Scheduling in robotic cells: process flexibility and cell layout

The focus of this study is the identical parts robotic cell scheduling problem with m machines under the assumption of process and operational flexibility. A direct consequence of this assumption is a new robot move cycle that has been overlooked in the existing literature. We prove that this new cycle dominates all classical robot move cycles considered in the literature for m?=?2. We also prove that changing the layout from an in-line robotic cell to a robot-centered cell reduces the cycle time of the proposed cycle even further, whereas the cycle times of all other cycles remain the same. For the m-machine case, we find the regions where the proposed cycle dominates the classical robot move cycles, and for the remaining regions present its worst case performance with respect to classical robot move cycles. Considering the number of machines as a decision variable, we also find the optimal number of machines that minimizes the cycle time of the proposed cycle.     

Bicriteria robotic cell scheduling with controllable processing times

The current study deals with a bicriteria scheduling problem arising in an m-machine robotic cell consisting of CNC machines producing identical parts. Such machines by nature possess the process flexibility of altering processing times by modifying the machining conditions at differing manufacturing costs. Furthermore, they possess the operational flexibility of being capable of processing all the operations of these identical parts. This latter flexibility in turn introduced a new class of robot move cycles, called pure cycles, to the literature. Within the restricted class of pure cycles, our task is to find the processing times on machines so as to minimise the cycle time and the manufacturing cost simultaneously. We characterise the set of all non-dominated solutions for two specific pure cycles that have emerged as prominent ones in the literature. We prove that either of these pure cycles is non-dominated for the majority of attainable cycle time values. For the remaining regions, we provide the worst case performance of one of these two cycles.     

Productivity analysis in a robotic cell

In this paper, we study the productivity advantage of a variety of scenarios in a robotic cell by comparing their cycle times. The robotic cell is made up of several machines and a single gripper robot in the centre of the cell, which loads, unloads and moves the parts. Considering deterministic robot travelling, loading and unloading time elements and stochastic part process time element, this paper focuses on examining the scenarios composed of the single part type part sequencing methods and the robot moves in a cell. First, the decrease (increase) virtual robotic cell, in which its machines are virtually arranged in order of processing time regardless of their physical location, is introduced to calculate the cycle time. Second, a flow-graph based model is developed to analyse the cycle times for the scenarios when the part processing time element is stochastic. A robotic cell composed of three machines and a robot in the centre of the cell is used as a base example throughout the paper to illustrate the application of the models.     

Sequencing of robot activities and parts in two-machine robotic cells

This paper deals with the development of analytical methods for determining an optimal sequence of parts and robot activities to minimize cycle time in robotic cells with two machines. A robot is used to feed parts to the two machines or in the absence of machines two robots perform processing operations on parts. Three different types of robotic cellular layouts, namely the robot-centered cell, the mobile robot cell, and the in-line robot cell have been considered in an automated flow line manufacturing system with no storage buffers. Optimal sequences have been established for both single and multiple part types when part production is performed in a repetitive fashion. In order to keep abreast with the current trend toward just-in-time manufacturing, production of a quantity known as the minimum part set (MPS) is considered for multiple part types. The analysis for a single MPS has further been extended to include the cyclic production of multiple MPSs. The problem of determining the optimal sequence of multiple part types has been shown equivalent to a two machines no-wait flow shop problem, and has been solved by Gilmore and Gomory's (1964) algorithm.     

Minimizing the cycle time in serial manufacturing systems with multiple dual-gripper robots

Robots are being used more and more extensively as material-handling systems for automated manufacturing systems. This is especially true for dual-gripper robots whose in-process buffer (the robot's second gripper) constitutes a further element of flexibility. When the number of stations to be served is high and the set of activities the robot must execute is great, the system throughput may depend on robot capability rather than on process times. In such conditions, the use of several robots leads to an increase in system productivity. Obviously, the design and the management of such a handling system becomes more complex: the minimum number of robots required, the work stations to be served by each of them and the robot move cycles must be all determined so as to minimize the cycle time of a multi-robot serial system. Since the aim of minimizing the cycle time could lead to a non-univocal configuration, a secondary objective may be pursued. To this aim, the classic case of a single dual-gripper robotic cell is preliminarily revisited, using a practical rather than a theoretical approach, to show that, under the conditions of minimum cycle time, it is possible to take into account both the reduction of the WIP and that of the length of the transitory periods.     

