Feeding sequence selection in a manufacturing cell with four parallel machines☆
Introduction
The paper deals with the problem of finding the optimum feeding sequence in manufacturing cells with machines fed by robots. In particular, the work was developed for a real cell that produces parts for the car manufacturing industry at the plant of Metaldyne International Spain SL (formerly R.J. Simpson International SL) located in Gavà, close to Barcelona (Spain), with the aim of optimizing its production. The cell, described in detail below, has one robot that feeds four identical machines that work alternately on two pallets and have random assistance requirements.
Each machine in the cell has some unproductive time when it is waiting for the robot to load the parts on it. This unproductive time depends on the machine working time on each pallet and on the sequence that the robot follows to feed the machines. Differences in the unproductive time can arrive up to two orders of magnitude for different feeding sequences; for instance, in a particular real case, the unproductive times of the machines for two different feeding strategies were 0.045% and 5.72%, respectively.
The working times of the machines on each pallet as well as the loading time of the parts in the machines depend on the type of part to be processed. Then, it is necessary to determine: “In which way should the robot feed the machines in order to optimize the productivity of the cell for a given part?” The objective of this work was the search of a function that, given the values of the variable times in the cell, returns the best robot loading sequence.
The determination of optimal feeding sequences for different types of cell under various conditions has been extensively studied, but the authors are not aware of any published general solution for the particular features of this cell. Most of the previous work in the field deal with the flowshop scheduling problem trying to determine exact solutions for deterministic problems. In the literature several variations of the feeding sequence and scheduling problems were addressed, considering for instance: (a) same/different types of parts; (b) existence/non-existence of storage buffers with a predetermined capacity; (c) fixed/variable working times of the machines on each type of part; (d) robots (or feeding elements) with one/several grippers; (e) machines have to execute a fixed sequence of operations (even on different parts) or can perform any work at any time; (f) loading and unloading times dependant/non-dependant on the type of part; (g) travelling time of the robot dependant/non-dependant on the robot load; (h) transitory conditions are considered/not-considered (i.e. the solution is dependant/non-dependant on the initial conditions); (i) some type of machine assistance (normally deterministic assistance) is needed/not-needed; (j) existence/non-existence of parallel machines; and, of course, (k) different number of machines and robots working in the cell.
Representative work in this area is as follows. Kise et al. [1] dealt with the problem of optimizing the movements of an Automated Guided Vehicle (AGV) that serves two machines without buffer storage, and provided algorithms for the minimization of the makespan for n parts; King et al. [2] dealt also with a two machine problem but considering unlimited buffers for the queue of each machine in a robotized cell and using a branch and bound approach. Crama and van de Klundert [3] considered the flowshop problem with one robot and parts of one type to demonstrate that the shortest cyclic scheduled for the robot can be solved in polynomial time in the number of machines. Afterwards, they proved that the sequence of activities whose execution produces exactly one part has optimal production rates for the case of three machine flowshop with one robot [4]. More recently, Crama et al. [5] presented a good survey of the specific problems and existing solution approaches to the called robotic flowshop scheduling problems. Hall et al. [6] also addressed the problem of bufferless robotized cells for identical parts, introducing a classification schema and dealing with cells with two and three machines; Kamoun et al. [7] dealt with the same problem for a three machine cell, and proposed a heuristic to find a solution that minimizes the average steady-state cycle time for the repetitive production of Minimal Part Sets (MPS). Sethi et al. [8] dealt with the problem of scheduling robot movements in dual-gripper robotic cells, they considered a single part problem without buffers between the machines and included a comparison of the dual and single gripper case for a cell with n machines. The problem of processing times dependant on the task state (i.e. dependant on the adopted solution instead being constant) was addressed by Wagneur and Sriskandarajah [9]. Although all these papers cover a wide range of manufacturing systems, none of them can be tailored to our particular problem due to the random assistance requirements.
When the presence of stochastic variations or the complexity of the manufacturing system preclude the existence of an analytical solution, discrete-event simulation has become an accepted successful tool for the performance improvement of manufacturing systems [10]. For instance, William and Narayanaswamy [11] studied the correct mix and sequencing of row materials and the reduction of material-handling costs in an AGV operated system, Duwayri et al. [12] reported a simulation study to evaluate the performance of different heuristics for scheduling setup changes in a semiconductor manufacturing system, and Korhonen et al. [13] studied the effect of queuing rules, buffer policies and lot sizes on custom service and cost efficiency of a printed circuit wiring board manufacturing. There are several software tools for the modelling and simulation of discrete-event systems like, for instance, Quest, Automod or Arena. In this work we use the Arena product family [14], a commercial tool that offers a comprehensive modelling capability, application-focused modelling templates and the ability to be integrated with databases or spreadsheets.
