# Linking Scheduling Criteria to Shop Floor Performance in Permutation Flowships
## 1 Introduction  
To handle the complexity of manufacturing decisions, these have been traditionally addressed in a hierarchical manner, in which the overall problem is decomposed into a number of sub-problems or decision levels [1]. Given a decision level, pertinent decisions are taken according to specific local criteria. It is clear that, for this scheme to work efficiently, the decisions among levels should be aligned to contribute to the performance of the whole system. Among the different decisions involved in manufacturing, here we focus on scheduling decisions. Scheduling (some authors use the term \"detailed scheduling\") is addressed usually after medium-term production planning decisions have been considered, since production planning decision models do not usually make distinction between products within a family, and do not take into account sequence-dependent costs, or detailed machine capacity [2]. A short-term detailed scheduling model usually assumes that there are several jobs--eachone with its own characteristics--that have to be scheduled so one or more _scheduling criteria_ are minimised. The schedule is then released to the shop floor, so the events in the shop floor are executed according to the sequence and timing suggested by the schedule [3]. Therefore, there is a clear impact of the chosen scheduling criteria on (medium/long term) shop floor performance, which is eventually reflected on shop floor performance measures such as the throughput of the system (number of jobs dispatched by time unit), cycle time (average time that the jobs spend in the manufacturing system), or work in process. As these performance measures can be linked to key aspects of the competitiveness of the company (e.g., throughput is related to capacity and resource utilisation, while cycle time and work in process are related to lead times and inventory holding costs), the chosen scheduling criterion may have an important impact in the performance of the company, so it is important to assess the impact of different scheduling criteria on shop floor performance measures. However, perhaps for historical reasons, the connection between shop floor performance measures and scheduling criteria has been neglected by the literature since, to the best of our knowledge, there are not contributions addressing this topic. In general, the lack of understanding and quantification of these connections has led to a number of interrelated issues:  
* Some widely employed scheduling criteria have been subject of criticism due to their apparent lack of applicability to real-world situations (see, e.g., the early comments in [4] on [PERSON]'s famous paper, or [5] and [1] on the lack of real-life application of makespan minimisation algorithms), which suggest a poor alignment of these criteria with the companies' goals. * Some justifications for using specific scheduling criteria are given without a formal proof. For instance, it is usual in the scheduling literature to mention that minimising the completion time in a flowshop leads to minimising work-in-process, whereas this statement--as we discuss in Section 2.2--is not correct from a theoretical point of view. * Some scheduling criteria employed in manufacturing have been borrowed from other areas. For instance, the minimisation of the completion time variance is taken from the computer scheduling context; therefore their potential advantages on manufacturing have to be tested. * There are different formulations for some scheduling criteria intuitively linked to shop floor performance: While machine idle time minimisation can be seen, at least approximately, as related to increasing the utilisation of the system, there are alternative, non-equivalent, manners to formulate idle time. Therefore, it remains an open question to know which formulation is actually better in terms of effectively increasing the utilisation of the system.