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The paper is concerned with the two-machine flow shop, where each jobrequires an additional resource (referred to as storage space) from the startof its first operation till the end of its second operation. The storagerequirement of a job is determined by the processing time of its firstoperation. At any point in time, the total consumption of this additionalresource cannot exceed a given limit (referred to as the storage capacity). Thegoal is to minimise the makespan, i.e. to minimise the time needed for thecompletion of all jobs. This problem is NP-hard in the strong sense. The paperanalyses how the parameter - a lower bound on the storage capacity specified interms of the processing times, affects the computational complexity.

On a borderline between the NP-hard and polynomial-time solvable cases of the flow shop with job-dependent storage requirements