In this paper we deal with a variant of the Job Shop Scheduling Proble
m. We consider the addition of release dates and deadlines to be met b
y all jobs. The objective is makespan minimization if there are no tar
dy jobs, and tardiness minimization otherwise. The problem is approach
ed by using a Shifting Bottleneck strategy. The presence of deadlines
motivates an iterative use of a particular one machine problem which i
s solved optimally. The overall procedure is heuristic and exhibits a
good trade-off between computing time and solution quality.