Approximations to optimal sequences in single-gripper and dual-gripper robotic cells with circular layouts

Abstract

This article considers the problems of scheduling operations in single-gripper and dual-gripper bufferless robotic cells in which the arrangement of machines is circular. The cells are designed to produce identical parts under the free-pickup criterion with additive intermachine travel time. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time required to produce a part or, equivalently, that maximizes the throughput. Obtaining an efficient algorithm for an approximation to an optimal k-unit cyclic solution (over all k≥ 1) is the focus of this article.The proposed algorithms introduce a new class of schedules, which are refered to as epi-cyclic cycles. A polynomial algorithm with a 5/3-approximation to an optimal k-unit cycle over all cells is developed. The performed structural analysis for dual-gripper cells leads to a polynomial-time algorithm that provides at worst a 3/2-approximation for the practically relevant case in which the dual-gripper switch time is less than twice the intermachine robot movement time. A computational study demonstrates that the algorithm performs much better on average than this worst-case bound suggests. The performed theoretical studies are a stepping stone for researching the complexity status of the corresponding domain. They also provide theoretical as well as practical insights that are useful in maximizing productivity of any cell configuration with either type of robot.

Good Production Cycles for Circular Robotic Cells

“…The authors also provide regions of optimality for classical cycles and a 5 3 -approximation of the best 1-cycle. Jung et al (2015) extend these results to k-cycles.…”

“…Depending on the type of robot used, the machines and the input and output stations can be disposed in several ways. Two main configurations are studied in the literature: on the one hand, linear or semi-circular layouts (Figure 1(a)), where the input and output buffers are separated and located respectively at each end of the line (Crama and van de Klundert, 1997), and on the other hand, circular layouts (Figure 1(b)), where the machines are arranged in a circle, with the input and output buffers either occupying the same spot (M 0 = M m+1 ), or very close (Rajapakshe et al, 2011;Jung et al, 2015).…”

“…However, dominant sequences for linear cells might not be dominant with a circular layout (Geismar et al, 2005). Most studies on circular cells consider models which relax the blocking constraints one way or another: robot with swapping ability (Jolai et al, 2012), dual-gripper robots (Sethi et al, 2001;Jung et al, 2015;Drobouchevitch et al, 2006), or machine buffers (Drobouchevitch et al, 2010). On the contrary, circular classical single gripper cells, studied by (Geismar et al, 2005;Rajapakshe et al, 2011;Jung et al, 2015) are not as well understood yet as their linear counterparts.…”

Throughput Optimization in Circular Dual‐Gripper Robotic Cells

“…With additive travel-time in a linear layout, Geismar et al (2007) develop a polynomial algorithm that provides a 10/7-approximation to an optimal k-unit cycle for single-gripper cells. For additive travel-time in a circular layout, Jung et al (2015) develop a polynomial algorithm that provides a 5/3-approximation (resp., a 3/2-approximation) to the optimum per-unit cycle time among all k-unit cycles, k ≥ 1, for single-gripper cells (resp., dual-gripper cells). For this, they introduced a new type of 2-unit cycle, called epi-cyclic cycles.…”

Pure cycles in two-machine dual-gripper robotic cells

“…Geismar et al [12] provided approximation algorithms to compare single gripper robots with dual gripper robots in a circular layout under the constant travel time assumption. Jung et al [19] studied the same problem with additive inter-machine travel times and introduced a new class of schedules, which were referred to as epi-cyclic cycles. Foumani et al [9] considered a cell in which a hub machine is revisited after each secondary operation is performed by a separate secondary machine located sequentially.…”