Multiprocessor open shop problem: literature review and future directions

Multi-processor open shop (MPOS) is a combination of the classical open shop and parallel shop environments. Although there exist wide application areas of this shop environment in both production and service facilities, the research in the field is still limited. In this paper, we provided a detailed review of the research on MPOS problem. With this survey, we aimed to provide a helpful guide to those who are willing to contribute to this open field of study. We have reviewed the studies in MPOS literature under the following topics: mathematical formulations, polynomial-time optimum solution algorithms for few special cases, approximation algorithms, dispatching rules, heuristics and metaheuristics. We further presented test data used in the literature and investigated the ways researchers evaluated their results. Solution representation and parameter tuning in metaheuristic applications have been also covered in detail. There is considerable room for improvement, especially in terms of near-optimal solution approaches. We closely investigated research topics that need particular attention in future research. We believe the review here will be a good starting point to study MPOS problem, even for those who have no prior knowledge of the field.