An examination of routeing flexibility for small batch assembly of printed circuit boards

In this paper, we examine and quantify the effects of introducing new processing flexibility in the rapidly changing environment of printed circuit board (PCB) assembly. Specifically, we perform experiments designed to establish the benefits and determine the limitations associated with the introduction of routeing flexibility. We examine system behaviour as batch sizes are reduced in an environment characterized by moderate set-up requirements. We further demonstrate that the performance of flexible routeing policies in this environment is adversely affected by larger batch sizes and that the introduction of routeing flexibility leads to improved system performance in small batch assembly.     

Non-exhaustive family based dispatching heuristics–exploiting variances of processing and set-up times

Group technology exploits similarities in product and process design to effectively meet the diversity of customer demand. In this paper we consider one of the implementations of this concept–heuristics for family based dispatching. Intrinsic to family based dispatching is the grouping of similar types of products for joint processing. Hence, the number of set-ups may be reduced. Consequently, lead time performance of the shop can be improved. Unfortunately, variances of processing and set-up times–as found in practice–have received little attention in heuristics’ construction and testing. To address this issue we propose several new, non-exhaustive heuristics. Whereas existing exhaustive heuristics set batch contents equal to all products available for a family, non-exhaustive heuristics allow for switching families, even when the current family queue is not empty. An extensive simulation study shows how this flexibility in batch composition improves shop performance, especially in case of high variances of processing and set-up times.     

An ant colony optimisation algorithm for balancing two-sided U-type assembly lines with sequence-dependent set-up times

Some practical arrangements in assembly lines necessitate set-up times between consecutive tasks. To create more realistic models of operations, set-up times must be considered. In this study, a sequence-dependent set-up times approach for two-sided u-type assembly line (TUAL) structures is proposed for the first time. Previous studies on TUAL have not included set-up times in their analyses. Furthermore, an algorithm based on the Ant Colony Optimization (ACO) algorithm, which is using a heuristic priority rule based procedure has been proposed in order to solve this new approach. In this paper, we look at the sequence-dependent set-up times between consecutive tasks and consecutive cycles, called the “forward set-up time” and the “backward set-up time”, respectively. Additionally, we examine the “crossover set-up time”, which arises from a new sequence of tasks in a crossover station. In order to model more realistic assembly line configurations, it is necessary to include sequence-dependent set-up times when computing all of the operational times such as task starting times and finishing times as well as the total workstation time. In this study, the proposed approach aims to minimize the number of mated-stations as the primary objective and to minimize the number of total workstations as a secondary objective. In order to evaluate the efficiency of the proposed algorithm, a computational study is performed. As can be seen from the experimental results the proposed approach finds promising results for all literature-test problems.     

Performance of serial assembly line designs under unequal operator speeds and learning

The traditional balanced assembly line designs can perform quite inefficiently under the presence of high labor turnover, low operator learning rates, and stochastic processing times. In these situations assembly line designs based on dynamic work allocation and work sharing principles have been shown to render a higher and less variable throughput. However, for situations where low labor turnover conditions and high operator learning rates exist, the traditional balanced lines still tend to be most productive. This paper has two objectives: to introduce a method based on work sharing principles, which we denominate Modified Work Sharing (MWS), and to develop some simple analytical tools that will allow us to compare the performance of this method with the traditional and other dynamic work allocation line designs. These results suggest that the traditional method is the most affected by the introduction of new operators in the production lines and thus the most affected by variability in general. On the other hand, dynamic work allocation methods appear to better absorb the variability introduced by new operators by sharing the workload of new operators with the more experienced members of the line.     

Intelligent scheduling of discrete automated production line via deep reinforcement learning

The reinforcement learning (RL) is being used for scheduling to improve the adaptability and flexibility of an automated production line. However, the existing methods only consider processing time certain and known and ignore production line layouts and transfer unit, such as robots. This paper introduces deep RL to schedule an automated production line, avoiding manually extracted features and overcoming the lack of structured data sets. Firstly, we present a state modelling method in discrete automated production lines, which is suitable for linear, parallel and re-entrant production lines of multiple processing units. Secondly, we propose an intelligent scheduling algorithm based on deep RL for scheduling automated production lines. The algorithm establishes a discrete-event simulation environment for deep RL, solving the confliction of advancing transferring time and the most recent event time. Finally, we apply the intelligent scheduling algorithm into scheduling linear, parallel and re-entrant automated production lines. The experiment shows that our scheduling strategy can achieve competitive performance to the heuristic scheduling methods and maintains stable convergence and robustness under processing time randomness.     

An event-based analysis of condition-based maintenance decision-making in multistage production systems

Condition-based maintenance (CBM) is becoming increasingly prevalent because of its capability to continuously track equipment health degradation and accurately predict unscheduled equipment failure. CBM helps to improve the business bottom line by preventing costly station failure. However, it is not uncommon that CBM needs to stop stations for maintenance during operation, which can severely impede the normal production. The objective of this paper is to develop a systematic method to predict the negative impact of CBM stoppage events on production in a multistage manufacturing system. The research helps to predict the real expense of applying CBM, which is the foundation to establish a comprehensive real-time CBM decision-making model. We start from the event-based analysis of system dynamics and develop a stochastic estimation method to predict the permanent production loss caused by a CBM stoppage event. The monotonicity property of permanent production loss is investigated. Simulation case studies are performed to illustrate the theoretical results and demonstrate their potential in facilitating CBM decision-making.     

