Pure cycles in flexible robotic cells

In this study, an m-machine flexible robotic manufacturing cell consisting of CNC machines is considered. The flexibility of the machines leads to a new class of robot move cycles called the pure cycles. We first model the problem of determining the best pure cycle in an m-machine cell as a special travelling salesman problem in which the distance matrix consists of decision variables as well as parameters. We focus on two specific cycles among the huge class of pure cycles. We prove that, in most of the regions, either one of these two cycles is optimal. For the remaining regions we derive worst case performances of these cycles. We also prove that the set of pure cycles dominates the flowshop-type robot move cycles considered in the literature. As a design problem, we consider the number of machines in a cell as a decision variable. We determine the optimal number of machines that minimizes the cycle time for given cell parameters such as the processing times, robot travel times and the loading/unloading times of the machines.     

Robotic Cells with Parallel Machines: Throughput Maximization in Constant Travel-Time Cells

We present a general analysis of the problem of sequencing operations in bufferless robotic cell flow shops with parallel machines. Our focus will be cells that produce identical parts. The objective is to find a cyclic sequence of robot moves that maximizes the steady state throughput. Parallel machines are used in the industry to increase throughput, most typically at bottleneck processes having larger processing times.Efficient use of parallel machines requires that several parts be processed in one cycle of robot movements. We analyze such cycles for constant travel-time robotic cells. The number of cycles that produce several parts is very large, so we focus on a subclass called blocked cycles. In this class, we find a dominating subclass called LCM Cycles.The results and the analysis in this paper offer practitioners (i) guidelines to determine whether parallel machines will be cost-effective for a given implementation, (ii) a simple formula for determining how many copies of each machine are required to meet a particular throughput rate, and (iii) an optimal sequence of robot moves for a cell with parallel machines under a certain common condition on the processing times.     

Cyclic scheduling of a robotic flexible cell with load lock and swap

In this paper, we study the problem of robotic cell scheduling with m machines with flexibility, load lock and swap assumptions. The robotic cell repetitively produces parts of identical types. We determine the cycle time of all 1-unit cycles in this type of robotic cell and present two new lower bounds for robot move cycles with load lock and swap, either there is flexibility or inflexibility. We also provide a new robot move cycle and prove that it dominates all classical robot move cycles considered in the existing literature of m-machine robotic cells.     

Bicriteria robotic cell scheduling

This paper considers the scheduling problems arising in two- and three-machine manufacturing cells configured in a flowshop which repeatedly produces one type of product and where transportation of the parts between the machines is performed by a robot. The cycle time of the cell is affected by the robot move sequence as well as the processing times of the parts on the machines. For highly flexible CNC machines, the processing times can be changed by altering the machining conditions at the expense of increasing the manufacturing cost. As a result, we try to find the robot move sequence as well as the processing times of the parts on each machine that not only minimize the cycle time but, for the first time in robotic cell scheduling literature, also minimize the manufacturing cost. For each 1-unit cycle in two- and three-machine cells, we determine the efficient set of processing time vectors such that no other processing time vector gives both a smaller cycle time and a smaller cost value. We also compare these cycles with each other to determine the sufficient conditions under which each of the cycles dominates the rest. Finally, we show how different assumptions on cost structures affect the results.     

Scheduling in Reentrant Robotic Cells: Algorithms and Complexity

We study the scheduling of m-machine reentrant robotic cells, in which parts need to reenter machines several times before they are finished. The problem is to find the sequence of 1-unit robot move cycles and the part processing sequence which jointly minimize the cycle time or the makespan. When m = 2, we show that both the cycle time and the makespan minimization problems are polynomially solvable. When m = 3, we examine a special class of reentrant robotic cells with the cycle time objective. We show that in a three-machine loop-reentrant robotic cell, the part sequencing problem under three out of the four possible robot move cycles for producing one unit is strongly -hard. The part sequencing problem under the remaining robot move cycle can be solved easily. Finally, we prove that the general problem, without restriction to any robot move cycle, is also intractable.     

