Lower and upper bounds for the job shop scheduling problem with min-sum criteria

The Job Shop Scheduling Problem is one of the most intractable NP-Hard combinatorial optimization problems. To solve optimally this problem in a reasonable computational time, we have to improve the lower and the upper bounds. In this paper we introduce a new lower bound to the job shop scheduling problem with min-sum criteria and compare two different genetic algorithms. The gap is computed by comparing the best upper bound with the lower bound.