Abstract
We consider two-machine open shops with job-dependent time lags in this chapter. The time lags model transportation delays, intermediate processes, or operations that are not constrained by resources. We give a new proof of NP-hardness of makespan minimization for two-machine open shop with time lags and unit-time operations. We present a \(O(n \log n)\) algorithm for a special case where all time lags are distinct. We observe that the algorithm produces ideal schedules that minimize makespan and total completion time at the same time. We then prove that the total completion time minimization is NP-hard in the strong sense for two-machine open shop with time lags and unit-time operations. This answers an open question. We review approximation algorithms for the makespan minimization problem, and inapproximability results for the problem with exact time lags. We also discuss some open problems.
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