Sequencing and Scheduling in Robotic Cells: Recent Developments

A great deal of work has been done to analyze the problem of robot move sequencing and part scheduling in robotic flowshop cells. We examine the recent developments in this literature. A robotic flowshop cell consists of a number of processing stages served by one or more robots. Each stage has one or more machines that perform that stage’s processing. Types of robotic cells are differentiated from one another by certain characteristics, including robot type, robot travel-time, number of robots, types of parts processed, and use of parallel machines within stages. We focus on cyclic production of parts. A cycle is specified by a repeatable sequence of robot moves designed to transfer a set of parts between the machines for their processing.We start by providing a classification scheme for robotic cell scheduling problems that is based on three characteristics: machine environment, processing restrictions, and objective function, and discuss the influence of these characteristics on the methods of analysis employed. In addition to reporting recent results on classical robotic cell scheduling problems, we include results on robotic cells with advanced features such as dual gripper robots, parallel machines, and multiple robots. Next, we examine implementation issues that have been addressed in the practice-oriented literature and detail the optimal policies to use under various combinations of conditions. We conclude by describing some important open problems in the field.     

An analysis of cyclic scheduling problems in robot centered cells

The focus of this study is a robot centered cell consisting of m computer numerical control (CNC) machines producing identical parts. Two pure cycles are singled out and further investigated as prominent cycles in minimizing the cycle time. It has been shown that these two cycles jointly dominate the rest of the pure cycles for a wide range of processing time values. For the remaining region, the worst case performances of these pure cycles are established. The special case of 3-machines is studied extensively in order to provide further insight for the more general case. The situation where the processing times are controllable is analyzed. The proposed pure cycles also dominate the rest when the cycle time and total manufacturing cost objectives are considered simultaneously from a bicriteria optimization point of view. Moreover, they also dominate all of the pure cycles in in-line robotic cells. Finally, the efficient frontier of the 3-machine case with controllable processing times is depicted as an example.     

Multi-degree cyclic scheduling of two robots in a no-wait flowshop

This paper addresses multi-degree cyclic scheduling of two robots in a no-wait flowshop, where exactly r(r > 1) identical parts with constant processing times enter and leave the production line during each cycle, and transportation of the parts between machines is performed by two robots on parallel tracks. The objective is to minimize the cycle time. The problem is transformed into enumeration of pairs of overlapping moves that cannot be performed by the same robot. This enumeration is accomplished by enumerating intervals for some linear functions of decision variables. The algorithm developed is polynomial in the number of machines for a fixed r, but exponential if r is arbitrary. Computational results with benchmark instances are reported. Note to Practitioners-This paper was motivated by the problem of cyclic scheduling of a no-wait production line, where a part must be processed without any interruption either on or between machines due to characteristics of the processing technology itself or the absences of storage capacity between operations of a part. Multi-degree schedules, in which multiple parts enter and leave the line during a cycle, usually have larger throughput rate than simple ones. This paper proposes an algorithm for multi-degree cyclic scheduling of a no-wait flowshop with two robots. Computational results show that the throughput rate can be really improved by using multi-degree schedules with two robots. However, we have not addressed the decision of the optimal value of the degree of the cycle. Furthermore, since we consider that the two robots travel along parallel tracks, the collision-avoidance constraints have been relaxed in the algorithm. In future research, we will address the two problems and generalize the algorithm to multi-robot cases.     

Throughput optimization in two-machine flowshops with flexible operations

In this study, a two-machine flowshop producing identical parts is considered. Each of the identical parts is assumed to require a number of manufacturing operations, and the machines are assumed to be flexible enough to perform different operations. Due to economical or technological constraints, some specific operations are preassigned to one of the machines. The remaining operations, called flexible operations, can be performed on either one of the machines, so that the same flexible operation can be performed on different machines for different parts. The problem is to determine the assignment of the flexible operations to the machines for each part, with the objective of maximizing the throughput rate. We consider various cases regarding the number of parts to be produced and the capacity of the buffer between the machines. We present solution methods for each variant of the problem.     

Bicriteria robotic operation allocation in a flexible manufacturing cell

Consider a manufacturing cell of two identical CNC machines and a material handling robot. Identical parts requesting the completion of a number of operations are to be produced in a cyclic scheduling environment through a flow shop type setting. The existing studies in the literature overlook the flexibility of the CNC machines by assuming that both the allocation of the operations to the machines as well as their respective processing times are fixed. Consequently, the provided results may be either suboptimal or valid under unnecessarily limiting assumptions for a flexible manufacturing cell. The allocations of the operations to the two machines and the processing time of an operation on a machine can be changed by altering the machining conditions of that machine such as the speed and the feed rate in a CNC turning machine. Such flexibilities constitute the point of origin of the current study. The allocation of the operations to the machines and the machining conditions of the machines affect the processing times which, in turn, affect the cycle time. On the other hand, the machining conditions also affect the manufacturing cost. This study is the first to consider a bicriteria model which determines the allocation of the operations to the machines, the processing times of the operations on the machines, and the robot move sequence that jointly minimize the cycle time and the total manufacturing cost. We provide algorithms for the two 1-unit cycles and test their efficiency in terms of the solution quality and the computation time by a wide range of experiments on varying design parameters.     

