Mixed-model Sequencing Problem Research Articles

Mixed-model sequencing with stochastic failures: A case study for automobile industry

In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint failure. These vehicles are pulled out of the sequence, and the vehicles in the succeeding positions are moved forward, potentially resulting in challenges for logistics or other scheduling concerns. This paper proposes a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provides improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the extensive equivalent formulation with an off-the-shelf solver. Moreover, we provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high-quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20% for both small- and large-sized instances.

Mixed-model sequencing with reinsertion of failed vehicles: a case study for automobile industry

In the automotive industry, some vehicles, failed vehicles, cannot be produced according to the planned schedule due to some reasons such as material shortage, paint failure, etc. These vehicles are pulled out of the sequence, potentially resulting in an increased work overload. On the other hand, the reinsertion of failed vehicles is executed dynamically as suitable positions occur. In case such positions do not occur enough, either the vehicles waiting for reinsertion accumulate or reinsertions are made to worse positions by sacrificing production efficiency. This study proposes a bi-objective two-stage stochastic program and formulation improvements for a mixed-model sequencing problem with stochastic product failures and integrated reinsertion process. Moreover, an evolutionary optimisation algorithm, a two-stage local search algorithm, and a hybrid approach are developed. Numerical experiments over a case study show that while the hybrid algorithm better explores the Pareto front representation, the local search algorithm provides more reliable solutions regarding work overload objective. Finally, the results of the dynamic reinsertion simulations show that we can decrease the work overload by 20% while significantly decreasing the waiting time of the failed vehicles by considering vehicle failures and integrating the reinsertion process into the mixed-model sequencing problem.

Mathematical modelling and a discrete cuckoo search particle swarm optimization algorithm for mixed model sequencing problem with interval task times

Mathematical modelling and a discrete cuckoo search particle swarm optimization algorithm for mixed model sequencing problem with interval task times

Adaptive local search algorithm for solving car sequencing problem

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines (MMAL) are often designed such that average station work satisfies the time allocated to each station, but some models with work-intensive options require more than the allocated time. Sequencing varying models in a mixed-model assembly line is the short-term decision problem that has the objective of preventing line stoppage resulting from a station work overload. Accordingly, a good allocation of models is necessary to avoid work overload. The car sequencing problem (CSP) is a specific version of the mixed-model sequencing problem that minimizes the work overload by controlling the sequence of models. In order to do that, CSP restricts the number of work-intensive options by applying capacity rules. Consequently, the objective is to find the sequence with the minimum number of capacity rule violations. In this study, we show that exact solution procedures are insufficient for application in industry. however, we provide five improved lower bounds for CSPLib instances by solving problems optimally with a subset of options. Additionally, we present four local search metaheuristics that are commonly used to solve CSP. The local search algorithms are compared over CSP benchmark instances, including CSPLib and ROADEF Challenge 2005. The computational experiments show that an Adaptive Local Search (ALS) provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Moreover, results show that the algorithmic effort should focus on randomly exploring more non-deteriorated solutions instead of systematic search or spending time visiting deteriorated solutions to escape local optima.

Completion time variance and the product rate variation problem

Just-in-time manufacturing necessitates finding short repeated sequences of products. The literature addressed this mixed model scheduling objective using the product rate variation (PRV), which maximises the deviation between the actual proportions and ideal proportions of jobs in the sequence. Researchers have reported application of PRV minimisation in manufacturing as well as in service industry. In this paper, we address this problem considering the completion times of the jobs in the sequence instead of the PRV, and show instances where maximising the sum of completion time variances (SCTVs) is an effective alternative to PRV for the mixed model sequencing problem. We propose algorithms using tabu search and genetic algorithms to solve the SCTV problem and show computational results.

Solving the mixed model sequencing problem with reinforcement learning and metaheuristics

This study presents a reinforcement learning (RL) approach for the mixed model sequencing (MMS) problem with a minimization of work overload situations. The proposed approach generates the sequence in a constructive way, so that an action denotes the model to be sequenced next. The trained policy quickly creates an initial sequence, which allows us to use the cutoff time to further improve the solution quality with a metaheuristic. Our numerical evaluation based on an existing benchmark dataset shows that our approach is superior to established methods if the demand plan follows its expected distribution from the learning process.

