Permutation flowshop scheduling problems with maximal and minimal time lags

In this paper, we study permutation flowshop problems with minimal and/or maximal time lags, where the time lags are defined between couples of successive operations of jobs. Such constraints may be used to model various industrial situations, for instance the production of perishable products. We present theoretical results concerning two-machine cases, we prove that the two-machine permutation flowshop with constant maximal time lags is strongly NP-hard. We develop an optimal branch and bound procedure to solve the mm-machine permutation flowshop problem with minimal and maximal time lags. We test several lower bounds and heuristics providing upper bounds on different classes of benchmarks, and we carry out a performance analysis.