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The sum of the maximum earliness and tardiness criteria is a new objective function for the job shop scheduling problem introduced in this work. A mixed integer linear programming (MIP) formulation of the job shop scheduling problem with the new objective function is developed. We design a set of experiments where we validate the MIP model on different problem sizes.

This is one of the most difficult problems in combinatorial optimization, with even modest sized instances being computationally intractable. Getting inspiration from a number of advances in solving this notoriously difficult problem, we develop a new approximate optimization approach, which is based on the imperialist competitive algorithm hybridized with an efficient neighborhood search. The effectiveness of the proposed approach is demonstrated through an experimental evaluation.