Scheduling in Robotic Cells: Classification, Two and Three Machine Cells

Abstract

This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on two or three machines served by a robot. We provide a classification scheme for scheduling problems in robotic cells. We discuss finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. For multiple part-type problems in a two-machine cell, we provide an efficient algorithm that simultaneously optimizes the robot move and part sequencing problems. This algorithm is tested computationally. For a three-machine cell with general data and identical parts, we address an important conjecture about the optimality of repeating one-unit cycles, and show that such a procedure dominates more complicated cycles producing two units. For a three-machine cell producing multiple part-types, we prove that four out of the six potentially optimal robot move cycles for producing one unit allow efficient identification of the optimal part sequence. Several efficiently solvable special cases with practical relevance are identified, since the general problem of minimizing cycle time is intractable. Finally, we discuss ways in which a robotic cell converges to a steady state.

Sequencing and Scheduling in Robotic Cells: Recent Developments

“…Hall, Kamoun, and Sriskandarajah (1997) show that for three-machine cells (problem RF 3 |(free, A, MP, CRM)|µ), the Gilmore and Gomory (1964) algorithm can be used to find the optimal part schedule for the three CRM sequences based on the cycles S 3 = (A 0 , A 1 , A 3 , A 2 ), S 4 = (A 0 , A 3 , A 1 , A 2 ), and S 5 = (A 0 , A 2 , A 3 , A 1 ). The problem is trivial for S 1 because the cycle time does not depend on the part schedule.…”

“…For additive travel-time cells (problem RF 2 |( free, A, MP, cyclic-k)|µ), (Hall, Kamoun, and Sriskandarajah, 1997) attack the two problems-part scheduling and robot move sequencingsimultaneously. They first show that, in general, CRM sequences are not optimal MPS robot move sequences.…”

“…For example, an MPS of five parts could be produced by the following cycle of robot move cycles: S 1,2 , S 2 , S 2 , S 2,1 , S 1 . Hall, Kamoun, and Sriskandarajah (1997) find this optimal cycle using an O(n 4 ) algorithm. Aneja and Kamoun (1999) improve upon this by providing an O(n log n) algorithm.…”

“…Finding the optimal part schedule for the CRM sequences based on the two remaining cycles, S 2 = (A 0 , A 2 , A 1 , A 3 ) and S 6 = (A 0 , A 3 , A 2 , A 1 ), is NP-hard, unless special conditions on the data are met (Hall, Kamoun, and Sriskandarajah, 1997). Despite the intractability of the general part scheduling problem for S 2 and S 6 , Hall, Kamoun, and Sriskandarajah (1998) develop a polynomial algorithm to find the robot waiting times at the different machines and the cycle time for a given part schedule for each of these sequences.…”

Bicriteria robotic cell scheduling

“…This is the only state where a transition from S 2 1 to S 2 2 or from S 2 2 to S 2 1 can happen. The transition moves of the robot from S 2 1 (resp., S 2 2 ) to S 2 2 (resp., S 2 1 ) is denoted as S 12 (resp., S 21 ) (Hall et al 1997). Under S 12 (resp., S 21 ), the robot uses cycle S 2 1 (resp., S 2 2 ) during processing of part i on the first machine, and cycle S 2 2 (resp., S 2 1 ) during processing on the second machine.…”