Cyclic Scheduling in Robotic Cells: An Extension of Basic Models in Machine Scheduling Theory

Abstract

There is a growing interest on cyclic scheduling problems both in the scheduling literature and among practitioners in the industrial world. There are numerous examples of applications of cyclic scheduling problems in different industries (see, e.g., Hall (1999), Pinedo (2001)), automatic control (Romanovskii (1967), Cohen et al. (1985)), multi-processor computations (Hanen and Munier (1995), Kats and Levner (2003)), robotics (Livshits et al. (1974), Kats and Mikhailetskii (1980), Kats (1982), Sethi et al. (1992), Lei (1993), Kats and Levner (1997a, 1997b), Hall (1999), Crama et al. (2000), Agnetis and Pacciarelli (2000), Dawande et al. (2005, 2007)), and in communications and transport (Dauscha et al. (1985), Sharma and Paradkar (1995), Kubiak (2005)). It is, perhaps, a surprising thing that many facts in scheduling theory obtained as early as in the 1960s, are re-discovered and rerediscovered by the next generations of researchers. About two decades ago, this fact was noticed by Serafini and Ukovich (1989). The present survey uniformly addresses cyclic scheduling problems through the prism of the classical machine scheduling theory focusing on their features that are common for all aforementioned applications. Historically, the scheduling literature considered periodic machine scheduling problems in two major classes – called flowshop and jobshop in which setup and transportation times were assumed insignificant. Indeed, many machining centers can quickly switch tools, so the setup times for these situations may be small or negligible. There are a lot of results about cyclic flowshop and jobshop problems with negligible setup/transportation times. Advantages of cyclic scheduling policies over conventional (non-cyclic) scheduling in flexible manufacturing are widely discussed in the literature, we refer the interested reader to Karabati and Kouvelis (1996), Lee and Posner (1997), Hall et al. (2002), Seo and Lee (2002), Timkovsky (2004), Dawande et al. (2007), and numerous references therein. At the same time, modern flexible manufacturing systems are supplied by computercontrolled hoists, robots and other material handling devices such that the transportation and setup operation times are significant and should not be ignored. Robots have become a standard tool to serve cyclic transportation and assembling/disassembling processes in manufacturing of airplanes, automobiles, semiconductors, printed circuit boards, food