Periodical capacity setting methods for make-to-order multi-machine production systems

The paper presents different periodical capacity setting methods for make-to-order, multi-machine production systems with stochastic customer required lead times and stochastic processing times to improve service level and tardiness. These methods are developed as decision support when capacity flexibility exists, such as, a certain range of possible working hours a week for example. The methods differ in the amount of information used whereby all are based on the cumulated capacity demand at each machine. In a simulation study the methods’ impact on service level and tardiness is compared to a constant provided capacity for a single and a multi-machine setting. It is shown that the tested capacity setting methods can lead to an increase in service level and a decrease in average tardiness in comparison to a constant provided capacity. The methods using information on processing time and customer required lead time distribution perform best. The results found in this paper can help practitioners to make efficient use of their flexible capacity.     

Sequence Dependent Machine Set-Up Times and Similarity of Parts: A Mathematical Model

This paper attempts to develop a mathematical relation between machine set-up times and similarity of parts. First, the task for setting up a machine was broken down into a distinct number of elements whose state was expressed as a binary vector called set-up task elimination vector. By introducing a corresponding rime vector, it was shown that sequence dependent set-up time is the product of the two vectors. Next, a quantitative relation between set-up tasks and the design characteristics of parts was defined as a binary interaction matrix while the similarity of parts was defined as a binary vector. It turned out that the set-up tasks elimination vector is the Boolean product of the interaction matrix and the similarity vector. Using this information, a machine set-up model was developed in terms of similarity of parts. The computation of machine set-up times and a sequencing heuristic using the model were illustrated.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

Integrating machine scheduling and self-healing maintenance by job-mix pull control

In general, machines degrade with use. But, for some manufacturing processes machine ageing can be reversed by processing alternative types of jobs. In the latter case, machines can run longer without breakdowns if job types are balanced and scheduling is optimised. However, when job arrivals are stochastic, even short-term fluctuations in job mixes can increase the risk of breakdown. This paper presents a proof of concept study on job-mix pull control to exploit the age-reversing, healing effect. Because adding pull control will impact the architecture of factory scheduling, three issues are addressed in the proof. First, it is shown that the new architecture would have a better performance than the existing dispatching approach. Second, a method of pulling jobs from upstream to reduce the probability of machine breakdown is developed. The condition of workload imbalance in which job mix control (JMC) should or should not be activated is analysed. Finally, the benefit of JMC is evaluated by using simulation to demonstrate potential improvements that can be achieved. Besides the proof of concept, this study produces an important finding. A lingering cumulative influence of the self-healing effect is discovered, pointing out a new direction for future maintenance scheduling research.     

Minimising interference for scheduling two parallel machines with a single server

In this paper, we consider the problem of scheduling a set of jobs on two parallel machines with set-up times. The set-up has to be performed by a single server. The objective is to minimise the forced idle time. The problem of minimising the forced idle time (interference problem) is known to be unary NP-hard for the case of two machines and equal set-up and arbitrary processing times. We propose a mixed integer linear programming model, which describes a special class of schedules where the jobs from a list are scheduled alternatively on the machines, and a heuristic algorithm is tested on instances with up to 100,000 jobs. The computational results indicate that the algorithm has an excellent performance even for very large instances, where mostly an optimal solution is obtained within a very small computational time.     

带漂移因子及停时的最优脉冲随机控制问题

通过把漂移参数引入到受控于Poisson过程的状态结构中,本文建立了一非对称型最优脉冲随机控制模型。在此模型的目标函数中,首次引进了停时因素。利用随机积分及脉冲控制理论,我们不但给出了最优回报函数应满足的充分性条件,而且在一定条件下得出了其显解及相应的最优控制策略。     

Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps

By introducing a new Gaussian process and a new compensated Poisson random measure, we propose an explicit prediction-correction scheme for solving decoupled forward backward stochastic differential equations with jumps (FBSDEJs). For this scheme, we first theoretically obtain a general error estimate result, which implies that the scheme is stable. Then using this result, we rigorously prove that the accuracy of the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results.     

Optimizing spatiotemporal sensors placement for nutrient monitoring: a stochastic optimization framework

Nutrient monitoring is very important for the area of food–energy–water nexus. The sensor network for nutrient monitoring requires dynamic sensing where the positions of the sensors change with time. In this work, we have proposed a methodology to optimize a dynamic sensor network which can address the spatiotemporal aspect of nutrient movement in a watershed. This is a first paper in the series where an algorithmic and methodological framework for spatiotemporal sensor placement problem is proposed. Dynamic sensing is widely used in wireless sensors, and the current approaches to solving this problem are data intensive. This is the first time we are introducing a stochastic optimization approach to dynamic sensing which is efficient. This framework is based on a novel stochastic optimization algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). A small case study of the dynamic sensor placement problem is presented to illustrate the approach. In the second paper of this series, we will present a detailed case study of nutrient monitoring in a watershed.     