Walking Workers systems: a sequence analysis for flexible mixed model lines

The Walking Workers (WW) systems are interesting for their flexibility attributes, especially in terms of ability to manage the product variety and market demand. This paper aims to study the mixed model sequencing problem considering un-paced, unbuffered WW systems. The authors propose an original algorithm, called “accordion algorithm” for the models sequence definition and the makespan minimization. This algorithm is tested and validated through a simulative study highlighting the influence of the task time variations and of the resources number on the system performances.

Impact of the Learning-Forgetting Effect on Mixed-Model Production Line Sequencing

In this study, the learning-forgetting (L-F) effect is considered in a mixed-model sequencing problem to investigate its impact on makespan minimization. To this end, mathematical models of the learning and forgetting effects are modified in accordance with a mixed-model production environment, and the L-F functions for a serial workstation and multiple products are established. Subsequently, their impact on production is demonstrated via data experiments. The relationships between the learning effect, forgetting effect, product model combination, and makespan are also discussed based on the experimental results. The results show that the learning and forgetting functions can significantly affect the work time in the mathematical scheduling model and that a balanced product model combination and small MPS (minimum part set) batch can help to reduce the L-F effect.

Applying available-to-promise (ATP) concept in mixed-model assembly line sequencing problems in a Make-To-Order (MTO) environment: problem extension, model formulation and Lagrangian relaxation algorithm

Mixed-model assembly line is known to be a special case of production lines where variety of product models similar to product characteristics are assembled. This article addresses available-to-promise (ATP) in mixed-model assembly line sequencing problems in a Make-To-Order environment in two stages. First, the customers are prioritized based on their corresponding profit values and a decision support system for order acceptance/rejection based on ATP is developed. By implementing this concept and developing a mathematical model, delivery quantity and date in a planning horizon are determined based on the inventories in the stock. The second stage is solving a mixed binary mathematical model to sequence accepted orders suitably according to demands due dates that guarantees the orders are not released too late or too early. The problem simultaneously considers following objectives: minimizing the total tardiness and earliness costs based on the determined priority of orders and minimizing the utility work and idle time of workers in the production line. An algorithm based on Lagrangian relaxation is developed for the problem, and tested in terms of solution quality and computational efficiency. To validate the performance of the proposed algorithm, various test problems in small size are solved using the CPLEX solver, and compared with the Lagrangian relaxation method. Finally, the proposed model is solved in large size problems to analyze the model performance. The drawback of the CPLEX is that it could not solve large problem instances in reasonable time. For the small sized problem, there is approximately 1% duality gap for the Lagrangian relaxation method. The maximum duality gap in the Lagrangian relaxation method for the large sized problem is always kept below 4% while the average computing time is very reasonable. Therefore, according to the results obtained from test problems, the developed Lagrangian relaxation method proved to be the suitable method for this problem.

Stochastic mixed-model assembly line sequencing problem: Mathematical modeling and Q-learning based simulated annealing hyper-heuristics

This paper presents a mixed-model sequencing problem with stochastic processing times (MMSPSP) in a multi-station assembly line. A new mixed-integer nonlinear programing model is developed to minimize weighted sum of expected total work-overload and idleness, which is converted into a mixed-integer linear programming model to deal with small-sized instances optimally. Due to the NP-hardness of the problem, this paper develops a novel hyper simulated annealing (HSA). The HSA employs a Q-learning algorithm to select appropriate heuristics through its search process. Numerical results are presented on several test instances and benchmark problems from the related literature. The results of statistical analysis indicate that the HSA is quite competitive in comparison with optimization software packages, and is significantly superior to several SA-based algorithms. The results highlight the advantages of the MMSPSP in comparison with traditional deterministic approaches in mixed-model sequencing contexts.