A tabu search algorithm with solution space partition and repairing procedure for cyclic robotic cell scheduling problem

This paper proposes a tabu search (TS) algorithm to solve an NP-hard cyclic robotic scheduling problem. The objective is to find a cyclic robot schedule that maximises the throughput. We first formulate the problem as a linear program, provided that the robot move sequence is given, and reduce the problem to searching for an optimal robot move sequence. We find that the solution space can be divided into some specific subspaces by the maximal number of works-in-process. Then, we propose a TS algorithm to synchronously perform local searches in each subspace. To speed up our algorithm, dominated subspaces are eliminated by lower and upper bounds of the cycle time during the iterations. In the TS, a constructive heuristic is developed to generate initial solutions for each subspace and a repairing procedure is proposed to maintain the feasibility of the solutions generated in the initialisation stage and the neighbours search process. Computational comparison both on benchmark instances and randomly generated instances indicates that our algorithm is efficient for the cyclic robotic scheduling problem.     

Bi-objective cyclic scheduling in a robotic cell with processing time windows and non-Euclidean travel times

This paper addresses bi-objective cyclic scheduling in a robotic cell with processing time windows. In particular, we consider a more general non-Euclidean travel time metric where robot’s travel times are not required to satisfy the well-known triangular inequality. We develop a tight bi-objective mixed integer programming (MIP) model with valid inequalities for the cyclic robotic cell scheduling problem with processing time windows and non-Euclidean travel times. The objective is to minimise the cycle time and the total robot travel distance simultaneously. We propose an iterative ε-constraint method to solve the bi-objective MIP model, which can find the complete Pareto front. Computational results both on benchmark instances and randomly generated instances indicate that the proposed approach is efficient in solving the cyclic robotic cell scheduling problems.     

The Effect of Restricting Cycle Times in the Economic Lot Scheduling Problem

The economic lot scheduling problem (ELSP) involves specifying economic cycle times for each of several products produced by a set of machines. The extensive, usually experimentally based, literature on the ELSP indicates that it may be desirable to restrict the possible choice of cycle times for each product to a small and very structured set of possible cycle times. In this paper we examine the economic impacts of such a restriction and give evidence that is highly supportive of this type of restriction; in particular, the “powers of 2” sets of possible cycle times used in practice appear to be very desirable from an economic viewpoint.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

Scheduling cluster tools for concurrent processing of two wafer types with PM sharing

We examine cyclic scheduling of single-armed and dual-armed cluster tools that concurrently process two wafer types by sharing a process module (PM). Because a PM is shared by two different wafers, the backward and swap sequences, which are prevalently used for single-armed and dual-armed tools without such complexity, respectively, are not effective. We therefore propose new sequences, called alternating backward and alternating swap sequences, for steady cycles of single-armed and dual-armed tools, respectively. We then develop optimality conditions for which the proposed sequences achieve the minimum cycle times in a fundamental cycle, and show that the optimality conditions hold for most practical cases. We also develop a condition for which a shared PM becomes the bottleneck and hence the PM sharing increases the cycle time. For general cycles, we propose heuristic scheduling methods that combine both the alternating backward (or swap) sequence and the conventional backward (or swap) sequence. Finally, we experimentally verify the efficiency and effectiveness of the proposed algorithm for dual-armed cluster tools.     

Modeling and simulation of percussive impact for robotic riveting system

Riveting is one of the major joining methods used in assembly,and the robotic riveting has been gradually introduced into aircraft industry.In this paper,a method is presented for modeling and simulation of percussive robotic riveting.In percussive riveting,vibration always exists.When an impact force is employed,a forced vibration will be induced.If it resonates with a robot natural frequency,the vibration will cause damage to the robot.The main content of this paper is divided into three parts.Firstly,a robot dynamic model is established to compute the driving torque for each joint.Secondly,vibration responses under impact are analyzed for the percussive riveting process.Thirdly,the effect of riveting on robot vibration is studied over the robot workspace.The purpose of this paper is to discuss the suitable regions for riveting where the robot vibration is very minimal.It is shown that based on the presented method an appropriate trajectory can be planned for robotic riveting.     