A multi-objective distribution-free model and method for stochastic disassembly line balancing problem

End-of-life product recycling is a hot research topic in recent years, which can reduce the waste and protect the environment. To disassemble products, the disassembly line balancing is a principal problem that selects tasks and assigns them to a number of workstations under stochastic task processing times. In existing works, stochastic task processing times are usually estimated by probability distributions or fuzzy numbers. However, in real-life applications, only their partial information is accessible. This paper studies a bi-objective stochastic disassembly line balancing problem to minimise the line design cost and the cycle time, with only the knowledge of the mean, standard deviation and upper bound of stochastic task processing times. For the problem, a bi-objective chance-constrained model is developed, which is further approximated into a bi-objective distribution-free one. Based on the problem analysis, two versions of the ?-constraint method are proposed to solve the transformed model. Finally, a fuzzy-logic technique is adapted to propose a preferable solution for decision makers according to their preferences. A case study is presented to illustrate the validity of the proposed models and algorithms. Experimental results on 277 benchmark-based and randomly generated instances show the efficiency of the proposed methods.     

A production scheduling problem with uncertain sequence-dependent set-up times and random yield

A scheduling problem in a real production line with uncertain sequence-dependent set-up times and a random yield is considered. The production line can produce multiple product types as production lots, each of which is composed of a number of products of the same product type. To changeover product types, a sequence-dependent set-up operation should be performed, and only the lower and upper bounds are known for the sequence-dependent set-up times. Moreover, the processing time to produce the required number of product for each production lot is uncertain due to the random yield. For the objective of minimising the average tardy probability of given production lots, a systematic approximation scheme to estimate tardy probabilities of lots in any given production sequence is developed by taking not only the uncertainties but also the computational efficiency into account. As practical solution approaches, a simulated annealing and a discrete particle swarm optimisation algorithms using the approximation scheme are developed, and their performance are evaluated by computational experiments. Since there has been no research on the scheduling problems with uncertain sequence-dependent set-up times and random yield, the authors expect this research will make an excellent contribution to develop practical scheduling methodologies in uncertain scheduling environments.     

Sequencing of parts on single-stage multifunctional machining systems using a chaos-embedded simulated annealing algorithm

This paper deals with the objective of determining an optimal part sequence on a single-stage multifunctional machining system (SSMS) with a view to achieve the broad objectives of cost minimization and time minimization. SSMS has become a preferred alternative for manufacturers to use the resource efficiently, owing to the flexibility and process variety offered by it. This paper formulates a mathematical model that considers the minimization of both set-up cost and time simultaneously. The option of hiring an additional fixture has also been considered that enables the reduction in tool magazine replenishment and re-fixturing operations, which in turn offers economic advantage by way of reducing set-up cost. This study has proposed a new heuristic by modifying the simulated annealing concept to solve the underlying problem. The conventional simulated annealing search scheme is replaced by a chaotic search that takes into account the ergodic and stochastic properties of chaotic systems. In order to restrict the premature convergence and to diversify the search space, a modified perturbation scheme has been employed. The performance of the proposed algorithm was tested on a simulated case study adopted from the literature and the results obtained reveal the effectiveness and scalability of the proposed algorithm. The results establish that the proposed approach is effective and reactive to severe disturbances and must take place in the manufacturing environment.     

Optimizing financial and physical assets with?chance-constrained programming in?the?electrical?industry

This paper deals with a Chance-Constrained Programming formulation and approximate resolution of an offer-demand equilibrium problem in the context of electricity markets. First, we state the probabilistic model. Computing the coefficients of the problem matrix is easy for financial assets, but a challenging task for physical assets. By introducing maximal production capacities, the computation becomes tractable for thermal plants but still leads to a combinatorial problem for hydraulic production. The obtained problem matrix is sparse, large scale and with random coefficients describing underlying uncertainty factors affecting the available power of assets. Second, we suggest some ways for approximately solving the obtained combinatorial chance-constrained program, which is in fact a stochastic multi-knapsack problem. A formal link between joint and individual chance constraints is exhibited and may lead to a simplified processing of the problem. Finally we illustrate our approximate algorithm on a stylized example.     

Single-machine group scheduling problem considering learning,forgetting effects and preventive maintenance

An integrated single-machine group scheduling model is proposed, which incorporates both learning and forgetting effects and preventive maintenance (PM) planning. The objective is to minimise the expected makespan by optimising job sequence and PM decisions. This model contains sequence-dependent set-up time, actual processing time, planned PM time and expected minimal repair time simultaneously. Based on the properties of group production, three learning functions under different circumstances are proposed to deduce the variable processing time of each part, considering the learning effect when consecutively producing identical or similar parts, together with the forgetting effect when transferring jobs interrupts the production process and makes retrogress in learning. Both run-based maintenance and minimal repair policies are specified to handle the uncertainty of machine breakdowns. The search algorithm for the model is developed, and the numerical example is studied. The computational results and sensitivity analysis show that this improved group scheduling model can well balance the machine resource requirements from different practical manufacturing-related activities.