Robotic Cell Problem Research Articles

Cyclic Flow Shop Robotic Cell Scheduling Problem With Multiple Part Types

This article considers the problem of cyclic flow shop (CFS) scheduling problems in robotic cells deploying several single and dual gripper robots. In this problem, different part types are successively processed on multiple machines with different pickup criteria including free pickup, pickup within time windows, and no-waiting times. The parts are transported between the machines by the robots. We propose a novel integer programming approach that determines the optimal sequence of parts simultaneously for the sequencing of the robots’ movements and the cyclic schedule, which also results in maximizing the throughput rate. The proposed mathematical model is validated on a number of randomly generated test instances. These problem instances are constructed by varying the number of machines, part types, robots, and gripper options. This allows a detailed analysis of the model including how it scales with increasing numbers of machines, part types, robots, and grippers. An experimental evaluation shows that our proposed model is very effective for a range of small medium-sized problems. In particular, we find that differing number of robots and gripper options directly affects the cycle time and in turn, the throughput rate. Overall, our integer programming model finds good feasible solutions for up to 20 machines and 10 part types, which is comparable to real-world industrial problems.

Throughput optimization for the Robotic Cell Problem with Controllable Processing Times

In this paper, we present a MIP-based heuristic and an effective genetic algorithm for the Robotic Cell Problem with Controllable Processing Times (RCPCPT). This problem arises in modern automated manufacturing systems and requires simultaneously scheduling jobs, machines, and transportation devices in order to maximize the throughput or minimize the makespan. The RCPCPT is modeled as a flow shop problem with blocking constraints, a single transport robot, and controllable processing times. This latter feature of the model refers to the fact that the processing times are not fixed but vary linearly with the acceleration cost and therefore should be determined as part of the problem output. We formulate the problem as a nonlinear mixed-integer programming formulation and we use its linearized form to derive LP- and MIP-based heuristics. In addition, we proposed a genetic algorithm consistently yields near-optimal solution and it encompasses several novel features including, an original solution encoding as well as a mutation operator that requires iteratively solving MIPs in order to generate feasible processing times. Finally, we present a computational study for the proposed formulation, heuristics and genetic algorithm and we provide an empirical evidence of the effectiveness of the MIP-based heuristic for small instances and the genetic algorithm for large instances.

Bacteria Foraging Optimization Algorithm for Robotic Cell Scheduling Problem

The present study deals with the application of BFO for solving robotic cell problem. One of the major disadvantages of Passino invented BFO is its applicability constrains for solving problems except those contain continuous domain. Thus to make BFO applicable in robotic cell problem, Pairwiseinterchange mutation is chosen for tumbling and swimming operation during chemotaxis.While cyclic-shift neighbourhood mutation is used for random movement duringElimination-Dispersal. The example related to the two-machine robotic cell scheduling problem with sequence-dependent setup times (2RCSDST) was used to demonstrate the performance of the proposed discrete bacteria foraging algorithm. Large part sized problems varying from 200 to 500 part size was considered during this study. The computational results thus obtained were compared with two other existing optimization techniques and found BFO as the better performer to solve such large sized problems.

Mixed Integer Linear Programs for Blocking and No Wait Job Shop Scheduling Problems in Robotic cells

Mixed Integer Linear Programs for Blocking and No Wait Job Shop Scheduling Problems in Robotic cells

Optimal robotic cell scheduling with controllers using mathematically based timed Petri nets

This paper presents an optimal solution to the robotic cell scheduling problem for robot movement controllers using timed Petri nets (TPNs). The suggested TPN approach is used to generate a mathematical transition model, based on a From/To transition matrix and the properties of the TPN, that considers all possible movements of robots between cell stations. The mathematical model thus obtained is solved to identify the optimal firing sequence of TPN transitions for the considered robotic cell problem to minimize the time elapsed before the firing of the last transition (the cycle time). Finally, the optimal sequence of transitions is used to generate robotic cell controllers and construct the final TPN model. A numerical example is used to demonstrate the proposed approach.

