Balancing printed circuit board assembly line systems

This paper considers the placement of components onto printed circuit boards (PCBs) using surface mount technology. Multiple automatic placement machines, a variety of PCB types and a large volume for each PCB type characterize the environment studied. The problem addressed is that of allocating and arranging the components on several placement machines, organized into one or several assembly lines, while considering a different assembly time if components are located at different feeder locations. The one assembly line problem is equivalent to balancing a multi-model assembly line where models are assembled in small batches without component rearrangement between model changes. The objective is tominimize the weighted sum of each assembly PCBcycle time, which is defined as the maximum time a PCB has to spend on each machine. We solve this problem with Lagrangian relaxation techniques. Industrial case study results are presented. We also compare the global performance of five placement machines if they are organized as a single assembly line or broken down into two or more assembly lines.     

A GA-based solution approach for balancing printed circuit board assembly lines

Printed circuit board (PCB) assembly lines consist of a number of different machines for mounting electronic components onto PCBs. While high-speed placement machines are employed to assemble standard components, so-called fine-pitch placement machines are used to mount complex electronic components with high precision and by use of specific nozzles. In this paper, we investigate a typical mass production environment where a single type of PCB is assembled in a line comprising high-speed as well as high-precision placement machines. The PCB assembly line balancing problem consists of assigning component feeders, each holding a specific electronic component type, and the corresponding placement operations to machines in the line so as to minimize the assembly cycle time. To solve this problem, a two-stage solution procedure based on genetic algorithm (GA) is proposed. In the first stage, component feeders are assigned to the placement machines with the objective of balancing the workload within the assembly line. A number of candidate solutions are then transmitted to the second stage, where specific machine optimization algorithms are applied to determine the feeder-slot assignment in the component magazine of the machines and the placement sequence of the various components. As a result, fine-tuned placement operation times are achieved which reflect the individual operation mode and the actual component setup of the placement machines. Finally, from the candidate solutions the one which minimizes the actual PCB assembly time is selected.     

Component allocation and job sequencing for two series-connected SMD placement machines

The problem of component allocation and sequencing PCB assembly jobs for two series-connected SMD placement machines is addressed. With the allocation of components, a balancing of the workload per PCB for the two machines should be achieved. Furthermore, when switching from one type of PCB to another, setup times must be considered. Two heuristic procedures are developed and tested in extensive numeric analyses of a number of realistic case models. The problem examined and the database used represent a concrete case of an industrial application in which very diversified small jobs are to be processed.     

Precedence constrained TSP arising in printed circuit board assembly

Component placement sequencing is a challenging problem that arises in automated assembly of printed circuit boards. While for some placement machines all placement sequences are acceptable, in other cases some sequences are not allowed because of the shape of the placement head. In such cases, while the head moves down to perform a placement, it might damage a previously placed component, and the problem of determining a minimum cost and at the same time acceptable sequence leads to a Precedence Constrained Travelling Salesman Problem formulation. In this study, a solution procedure to such a formulation is developed and its implementation in a real PCB assembly environment is discussed.     

PCB assembly scheduling for collect-and-place machines using genetic algorithms

In printed circuit board (PCB) assembly, collect-and-place machines, which use a revolver-type placement head to mount electronic components onto the board, represent one of the most popular types of assembly machinery. The assignment of feeders to slots in the component magazine and the sequencing of the placement operations are the main optimisation problems for scheduling the operations of an automated placement machine. In this paper, we present different genetic algorithms (GAs) for simultaneously solving these highly interrelated problems for collect-and-place machines in PCB assembly. First we consider single-gantry machines as the basic type of machinery. In the conventional GA approach all placement operations and the feeder-slot assignment are represented by a single chromosome. In order to increase the efficiency of the genetic operators, we present a novel GA approach, which integrates a clustering algorithm for generating sub-sections of the PCB and grouping the corresponding placement operations. It is shown that the proposed GAs can be extended to schedule dual-gantry placement machines, which are equipped with two independent placement heads and two dedicated component magazines. Hence, component feeders have to be allocated between the two magazines. To solve this allocation problem, two different heuristic strategies are proposed. Finally, detailed numerical experiments are carried out to evaluate the performances of the proposed GAs.     

Analysis of partial setup strategies for solving the operational planning problem in parallel machine electronic assembly systems

In this paper, we analyse the operational planning problem in an electronic assembly system with multiple placement machines operating in parallel. The partial setup strategy is proposed as an effective methodology for this problem. This strategy attempts to determine the balance between processing time and changeover time during system operation. The Tour primary issues are determining the assignment of products to machines, the sequence of products on each machine, the assignment of components to feeder locations for each product, and the component placement sequence for each product. Four solution procedures for unique and partial setup strategies are developed and tested. The computation results show that for low to medium volume high mix environments, the partial setup procedures offer significant improvement over the unique setup strategies. The results also show that no single fixed strategy dominates in all scenarios, and therefore, an adaptable procedure that will choose the best solution for each set of requirements is needed.     

