Hybrid flowshop scheduling with machine and resource-dependent processing times

On flowshop scheduling problems with the aging effect and resource allocation

“…For both cases, C (2) π(i+1) −C (2) π (i+1) > 0; thus, the permutation π cannot be optimal and the non-increasing order of a (z) j (for fixed z ∈ {1, 2}) gives the optimal solution to the considered problem.…”

“…On this basis, we prove the following properties: (2) ,ū j = u, u j ≤R|C max can be solved optimally in O(n log n) steps by allocating the resource in the non-increasing maximal possible amount starting from the jobs with the maximal value of parameter γ j and by scheduling jobs according to the non-increasing values of resource ratios γ j .…”

“…However, in the further part, we will analyse its special cases with two machines, where job processing times on M 2 are constant, i.e. p (2) …”

“…It follows from the observations that algorithms constructed on the basis of the classical models usually provide unsatisfactory (unstable) solutions for real-life flowshop problems, since these models do not take into consideration additional factors that are significant in practice, e.g. sequence-dependent setup times [16,20] or variable processing times [2,4,5,23,27,31]. To this group belong the described real-life problems, where a deterioration of machines (understood as chemical cleaning baths, lathe machines, human workers etc.)…”

“…of the bath by heating up the pickle using an additional energy), can be modelled by additional resources (e.g. [2,11,22]), i.e. gas or electric energy (to heat up the pickle) and/or the active substance.…”