1-unit Cycle Research Articles

Cyclic scheduling of parts and robot moves in m-machine robotic cells

We consider a flow shop type manufacturing cell consisting of m machines and a material handling robot producing multiple parts. The robot transfers the parts between the machines and loads/unloads the machines. We consider the cyclic scheduling of the parts and the robot moves with the objective of maximizing the throughput rate. We develop a mixed integer linear programming formulation of the problem. The formulation is improved with several valid inequalities and reformulations of the constraints. We also develop a hybrid metaheuristic algorithm for this strongly NP-Hard problem. The algorithm is modified to handle both 1-unit and multi-unit robot cycles. Multi-threading is used to parallelize the algorithm in order to improve its efficiency. After calibrating the parameters of the heuristic algorithm, an extensive computational study is performed to evaluate its performance. The results of this study revealed that the developed heuristic provides near-optimal solutions in reasonable solution times. The effects of parallelization and the benefits of considering multi-unit cycles instead of 1-unit cycles are also quantified. Our computational tests show that multi-unit cycles improve the throughput rate by 9% on the average. The improvement can reach to 20% depending on the problem parameters.

On the optimality of 1-unit cycles in flow-shop networks

In this paper, a cyclic scheduling problem in a flow-shop network including a robot and several machines is studied. The cyclic scheduling problem deals with the planning of operations that have to be repeated in a timely fashion infinitely often. Obtaining the optimal schedule is an NP-hard problem in general. It is proven that the optimal schedule is always among a limited number of schedules known as 1-unit cycles for up to three machines in a flow-shop network. This paper proves that the optimal cycle is a 1-unit cycle for an arbitrary number of machines.

Quantifying the Impact of Layout on Productivity: An Analysis from Robotic-Cell Manufacturing

Although the impact of layout on the productivity of manufacturing systems is well recognized, a quantification of this impact is an issue that is often ignored or crudely approximated in practice. When evaluating competing layouts for a manufacturing system, the trade-off between their relative benefits and their relative costs underlines the need for a reasonably accurate comparison of the productivity offered by these potential layouts. In this paper, we argue for this approach by comparing the productivity of two well-known layouts in robotic-cell manufacturing: circular and linear. We consider the problem of optimizing throughput in single-gripper, bufferless robotic cells that produce identical parts under the free-pickup criterion and the additive-travel-time metric. For cells with a circular layout, we show that the problem of finding an optimal 1-unit cycle is NP-hard. Our main algorithmic result is a polynomial-time 5/3-approximation algorithm for this problem. We then demonstrate that our algorithm provides near-optimal solutions by compiling its performance on an extensive test bed of practically-relevant instances. Finally, we use the algorithm to assess the increase in throughput for cells with a circular layout over those with a linear layout. We show that a circular layout offers a significant improvement in productivity and demonstrate the robustness of this improvement by examining the sensitivity with respect to changes in the design parameters of the robotic cell. Thus, our work provides operations managers with a tool to trade off the resulting increase in revenue with the additional cost of acquiring and maintaining a robot that can exploit a circular layout.

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 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.

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 dual gripper robotic cell: One-unit cycles

We consider the scheduling problem of cyclic production in a bufferless dual-gripper robot cell processing a family of identical parts. The objective is to find an optimal sequence of robot moves so as to maximize the long-run average throughput rate of the cell. While there has been a considerable amount of research dealing with single-gripper robot cells, there are only a few papers devoted to scheduling in dual-gripper robotic cells. From the practical point of view, the use of a dual gripper offers the attractive prospect of an increase in the cell productivity. At the same time, the increase in the combinatorial possibilities associated with a dual-gripper robot severely complicates its theoretical analysis. The purpose of this paper is to extend the existing conceptual framework to the dual-gripper situation, and to provide some insight into the problem. We provide a notational and modelling framework for cyclic production in a dual-gripper robotic cell. Focusing on the so-called active cycles, we discuss the issues of feasibility and explore the combinatorial aspects of the problem. The main attention is on 1-unit cycles, i.e., those that restore the cell to the same initial state after the production of each unit. For an m-machine robotic cell served by a dual-gripper robot, we describe a complete family of 1-unit cycles, and derive an analytical formula to estimate their total number for a given m. In the case when the gripper switching time is sufficiently small, we identify an optimal 1-unit cycle. This special case is of particular interest as it reflects the most frequently encountered situation in real-life robotic systems. Finally, we establish the connection between a dual-gripper cell and a single-gripper cell with machine output buffers of one-unit capacity and compare the cell productivity for these two models.

