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We consider the problem of minimizing the makespan on batch processingidentical machines, subject to compatibility constraints, where two jobs arecompatible if they can be processed simultaneously in a same batch. Theseconstraints are modeled by an undirected graph $G$, in which compatible jobsare represented by adjacent vertices. We show that several subproblems arepolynomial. We propose some exact polynomial algorithms to solve thesesubproblems. To solve the general case, we propose a mixed-integer linearprogramming (MILP) formulation alongside with heuristic approaches.Furthermore, computational experiments are carried out to measure theperformance of the proposed methods.

Compatibility graphs in scheduling on batch processing machines