AUTOMATED PROCESS PLANNING FOR PRINTED CIRCUIT CARD ASSEMBLY

Printed circuit card assemblies form the core of a vast array of contemporary manufactured products. The technologies for assembling printed circuit cards require a hierarchy of complex decisions for grouping card types and processes, staging components at assembly machines, arranging feeders, and sequencing placement operations. This paper is motivated by the largely unmet needs of industrial process planners for computer aids. Our objective is to develop a framework for the printed circuit card assembly process planning problem and to assess the current state of the research on appropriate models and solution methods. We first provide an overview of the essential elements of printed circuit card terminology, assembly technologies, and assembly system operations. Then we propose a decision hierarchy, survey the published literature, and identify needs for future research.     

Worker allocation in lean U-shaped production lines

U-shaped lines are widely used in lean systems. In U-shaped production lines, each worker handles one or more machines on the line: the worker allocation problem is to establish which machines are handled by which worker. This differs from the widely-investigated U-line assembly line balancing problem in that the assignment of tasks to line locations is fixed. This paper address the worker allocation problem for lean U-shaped production lines where the objectives are to minimize the quantity of workers and maximize full work: such allocations provide the opportunity to eliminate the least-utilized worker by improving processes accordingly. A mathematical model is developed: the model allows for any allocation of machines to workers so long as workers do not cross paths. Walking times are considered, where workers follow circular paths and walk around other worker(s) on the line if necessary. A heuristic algorithm for tackling the problem is developed, along with a procedure representing the ‘traditional’ approach of constructing standard operations routines. Computational experiments considering three line sizes (up to 20 machines) and three takt time levels are performed. The results show that the proposed algorithm both improves upon the traditional approach and is more likely to provide optimal solutions.     

A note on ‘balancing printed circuit board assembly line systems’

In a recent paper of (Lapierre, S.D., Debargis, L. and Soumis, F., Balancing printed circuit board assembly line systems. Int. J. Prod. Res., 2000, 38, 3899–3911.), the authors considered the balancing of a PCB assembly line consisting of several pick-and-place machines. The authors claimed that, for the particular machine type they considered, the component placement time is independent of the placement sequence of the components and then concentrated on allocating component types to machines and configuring the feeders on each machine to balance the line. We show that, the placement time is actually dependent on the placement sequence and thus, it needs to be accounted for if a more accurate line balance is looked for.     

Estimating printed circuit board assembly times using neural networks

Several production planning tasks in the printed circuit board (PCB) assembly industry involve the estimation of the component placement times for different PCB types and placement machines. This kind of task may be, for example, the scheduling of jobs or line balancing for single or multiple jobs. The simplest approach to time estimation is to let the production time be a linear function of the number of components to be placed. To achieve more accurate results, the model should include more parameters (e.g. the number of different component types, the number of different component shapes, the dimensions of the PCBs, etc.). In this study we train multilayer neural networks to approximate the assembly times of two different types of assembly machines based on several parameter combinations. It turns out that conventional learning methods are prone to overfitting when the number of hidden units of the network is large in relation to the number of training cases. To avoid this and complicated training and testing, we use Bayesian regularisation to achieve efficient learning and good accuracy automatically.     

Workload planning in small lot printed circuit board assembly

The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.     

Balancing and scheduling of surface mount technology lines

A mixed-integer programming approach to simultaneous or sequential balancing and scheduling of surface mount technology (SMT) lines for printed wiring board (PWB) assembly is presented. The SMT line consists of several processing stages in series separated by finite intermediate buffers, where each stage has one or more identical parallel machines. In the line, different types of PWBs are assembled using various types of electronic components. The components are assigned to feeder slots of a feeder carrier at each placement station. Different types of components occupy a different number of feeder slots. The total number of slots available at each station was limited. The problem objective was to determine an assignment of components to feeder slots at each placement station and to determine an assembly schedule for a mix of board types to complete the boards in minimum time. Numerical examples and some computational results are presented to illustrate applications of the proposed approach.     

Circuit Card Assembly on Tandem Turret-Type Placement Machines

This paper describes a set of heuristics for prescribing the inter-related decisions that form a process plan for assembling a given type of circuit card on a series of turret-type placement machines. Our goals are to prescribe a near-optimal (minimum) cycle time and to do so within a short run time to support process planning. A set of five practical considerations that affect cycle time are addressed. Two sets of test instances are used to evaluate the heuristics, which have polynomial-time complexity. Our tests determine empirically that our heuristics consistently achieve "near-optimal" cycle times and that their run times are bounded by polynomial functions of problem size in the average case.     

