV does not belong to the traditional optimization approaches. Non-linear and other MLPPs will be discussed in Chapter 3.