An expert system to minimize operational costs in mixed-model sequencing problems with activity factor

One of the major issues in industrial environments is currently maximizing productivity while reducing manufacturing cost. This can be seen clearly reflected in mixed-model assembly lines based systems, where obtaining efficient manufacturing sequences is a key to be competitive in a dynamic and globalized market. However, this continuous cost reduction and productivity growth should not penalize the welfare of employees. This work is intended to address this lack of compatibility between the economic and social objectives through the study of the mixed-model sequencing problem from both the business and labor perspective. This is done by considering the possibility of reducing or increasing processing times of operations by varying the work pace of line's operators within the permissible legal boundaries. Thus, depending on this flexible activation time of operators, the amount of completed work and idle time will be one or the other and, consequently, the productivity of the line will also improve or get worse. In this regard, we propose new approach to the sequencing problem without incurring cost increases and providing a safe working environment, in accordance with applicable law. This new approach leads to obtain efficient manufacturing sequences, in terms of both productivity and labor conditions. Specifically, the objective of the new problem is minimizing the unproductive costs of the line by incorporating the possibility of increasing production through the variation of the work pace of line's operators. Increasing the work pace of operators, the amount of non-completed work or the preventable idle time can be reduced and therefore, their associated costs too. In addition, and without losing sight of the effort involved in working with a work pace above the normal, we propose several economic criteria to compensate the activation of workers where necessary.

Mixed-model sequencing problem under capacity and machine idle time constraints in JIT production systems

Abstract Sequencing problems in mixed-model production systems assume a negligible set-up time that permits unconstrained product interspersing. This assumption offers better production sequences in terms of just-in-time objectives such as minimizing parts usage rate variation and minimizing Production Rate Variation (PRV). However, set-up times turn out to be critical in many realistic situations. The present paper addresses the sequencing problem in mixed-model production systems, where internal and external set-up times are considerable measures. Internal set-up time limits free mixing of products, resulting in batching of products; while external set-up time causes machine idle time. The authors present a mathematical model for the problem to find sequences that minimize PRV, satisfying capacity and zero machine idle time constraints. LINGO 15.0 solver could solve the model for small-size problems in a reasonable computational time. For large-size problems, a modified bit-wise mutation algorithm that uses a single unary genetic operator has been developed. The authors have applied the algorithm for diverse problem instances at different production capacities. The same problems are also analyzed by relaxing the zero machine idle time constraint. Results demonstrate how the constraints on capacity and machine idle time disturb the leveling of sequences in mixed-model production systems. The model provides decision makers with the opportunity to select smooth sequences based on the available production time and acceptable machine idle time.

Free and regular mixed-model sequences by a linear program-assisted hybrid algorithm GRASP-LP

A linear program-assisted hybrid algorithm (GRASP-LP) is presented to solve a mixed-model sequencing problem in an assembly line. The issue of the problem is to obtain manufacturing sequences of product models with the minimum work overload, allowing the free interruption of operations at workstations and preserving the production mix. The implemented GRASP-LP is compared with other procedures through a case study linked with the Nissan’ Engine Plant from Barcelona.

Multi-level assembly process complexity analysis and its application for mixed-model assembly sequencing

This research aims at understanding the process complexity in assembly system, and the complexity is defined to describe the complexity for the production activities and their sequences. Four primary integer layers and other fractal layers are decomposed from the whole assembly process according to the idea of fractal theory. The four kinds of complexities are station operation complexity, assembly flow complexity, production sequence complexity and production cycle complexity; they are proposed to present the complexity characteristic for different integer layers. The information entropy is adopted to measure these process complexities, and two different measurements are proposed for the pull and push production models respectively. For conquering the two contradictory problems, high operation failure rate and decrease of working emotion, which are caused by inappropriate product similarity distribution, the optimisation objective minimising the diversity of the assembly flow complexity is exploited. Then the multi-objective genetic algorithm is adopted to modelling the mixed-model assembly sequencing problem with two optimisation objectives, and a case study is implemented to demonstrate the approach.

A hybrid dynamic programming for solving a mixed-model sequencing problem with production mix restriction and free interruptions

In this article, we propose a hybrid procedure based on bounded dynamic programming assisted by linear programming to solve the mixed-model sequencing problem with workload minimization with serial workstations, free interruption of the operations and with production mix restrictions. We performed a computational experiment with 23 instances related to a case study of the Nissan powertrain plant located in Barcelona. The results of our proposal are compared with those obtained by mixed integer linear programming.