A polynomial algorithm for multi-robot 2-cyclic scheduling in a no-wait robotic cell

This paper addresses the multi-robot 2-cyclic scheduling problem in a no-wait robotic cell where exactly two parts enter and leave the cell during each cycle and multiple robots on a single track are responsible for transporting parts between machines. We develop a polynomial algorithm to find the minimum number of robots for all feasible cycle times. Consequently, the optimal cycle time for any given number of robots can be obtained with the algorithm. The proposed algorithm can be implemented in O(N⁷) time, where N is the number of machines in the considered robotic cell.     

Loading of pallets on identical CNC machines with cyclic schedules

Flexible manufacturing systems (FMS) are generally set up to process a wide variety of parts with low to medium volume demand. The loading problem in FMS is a short-term decision issue, which addresses the simultaneous processing of a set of different parts in an efficient manner on capital-intensive resources. This study focuses on cyclic schedules in loading pallets carrying groups of identical parts to CNC machining centers. A predefined stream of pallets fixtured for different part types is repeatedly supplied to every CNC machine in cycles. Moreover, a limited number of pallets have to be shared among the cycles of machines to keep utilization and the overall throughput rate at acceptably high levels. The solution approach is an integrated mix of optimization and simulation methodologies. The validation of the model is based on data from past 6 months of operation. Comparisons are made retrospectively.     

Robot performance measurements using automatic laser tracking techniques

This paper describes two laser tracking techniques currently under development at the National Bureau of Standards for robot performance measurements. Tests indicate that the system can be used in real-time to determine the three-dimensional static and dynamic positioning accuracy of a robot end-effector to a few parts in 100,000 (i.e. 12.5–50 μm for a medium to large size robot), and wrist orientations to within 2 sec of arc. Both systems would be simple and compact enough to be considered as a general-purpose portable calibrating tool for robots (or CNC machines), or as an integral part of a robotic system providing real-time position feedback of the end-effector independent of the position and angle feedback of joint members. The ability to dynamically and statistically measure the position of an end-effector to the above accuracy has significant ramifications with regard to meaningful robot performance measurements, and the potential of these systems in other industrial and engineering applications.     

Steady-State Throughput and Scheduling Analysis of Multicluster Tools: A Decomposition Approach

Cluster tools are widely used as semiconductor manufacturing equipment. While throughput analysis and scheduling of single-cluster tools have been well-studied, research work on multicluster tools is still at an early stage. In this paper, we analyze steady-state throughput and scheduling of multicluster tools. We consider the case where all wafers follow the same visit flow within a multicluster tool. We propose a decomposition method that reduces a multicluster tool problem to multiple independent single-cluster tool problems. We then apply the existing and extended results of throughput and scheduling analysis for each single-cluster tool. Computation of lower-bound cycle time (fundamental period) is presented. Optimality conditions and robot schedules that realize such lower-bound values are then provided using ldquopullrdquo and ldquoswaprdquo strategies for single-blade and double-blade robots, respectively. For an -cluster tool, we present lower-bound cycle time computation and robot scheduling algorithms. The impact of buffer/process modules on throughput and robot schedules is also studied. A chemical vapor deposition tool is used as an example of multicluster tools to illustrate the decomposition method and algorithms. The numerical and experimental results demonstrate that the proposed decomposition approach provides a powerful method to analyze the throughput and robot schedules of multicluster tools.     

Optimal multi-degree cyclic scheduling of multiple robots without overlapping in robotic flowshops with parallel machines

This paper considers scheduling robotic flowshops with parallel machines and multiple robots. Robots share the same track and cannot crossover each other. To avoid conflicts among robots, the principle without overlapping is applied. Identical parts with time window constraints are produced. It is challenging to obtain better cyclic schedules to improve the throughput. Moreover, multi-degree cycles are considered to obtain better schedules comparing to simple cycles, i.e. 1-degree cycles. To our knowledge, this is the first work to deal with the multi-degree cyclic scheduling in this complicated scenario. This is the main contribution of this research. The objective is to maximize the throughput of the flowshop by obtaining optimal schedules. As for given degree cycles, it is equivalent to minimizing the cycle time. Operations in robotic flowshops considering multi-degree cycles are analyzed in detail. Based on the analyses, a mixed integer linear programming model is formulated for this challengeable problem. A numerical example modified from the previous work is used to illustrate the model proposed, which is solved by CPLEX. Results show the benefits of the model, especially considering multi-degree cycles.     

