Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations

Abstract

The paper establishes the NP-hardness in the strong sense of a two-machine flow shop scheduling problem with unit execution time (UET) operations, dynamic storage availability, job dependent storage requirements, and the objective to minimise the time required for the completion of all jobs, i.e. to minimise the makespan. Each job seizes the required storage space for the entire period from the start of its processing on the first machine till the completion of its processing on the second machine. The considered scheduling problem has several applications, including star data gathering networks and certain supply chains and manufacturing systems. The NP-hardness result is complemented by a polynomial-time approximation scheme (PTAS) and several heuristics. The presented heuristics are compared by means of computational experiments.