Analysis of an automobile assembly line as a network of closed loops working in both,stationary and transitory regimes

In this work a real automobile assembly line and the correspondent preassembly lines have been analyzed as a network of closed loops of machines decoupled by intermediate buffers. This work deals with some important aspects, which have still not been investigated in earlier literature, such as: machines processing pallets, which are not related to each other and depend on an external variable in a network with closed loops of machines and intermediate buffers, machines working at different cycle times in a network of closed loops of machines and intermediate buffers, machines working in both, stationary and transitory regime and the relationships between the cycle times of the machines in the stationary working regime in order to guarantee the production rate of the system. Finally how the transient results can be used to improve the performance of the system under certain working conditions is discussed.     

PRODUCTION PLANNING DECISIONS IN FLEXIBLE MANUFACTURING SYSTEMS WITH RANDOM MATERIAL FLOWS

In this paper, we consider the FMS planning problem of determining optimal machine workload assignments in order to rninimize mean part flow time. We decompose this problem into the subproblems of first forming machine groups and next assigning operations to these groups. Three types of grouping configurations—no grouping, partial grouping and total grouping—are considered. In both no grouping and partial grouping, each machine is tooled differently. While each operation is assigned to only one machine in no grouping, partial grouping permits multiple operation assignments. On the other hand, total grouping partitions the machines into groups of identically-tooled machines; each machine within a group is capable of performing the same set of operations. Within this grouping framework, we consider three machine loading objectives—minimizing the total deviation from the optimal group utilization levels, minimizing part travel and maximizing routing flexibility, for generating a variety of system configurations.

A queueing network model of an FMS is used to determine the optimal configurations and machine workload assignments for the no grouping and total grouping cases. It is shown that under total grouping, the configuration of M machines into G groups that minimizes flow time is one in which the sizes of the machine groups are maximally unbalanced and the workload per machine in the larger groups is higher. This extends previous results on the optimality of unbalancing both machine group sizes and machine workload to the mean flow time criterion.

A simulation experiment is next conducted to evaluate the alternative machine configurations to understand how their relative performance depends upon the underlying system characteristics, such as system utilization level and variation among operation processing times. We also investigate the robustness of these configurations against disruptions, such as machine unreliability and variation in processing batch sizes. While different configurations minimize mean flow time under different parameter values, partial grouping with state-dependent part routing performs well across a wide range of these values. Experimental results also show that the impact of disruptions can be reduced by several means, such as aggregating operations of a part to be performed at the same machine, in addition to providing routing flexibility.     

A cross-entropy method for optimising robotic automated storage and retrieval systems

In this paper, we consider a robotic automated storage and retrieval system (AS/RS) where a Cartesian robot picks and palletises items onto a mixed pallet for any order. This robotic AS/RS not only retrieves orders in an optimal sequence, but also creates an optimal store ready pallet of any order. Adapting the Travelling Salesman Problem to warehousing, the decision to be made includes finding the optimal sequence of orders, and optimal sequence of items inside each order, that jointly minimise total travel times. In the first phase, as a control problem, we develop an avoidance strategy for the robot (or automatic stacker crane) movement sequence. This approach detects the collision occurrence causing unsafe handling of hazardous items and prevents the occurrence of it by a collision-free robot movement sequence. Due to the complexity of the problem, the second phase is attacked by a Cross-Entropy (CE) method. To evaluate the performance of the CE method, a computational analysis is performed over various test problems. The results obtained from the CE method are compared to those of the optimal solutions obtained using CPLEX. The results indicate high performance of the solution procedure to solve the sequencing problem of robotic AS/RSs.     

Scheduling preventive maintenance on a single CNC machine

In this study we attempt to deal with process planning, scheduling and preventive maintenance (PM) decisions, simultaneously. The objective is to minimize the total completion time of a set of jobs on a CNC machine. During the process planning, we decide on the processing times of the jobs which are controllable (i.e. they can be easily changed) on CNC machines. Using shorter processing times (higher production rates) would result in greater deterioration of the machine, and we would need to plan more frequent PM visits to the machine, during which it would not be available. Therefore, the selected processing times determine not only the completion times but also the PM visit times. We first provide optimality properties for the joint problem. We propose a new heuristic search algorithm to determine simultaneously the processing times of the jobs, their sequence and the PM schedule.     