Increasing throughput for robotic cells with parallel Machines and multiple robots

We address the problem of scheduling robots' moves in a robotic cell that is used by a Dallas-area semiconductor equipment manufacturer. The cell has parallel machines, multiple robots, and Euclidean travel times. We describe a plan of operation that allows the robots to operate concurrently, efficiently, and with no risk of colliding. We propose a set of sequences of robot moves, analytically determine this scheme's throughput, and determine problem instances for which it is optimal. Through simulation, we demonstrate that our scheme is superior to the heuristic dispatching rule currently in use by the manufacturer.

Note to Practitioners-Efficient scheduling of a robotic cell can greatly increase productivity and revenue for manufacturers in many different industries. This increase becomes more pronounced for larger cells that employ multiple robots and parallel machines at various production stages. This paper describes a schedule of robotic actions that is optimal under a common set of conditions for such large cells, in addition to many other types of cells. When this set of conditions does not hold, even though optimality could not be proven, this schedule is shown to be superior to one currently in use by some semiconductor manufacturers. We also present a scheme that allows the robots to operate concurrently, efficiently, and with no risk of colliding. Additionally, an approximation to the improvement in revenues realized by using this schedule is provided.     

Bicriteria scheduling of a material handling robot in an m-machine cell to minimize the energy consumption of the robot and the cycle time

This study considers a flowshop type production system consisting of m machines. A material handling robot transports the parts between the machines and loads and unloads the machines. We consider the sequencing of the robot moves and determining the speeds of these moves simultaneously. These decisions affect both the robot’s energy consumption and the production speed of the system. In this study, these two objectives are considered simultaneously. We propose a second order cone programming formulation to find Pareto efficient solutions. We also develop a heuristic algorithm that finds a set of approximate Pareto efficient solutions. The conic formulation can find robot schedules for small cells with less number of machines in reasonable computation times. Our heuristic algorithm can generate a large set of approximate Pareto efficient solutions in a very short computational time. Proposed solution approaches help the decision-maker to achieve the best trade-off between the throughput of a cell and the energy efficiency of a material handling robot.     

Genetic algorithm for balancing reconfigurable machining lines

We consider the problem of designing a reconfigurable machining line. Such a line is composed of a sequence of workstations performing specific sets of operations. Each workstation is comprised of several identical CNC machines (machining centers). The line is required to satisfy the given precedence order, inclusion, exclusion and accessibility constraints on the given set of operations. Inclusion and exclusion are zoning constraints which oblige or forbid certain operations to be performed on the same workstation. The accessibility constraints imply that each operation has a set of possible part positions under which it can be performed. All the operations performed on the same workstation must have a common part position. Workstation times are computed taking into account processing and setup times for operations and must not exceed a given bound. The number of CNC machines at one workstation is limited, and the total number of machines must be minimized. A genetic algorithm is proposed. This algorithm is based on the permutation representation of solutions. A heuristic decoder is suggested to construct a solution from a permutation, so that the output solution is feasible w.r.t. precedence, accessibility, cycle time, and exclusion constraints. The other constraints are treated with a penalty approach. For a local improvement of solutions, a mixed integer programming model is suggested for an optimal design of workstations if the order of operations is fixed. An experimental evaluation of the proposed GA on large scale test instances is performed.     

Complexity of One-Cycle Robotic Flow-Shops

We study the computational complexity of finding the shortest route the robot should take when moving parts between machines in a flow-shop. Though this complexity has already been addressed in the literature, the existing attempts made crucial assumptions which were not part of the original problem. Therefore, they cannot be deemed satisfactory. We drop these assumptions in this paper and prove that the problem is NP-hard in the strong sense when the travel times between the machines of the cell are symmetric and satisfy the triangle inequality. We also impose no restrictions on the times of robot arrival at and departure from machines as it is the case in the related, but different, hoist scheduling problem. Our results hold for processing times equal on all machines in the cell. However, the equidistant case for equal processing times can be solved in O(1) time.     

Two-machine robotic cell scheduling problem with sequence-dependent setup times

In this paper, we introduce a new and practical two-machine robotic cell scheduling problem with sequence-dependent setup times (2RCSDST) along with different loading/unloading times for each part. Our objective is to simultaneously determine the sequence of robot moves and the sequence of parts that minimize the total cycle time. The proposed problem is proven to be strongly NP-hard. Using the Gilmore and Gomory (GnG) algorithm, a polynomial-time computable lower bound is provided.