0-1 integer interval number programming approach for the multilevel generalized assignment problem

In this paper, an approach is suggested to solve the multilevel generalized assignment problem with 0-1 integer interval number programming. The multilevel generalized assignment problem (MGAP) differs from the classical GAP in that agents can perform tasks at more than one efficiency level. The large number of variables in the related 0–1 integer program makes it hard to ?nd optimal solutions to these problems, even when using powerful commercial optimization packages. In the real world, however, the parameters are seldom known exactly and have to be estimated. Interval programming is one of the tools to tackle uncertainty in mathematical programming models. In the multilevel generalized assignment problem (MGAP) agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. A parametric study is carried out for the problem of concern.