Application of Fuzzy Logic to Multi-Objective Scheduling Problems in Robotic Flexible Assembly Cells

This paper is aimed at developing a methodology to solve a multi-objective problem in robotic flexible assembly cells. The proposed methodology is based on three main steps: (1) scheduling of the RFACs using different common rules, (2) normalisation of the scheduling outcomes, and (3) selection of the optimal scheduling rules, using a fuzzy inference system. In this paper, four rules, namely short processing time, long processing time, earlier due date and random, are examined. Four objectives are considered simultaneously: scheduling length, total transportation time, utilisation rate and workload rate. A realistic case study is provided for demonstrating applicability of the suggested methodology. The results show that the methodology is practical and works in RFACs settings.

Developing petri net model and meta-heuristic algorithms for cyclic scheduling in 2- machine robotic cells

In this paper, the cyclic scheduling problems in 2-machine robotic cells have been studied. We investigated the timed Petri network graph for modeling the part sequencing and the optimal robot moves sequence in robotic manufacturing cells. The robotic manufacturing cell considered in this study has two identical machines and one single gripper robot. Also, we have assumed that the manufacturing cell is capable of producing identical and different parts. The main objective of this study is to minimize the cycle time. To solve this problem, we have proposed two meta-heuristic algorithms called particle swarm optimization (PSO) and simulated annealing (SA) and compared the obtained results with the exact solutions by LINGO. Also the complexity of the proposed model has been analyzed. Key words: Cycle time, 2-machine robotic cell, Petri net, part sequencing, robot moves sequence, cyclic scheduling, meta-heuristic algorithms.

Exact methods for the robotic cell problem

This paper investigates an exact method for the Robotic Cell Problem. We present a branch-and-bound algorithm which is the first exact procedure specifically designed with regard to this complex flow shop scheduling variant. Also, we propose a new mathematical programming model as well as new lower bounds. Furthermore, we describe an effective genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that medium-sized instances, with up to 176 operations, can be optimally solved. Also, we found that the new proposed lower bounds outperform lower bounds from the literature. Finally, we show, that the genetic algorithm delivers good solutions while requiring short CPU times.

Exact Method for Robotic Cell Problem

Abstract This study investigates an exact method for the Robotic Cell Problem. We present an exact branch and bound algorithm which is the first exact procedure specifically designed for this strongly NP-hard problem. In this paper, we propose a new mathematical formulation and we describe a new lower bound for the RCP. In addition, we propose a genetic algorithm. We report that the branch and bound algorithm is more effective than the proposed mathematical formulation which can solve small sized problem. Also, computational study provides evidence that the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times to solve this problem.

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.

Scheduling of coupled tasks and one-machine no-wait robotic cells

Coupled task scheduling problems have been known for more than 25 years. Several complexity results have been established in the meantime, but the status of the identical task case remains still unsettled. We describe a new class of equivalent one-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresponds to the production of a single part type in the robotic cell. We shall describe new algorithmic procedures to solve this robotic cell problem, allowing lower and upper bounds on the production time and discussing in particular cyclic production plans.

SCHEDULING OF COUPLED TASKS AND ONE-MACHINE NO-WAIT ROBOTIC CELLS

Coupled task scheduling problems are known since more than 25 years. Several complexity results have been established in the meantime, but the status of the identical task case remains still unsettled. We describe a new class of equivalent 1-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresponds to the production of a single part type in the robotic cell. We shall describe new algorithmic procedures to solve this robotic cell problem, allowing lower and upper bounds on the production time and discussing in particular cyclic production plans.

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

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 of Parts in Robotic Cells

This paper considers scheduling problems in robotic cells that produce a set of part types on several machines served by one robot. We study the problem of sequencing parts of different types in a cell to minimize the production cycle time when the sequence of the robot moves is given. This problem is NP-hard for most of the one-unit robot move cycles in a robotic cell with more than two machines and producing more than two part types. We first give a mathematical formulation to the problem, and then propose a branch-and-bound algorithm to solve it. The bounding scheme of this algorithm is based on relaxing, for all of the machines except two, the constraints that a machine should be occupied by a part for a period at least as long as the processing time of the part. The lower bound obtained in this way is tight. This relaxation allows us to overcome the complexity of the problem. The lower bound can be computed using the algorithm of Gilmore and Gomory. Computational experiments on part sequencing problems in three-machine robotic cells are given.