Scheduling in a three-machine robotic flexible manufacturing cell

In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on which the loading and unloading of machines are made by a robot. The machines used in FMCs are predominantly CNC machines and these machines are flexible enough for performing several operations provided that the required tools are stored in their tool magazines. Traditional research in this area considers a flowshop type system. The current study relaxes this flowshop assumption which unnecessarily limits the number of alternatives. In traditional robotic cell scheduling literature, the processing time of each part on each machine is a known parameter. However, in this study the processing times of the parts on the machines are decision variables. Therefore, we investigated the productivity gain attained by the additional flexibility introduced by the FMCs. We propose new lower bounds for the 1-unit and 2-unit robot move cycles (for which we present a completely new procedure to derive the activity sequences of 2-unit cycles in a three-machine robotic cell) under the new problem domain for the flowshop type robot move cycles. We also propose a new robot move cycle which is a direct consequence of process and operational flexibility of CNC machines. We prove that this proposed cycle dominates all 2-unit robot move cycles and present the regions where the proposed cycle dominates all 1-unit cycles. We also present a worst case performance bound of using this proposed cycle.

Approximation algorithms for k-unit cyclic solutions in robotic cells

This paper considers the problem of scheduling operations in bufferless robotic cells that produce identical parts. Finding a multi-unit cyclic solution which minimizes the long-run average time to produce a part is an open problem. Most research has been focused on finding an optimal 1-unit cyclic solution. However, it is known that an optimal multi-unit cyclic solution can be better than an optimal 1-unit cyclic solution for cells with four or more machines. We present polynomial algorithms that produce multi-unit cyclic solutions whose per unit cycle times are within a constant factor of the optimum for the three most common classes of robotic cells viz., additive, constant, and Euclidean travel-time. The approximation guarantees obtained for these three classes of cells are 1.5, 1.5, and 4, respectively. As a by-product, we obtain upper bounds on the difference in the per unit cycle times between an optimal multi-unit cycle and an optimal 1-unit cycle for each of these three classes of cells.

Cyclic scheduling in 3-machine robotic flow shops

We consider a robotic flow shop model in which a single robot is responsible for the transportation of parts between machines. For reasons of simplicity, when the shop is to produce a large number of identical parts, the robot usually performs repeatedly a fixed sequence of activities. This sequence of activities is called a 1-unit cycle if each execution of the sequence results in the production of exactly one part. It has been conjectured that 1-unit cycles yield optimal production rates for 3-machine robotic flow shops. We establish the validity of this conjecture. Copyright © 1999 John Wiley & Sons, Ltd.

Bayesian reliability assessment from test data : James E. Wolf. Proc. A. Reliability and Maintainability Symposium, Nevada, U.S.A. p. 411 (20–22 Jan. 1976)

In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on which the loading and unloading of machines are made by a robot. The machines used in FMCs are predominantly CNC machines and these machines are flexible enough for performing several operations provided that the required tools are stored in their tool magazines. Traditional research in this area considers a flowshop type system. The current study relaxes this flowshop assumption which unnecessarily limits the number of alternatives. In traditional robotic cell scheduling literature, the processing time of each part on each machine is a known parameter. However, in this study the processing times of the parts on the machines are decision variables. Therefore, we investigated the productivity gain attained by the additional flexibility introduced by the FMCs. We propose new lower bounds for the 1-unit and 2-unit robot move cycles (for which we present a completely new procedure to derive the activity sequences of 2-unit cycles in a three-machine robotic cell) under the new problem domain for the flowshop type robot move cycles. We also propose a new robot move cycle which is a direct consequence of process and operational flexibility of CNC machines. We prove that this proposed cycle dominates all 2-unit robot move cycles and present the regions where the proposed cycle dominates all 1-unit cycles. We also present a worst case performance bound of using this proposed cycle.