Genetic algorithm for the permutation flow-shop scheduling problem with linear models of operations

The paper deals with a permutation flow-shop problem where processing times of jobs on some machines are linear, decreasing functions with respect to the amount of continuously-divisible, non-renewable, locally and totally constrained resources, e.g. energy, catalyzer, raw materials, etc. The purpose is to find a processing order of jobs that is the same on each machine and a resource allocation that minimizes the length of the time required to complete all jobs, i.e. makespan. Since the problem is strongly NP-hard, some heuristic algorithms of a genetic type were applied to solve it. These algorithms strongly employ some substantial problem properties, which were proved. The results of some computational experiments are also included.