Open-shop problems with transportation delays

IIn an open-shop problem with transportation delays additionally transportation delays (time-lags between the operations) are considered which arise when a job changes from one machine to another.

If job i changes from machine Mk to Ml, a job- and machine-dependent transportation delay t ikl occurs. If these delays are job-independent or machine-independent, we write t kl or t i. Constant tranportation delays are denoted by t ikl=T and t i {T 1,T 2} means that the transportation delays may take only two values. The transportation delays may be symmetric, which is indicated by t ikl=t ilk.