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Implicit Enumeration for the Pure Integer 0/1 Minimax Programming Problem

We present an implicit enumeration procedure for solving pure integer 0/1 minimax problems which arise in the context of Benders decomposition for mixed integer 0/1 linear programming problems, or in various practical settings such as the location of facilities and assembly line balancing. The procedure is an extension of the additive algorithm of E. Balas for pure integer 0/1 programming problems. We solve minimax problems directly i.e., as minimax problems, not as mixed integer programming problems. A numerical example is used to illustrate the procedure. Extensions of the basic algorithm are discussed.