A Heterogeneous Virtual Machines Resource Allocation Scheme in Slices Architecture of 5G Edge Datacenter

In the paper, we investigate the heterogeneous resource allocation scheme for virtual machines with slicing technology in the 5G/B5G edge computing environment. In general, the different slices for different task scenarios exist in the same edge layer synchronously. A lot of researches reveal that the virtual machines of different slices indicate strong heterogeneity with different reserved resource granularity. In the condition, the allocation process is a NP hard problem and difficult for the actual demand of the tasks in the strongly heterogeneous environment. Based on the slicing and container concept, we propose the resource allocation scheme named Two-Dimension allocation and correlation placement Scheme (TDACP). The scheme divides the resource allocation and management work into three stages in this paper: In the first stage, it designs reasonably strategy to allocate resources to different task slices according to demand. In the second stage, it establishes an equivalent relationship between the virtual machine reserved resource capacity and the Service-Level Agreement (SLA) of the virtual machine in different slices. In the third stage, it designs a placement optimization strategy to schedule the equivalent virtual machines in the physical servers. Thus, it is able to establish a virtual machine placement strategy with high resource utilization efficiency and low time cost. The simulation results indicate that the proposed scheme is able to suppress the problem of uneven resource allocation which is caused by the pure preemptive scheduling strategy. It adjusts the number of equivalent virtual machines based on the SLA range of system parameter, and reduces the SLA probability of physical servers effectively based on resource utilization time sampling series linear. The scheme is able to guarantee resource allocation and management work orderly and efficiently in the edge datacenter slices.     

Assembly tolerance allocation using a coalitional game method

Assembly tolerance allocation in modern manufacturing industries is important because it directly affects product quality and manufacturing cost. Loose tolerances may cause quality deficiency while tight tolerances can increase the cost. It is significant to develop a reasonable tolerance allocation strategy for every assembly component combining the cost and quality demands. Traditionally, designers often adopt the single objective optimization with some kind of constraint or establish a comprehensive evaluation function combining several optimization objectives with different weights to solve the tolerance allocation problem. These approaches may not be desirable as it is difficult to adequately consider the interaction and conflict between the cost and quality demands. In this article, an assembly tolerance allocation method using coalitional game theory is proposed in an attempt to find a trade-off between the assembly cost and the assembly quality. First, the assembly tolerance allocation problem is formulated as a multi-objective optimization problem and the concept of the Pareto-optimal solution is introduced. Then, how the assembly tolerance allocation model is transformed into a coalitional game model is discussed, and a key technique of transforming the tolerance design variables into the game strategies is presented. Further, the Shapley value method of coalitional game based on each player's contribution evaluation to the profit of the whole coalition is given. Finally, the feasibility of the procedure is demonstrated through an example of vehicle front structure assembly.     

Heuristic procedures for the parallel machine problem with tool switches

We address the problem of scheduling a set of parts with given processing times and tool requirements on m identical parallel machines. The problem is to find an allocation of the machines to the parts, a proper sequence for the parts assigned to each machine, and a corresponding tool-switching plan for each machine so as to minimize the makespan. It is demonstrated that this problem is np-hard , and three heuristic procedures are proposed for solving it. The first procedure is a multi-start local improvement procedure, and various neighborhood structures and search strategies are discussed in this context. The second procedure is a variation of the list-processing routine that is commonly used for the parallel machine problem. Finally, the last procedure is an adaptation of a well-known constructive procedure for the k -travelling salesman problem. Results of a limited computational experiment are also presented in which the makespan obtained via each heuristic procedure is compared with a proposed lower bound and with other reference values.     

Aggregate Capacitated Lot-Size Scheduling for a Class of Flexible Machining and Assembly Systems

A class of flexible machining and assembly systems is considered. In this class, each end item is assembled from a number of components. Each component undergoes a sequence of operations on various machines. The assembly structure of all items is flat. At least for some operations on some machines, setups are not negligible. Aggregation of constraints and items is employed and the problem of aggregate capacitated lot-size scheduling is formulated. Three different approaches for efficiently solving the resulting mixed binary programming problem are presented and discussed. The first is based on Lagrangian relaxation, die second on a mixed-integer network flow reformulation, while the third is based on a sub-linearization scheme.     

An extended distance-based facility layout problem

The distance-based facility layout problem with unequal-area departments has been studied by many researchers for over 30 years. Still, current approaches require certain assumptions that limit the type of solutions obtained. In this paper, we consider manufacturing systems in which replicates of the same machine type may exist in the facility, and propose an extended distance-based facility layout problem that concurrently determines the number and shape of the departments, the assignment of machines to departments, and the allocation of part flow volume to individual machines. A non-linear mixed-integer program that accurately captures the extended facility layout and part flow allocation problem, a decomposition approach that exploits the structure of the formulation using a heuristic solution procedure, as well as computational results that evaluate the proposed approach, are presented.