The analysis of the simulation results is complex. Metamodels or factorial designs are used when comparing a set of alternative models. Pattern recognition techniques were also used to classify simulation results and find a way to select the best alternative as a function of the system parameters in a wide variety of problems. Good bibliography on the use of pattern recognition, including the principles of the theory used in this work, was provided by Meisel [15], Fukunaga [16], Tou and González [17], Young and Calvert [18], and more recently by Schalkoff [19]. Other approaches, like neural networks, were given by Bishop [20], and their application to jobshop scheduling problems was treated by Alifantis and Robinson [21].
As previous works by the authors, Suárez and Rosell [22] and Suárez et al. [23], respectively presented a first analysis of the cell considered in this work and introduced the application of pattern recognition techniques to look for simple solutions.
Section snippets
Description of the cell
Fig. 1 shows the layout of the manufacturing cell. The cell is composed of four machines , , in a row, all of them of the same type. Each machine operates alternatively over two different pallets, A and B, whose positions are interchanged by a pallet shuttle in a time . The robot loads a part into the pallet in the outer position of the shuttle, either type A or type B, while the machine is working on the pallet in the inner position.
Each part to be manufactured must first be loaded
Feeding strategies analysis
Only fixed sequences that include all the machines only once were considered, otherwise some machines would double the production of some others producing undesired effects like, for instance, different maintenance routines. Only variable strategies that require binary causal signals (i.e. binary signals available at the moment of the decision) were considered. With these constraints, the following strategies were analyzed following the directions of the personnel responsible for the cell.
Fixed
Cell analysis
Let us define:
Machine Activity (MA): the time that a machine needs, after being fed by the robot, to be ready for a new load.
Robot Activity (RA): the time that the robot needs, after feeding a machine , to feed all the other available machines (i.e. those that are not under assistance) and be ready to feed again the machine .
Robot Moves (RM): the time due to the robot moves (displacements) from a machine to another during RA.
Robot Loads (RL): the time dedicated to unload and load machines
Feeding strategy selection
Since there is no general theoretical solution for the mentioned type of cell under the real condition of random assistance requirements by the machines, a two-step procedure was followed. First, the simulator of the cell was used to analyze the machine waste time for different sequences with different working times. Second, pattern recognition techniques were used to identify the domain in which a given feeding sequence is better than another.
One fixed (FM-I) and one variable (FIFO) feeding
Case of variable loading times
As it was mentioned in Section 2 loading times and can be reduced for simple parts that allow more simple robot movements when positioning the part in the pallet. The reduction in loading times can be up to a 25% of the nominal values and . This introduces a change in the operation that may alter the results regarding the best feeding strategy.
In order to minimize the increment of the sample space dimension, the effect of different loading times and was not
Conclusions
The problem of feeding in an optimal way a manufacturing cell composed by four parallel machines was addressed using discrete event simulation and the theory of linear discriminant functions. The cell is located in a car-parts manufacturing company and has some features that make the problem a special case, and therefore there is no general solution available in the literature. For some conditions, differences in the unproductive time of the machines can be quite significative, so choosing the
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Cited by (13)
Scheduling automated transport vehicles for material distribution systems
2019, Applied Soft Computing JournalCitation Excerpt :Hurink and Knust [40] propose a tabu search approach to solve a single robot task scheduling problem in a job shop environment. Suárez and Rosell [41] propose dispatching rules based on the theory of linear discriminant functions to solve optimum part feeding problems by using a single robot. Maimon et al. [42] propose a neural network approach to solve the robot task-scheduling problem.
Material supply scheduling in a ubiquitous manufacturing system
2017, Robotics and Computer-Integrated ManufacturingCitation Excerpt :Askin and Standridge [13] proposed the closest insertion algorithm. Suárez and Rosell [14] used dispatching rules to determine the sequence of tasks. These algorithms showed good performance in short computation time.
Two-machine robotic cell scheduling problem with sequence-dependent setup times
2013, Computers and Operations ResearchCitation Excerpt :The classification criteria, mainly obtained from [1], are represented as the number of machines (M), single part type (SP), multiple part types (MP), units per cycle (U/C), robot moves sequence problem (RMS), parts sequence problem (PS) and the main contributions. Studies addressing robotic problems are more extensive than those listed in Table 1; however, other studies, such as those conducted by Suárez and Rosell [31], Soukhal and Martineau [32], Alcaide et al. [33], Brucker and Kampmeyer [34], Yoosefelahi et al. [35] and Levner et al. [36], use different criteria, production strategies, number of robots, cell layouts, types of machines and types of robot applications than those used in this paper and the papers discussed in Table 1. For related applications of TSP to this work, the reader is referred to Bagchi et al. [4], Deineko et al. [37], Zahrouni and Kamoun [29] and Laporte et al. [38].
Compilation of references
2023, Handbook of Research on AI and Knowledge Engineering for Real-Time Business IntelligenceRobotic cell scheduling problems and their solution procedures: A survey and future research directions
2023, Handbook of Research on AI and Knowledge Engineering for Real-Time Business IntelligenceAn integrated approach for line balancing and AGV scheduling towards smart assembly systems
2020, Assembly Automation
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This work was partially supported by the CICYT projects DPI2001-2202 and DPI2002-03540 and Metaldyne International SL.