A branch and bound algorithm for optimal cyclic scheduling in a robotic cell with processing time windows

A branch and bound algorithm is described for optimal cyclic scheduling in a robotic cell with processing time windows. The objective is to minimise the cycle time by determining the exact processing time on each machine which is limited within a time window. The problem is formulated as a set of prohibited intervals of the cycle time, which is usually applied in the robotic cyclic scheduling problem with fixed processing times. Since both bounds of these prohibited intervals are linear expressions of the processing times, we divide these prohibited intervals into a series of the subsets and transform the problem into enumerating the non-prohibited intervals of cycle time in each subset. This enumeration procedure is completed by an efficient branch and bound algorithm, which could find an optimal solution by enumerating partial non-prohibited intervals. Computational results on the benchmark instances and randomly generated test instances indicate that the algorithm is effective.     

Industrial robot layout based on operation sequence optimisation

The robot layout is one of the primary problems in the robot work cell design. An optimal layout not only makes the robotic end-effector reach the desired position with the desired orientation, but also minimises the robot cycle time for completing a given task with collision avoidance. There may be many feasible robot operation sequences for a given task. The optimisation of operation sequence for a robot placed in a fixed location is NP-complete. There may be different optimal operation sequences as the robot is placed in the different locations. Hence the problem of robot layout is quite complex. This paper presents a method of industrial robot layout based on operation sequence optimisation. The robot motion control model with velocity, acceleration and jerk is established. The feasible space of robot base is calculated and then divided into discrete grids before the optimisations. Then the ant colony algorithm is applied to optimise the operation sequence for each grid. The adjacent grids are merged or divided enough times to form the bigger grids. The pattern search algorithm is adopted to solve the local optimal position and orientation of the robot base in each big grid, and the global optimal layout is found through the comparison of the local solutions. The industrial robot layout method has been applied to the work cell design for car door welding.     

Dynamic Operational Policies in an Automated Warehouse

In this paper we consider the optimal relocation of pallets with a high expectancy of retrieval within each storage rack of an automated warehouse to meet the fluctuating, short-term throughput requirements imposed on the automated storage-retrieval machines. The prepositioning of these pallets closer to the input/output point of each rack during off-peak periods will reduce the expected travel time for the storage/retrieval machines during future peak periods of the planning horizon.

As the model has been abstracted from an actual operating environment, we first describe the environment in which the problem has been posed. We then exploit the special structure of the problem to develop conditions that an optimal relocation policy should satisfy. Based on these optimality conditions, we develop a very efficient optimal relocation algorithm. Finally, we present the performance of several relocation policies in the warehouse studied.     

Optimization of cycle time and kinematic energy in a robot/conveyor system with variable pick-up locations

In automated manufacturing, a robot/conveyor system uses a robot to pick up parts that continuously arrive from a moving conveyor. To improve system efficiency, a variable pick-up location approach directs the robot to pick up parts before they reach the end of conveyor at a fixed point. The trade-off between robot move cycle time and kinematic energy is balanced by an optimization model based on optimum control theory in minimizing both simultaneously. Simulation results of several numerical examples show that the variable pick-up location approach consistently outperforms the conventional fixed pick-up method. Both cycle time and kinematic energy are reduced. The research results may be used for robot system planning by providing guidelines to detailed trajectory planning. Future research can include applications to the control of other robotic systems, such as manufacturing cells.     

Determination of robotic melon harvesting efficiency: a probabilistic approach

To automate the harvesting of melons, a mobile Cartesian robot is developed that traverses at a constant velocity over a row of precut melons whose global coordinates are known. The motion planner is programmed to have the robot harvest as many melons as possible. Numerous simulations of the robot over a field with different sets of randomly distributed melons resulted in nearly identical percentages of melons harvested. This result holds true over a wide range of robot dimensions, motor capabilities, velocities and melon distributions. Using probabilistic methods, we derive these results by modelling the robotic harvesting procedure as a stochastic process. In this simplified model, a harvest ratio is predicted analytically using Poisson and geometric distributions. Further analysis demonstrates that this model of robotic harvesting is an example of an infinite length Markov chain. Applying the mathematical tools of Markov processes to our model yields a formula for the harvest percentage that is in strong agreement with the results of the simulation. The significance of the approach is demonstrated in two of its applications: to select the most efficient actuators for maximal melon harvesting and determine the set of optimal velocities along a row of melons of varying densities.