Two-machine flow shop with dynamic storage space

Abstract

The publications on two-machine flow shop scheduling problems with job dependent storage requirements, where a job seizes a portion of the storage space for the entire duration of its processing, were motivated by various applications ranging from supply chains of mineral resources to multimedia systems. In contrast to the previous publications that assumed that the availability of the storage space remains unchanged, this paper is concerned with a more general case when the availability is a function of time. It strengthens the previously published result concerning the existence of an optimal permutation schedule, shows that the variable storage space availability leads to the NP-hardness in the strong sense even for unit processing times, and presents a polynomial-time approximation scheme together with several heuristic algorithms. The heuristics are evaluated by means of computational experiments.

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

“…Case 2.1(b): π(j) ∈ L 2 . According to the algorithm either R j−1 (π) > 2a max or R j−1 (π) ≥ 3 2 a max and R j−1 (π) + ∆ π(j) + µ(i 0 ) ≥ a max , where i 0 is specified according to Algorithm 1. Thus, we have…”

“…The generalisation of the PP-problem where the storage requirement of a job is not necessarily determined by the processing time of one of its operations was considered in [26]. Other variations and generalisations of the PP-problem, considered in the literature, include the relaxation of the assumption that the storage capacity is a constant [3]; the replacement of the assumption that there exists only one pair of machines by the assumption that each job can be processed by one of several disjoint pairs of machines, each pair being assigned a storage capacity, which varies from pair to pair [8]; a flexible flow shop with batch processing [12]; as well as different objective functions.…”