Sequencing of Parts and Robot Moves in a Robotic Cell

Cyclic scheduling of a 2-machine robotic cell with tooling constraints

“…With the settings of this study, we prove that the optimal solution is not necessarily a 1-unit cycle as in the case of Sethi et al (1992) and that a 2-unit cycle can also give the optimal cycle time for some parameter values. We also show that the problem considered by Sethi et al (1992) is a special case of the problem under consideration in this study.…”

“…Hall et al (1997) considered three machine cells producing single part-types and proved that the repetition of 1-unit cycles dominates more complicated policies that produce two units. The validity of the conjecture of Sethi et al (1992) for 3-machine robotic flowshops is established by Crama and van de Klundert (1999). Brauner and Finke (1997) disproved this conjecture for cells of size four or large.…”

“…For 2-machines, no-buffer, identical parts robotic cell scheduling problem, Sethi et al (1992) proved that the optimal solution is a 1-unit cycle where an n-unit cycle can be defined as, starting with an initial state of the system, loading and unloading all of the machines exactly n times and returning to the initial state of the system (note that in an n-unit cycle exactly n parts are produced). They also conjectured that optimal 1-unit cycles are superior to every n-unit cycle, for n P 2.…”

Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints

“…The problem is to identify a cyclic hoist schedule to minimize the cycle time, with the processing times either fixed or confined within time intervals. Most of the related work considered the single product case, and can be found in the work by Suprunenko et al (1962), Tanaev (1964), Livshits et al (1974), Phillips and Unger (1976), Shapiro and Nuttle (1988), Kise (1991), Sethi et al (1992), Lei (1993), Armstrong et al (1994), Levner (1998, 2002), Sriskandarajah et al (1998), Lei and Wang (1994), Lei and Liu (2001), Agnetis and Pacciarelli (2000), Brucker et al (2002), and Che and Chu (2005). A thorough review in this area can be found in the surveys by Hall (1999) and Crama et al (2000).…”

On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices

“…Furthermore, let φ be defined so that 0 < b φ(1) ≤ b φ(2) ≤ · · · ≤ b φ (n) . In order to show that C φ has the Monge property, we need to prove that c iφ(j ) + c i φ(j) ≥ c iφ(j ) + c i φ(j ) for (Arora and Rana 1980) Two-machine bufferless robotic cell Gilmore-Gomory a,b Subtour patching O(n log n) (Sethi et al 1992) scheduling Two-machine bufferless robotic cell b-decomposable a,b…”