Heuristic approaches for mixed-model sequencing problem with stochastic processing times

Despite many pioneering efforts and works over the past decades, stochastic events have not been studied extensively in mixed-model assembly lines thus far. For a mixed-model sequencing problem with stochastic processing times, this paper aims to minimise expected total work overload. It also focuses on the most critical workstation of the line. In practice, this assumption is useful when the whole or a big portion of the assembly line is considered as a single station. In order to tackle the problem, a dynamic programming (DP) algorithm as well as two greedy heuristics from the literature is employed. However, it is realised that the DP cannot guarantee the optimal sequence neither for stochastic nor deterministic problems. It is because the calculation of work overload is involved in a recursive procedure that affects the states’ value functions. Therefore, by the use of network representation, the problem is modelled as a shortest path problem and a new heuristic, inspired by Dijkstra’s algorithm is developed to deal with it. Numerical results show that the proposed method outperforms other algorithms strongly. Finally, some discussion is provided about why one should consider stochastic parameters and why the proposed heuristic performs well in this regard.

Modeling of Order Oriented Planning for Printed Circuit Board Assembly Line

Printed circuit board (PCB) assembly planning problem has been given lot of attention to efficiently manage the orders of different PCB products. However, little effort has been paid to describe its comprehensive model which can demonstrate all the planning problems collectively considering in the surface mount technology (SMT) lines. A mixed integer model for PCB assembly line which includes the integration of different levels of the planning problems and considered component allocation problem (line balancing), PCB model sequencing problem (mixed model sequencing problem), feeder arrangement problem and component placement sequencing problem on different SMT machines collectively. Current research is significant to solve different planning problems of the PCB assembly line simultaneously to get the overall global solution of the problem in future.

Consideration of human resources in the Mixed-model Sequencing Problem with Work Overload Minimization: Legal provisions and productivity improvement

Beginning with a variation of the sequencing problem in a mixed-products line (MMSP-W: Mixed-Model Sequencing Problem with Workload Minimization), we propose two new models that incorporate a set of working conditions in regard with human resources of workstations on the line. These conditions come from collective agreements and therefore must be respected by both company and labor unions. The first model takes into account the saturation limit of the workstations, and the second model also includes the activation of the operators throughout the working day. Two computational experiments were carried out using a case study of the Nissan motor plant in Barcelona with two main objectives: (1) to study the repercussions of the saturation limit on the decrease in productivity on the line and (2) to evaluate the recovery of productivity on the line via both activation of operators, while maintaining the same quality in working conditions achieved by limiting the saturation, and auxiliary processors. By results we state that saturation limitation leads an important increase of work overload, which means average economic losses of 28,731.8 Euros/day. However, the productivity reduction may be counteracted by the work pace factor increase, at certain moments of workday, and/or by the incorporation of auxiliary processors into the line.

A bit-wise mutation algorithm for mixed-model sequencing in JIT production systems

Product sequencing in a mixed-model production system is an operational level problem and is computationally hard. This necessitates the use of non-traditional optimisation methods to solve it in a short time. In the first phase, this study addresses the mixed-model sequencing problem with the objective of minimising production rates variation (PRV) which is a just-in-time objective. We formulated a mixed integer quadratic assignment model for this problem. LINGO 14.0 solver could solve this model for small- and medium-size problems. The study presents a bit-wise mutation algorithm to solve the sequencing problem with the same objective. This algorithm uses a single unary operator which makes it simpler and faster. Computational results show that the algorithm succeeds in solving large-size PRV problems in a reasonable time, for which the algorithms reported in the literature could only get near-optimal solutions. In the second phase, we consider both PRV and one of the system performance measures, makespan as objectives for the mixed-model sequencing problem. A mathematical description of the underlying model is provided. The bit-wise mutation algorithm is modified to generate a set of non-dominated solutions which provide the decision-maker with the opportunity to trade-off between the two objectives.

Two-stage approach to the mixed-model sequencing problem

This paper proposes a method to address a mixed–model sequencing problem that currently exists in automobile manufacturing. From the standpoint of supply chain management, we proposed a new sequencing method that aims at: 1) levelling the workloads for each process on an assembly line; 2) maintaining a constant rate of production for all the parts in the production process; 3) meeting delivery dates of distributors when the final products are delivered by specialised shipping vessels. In order to simultaneously satisfy these three goals, a two–stage approach is proposed. First, by dividing the production period into shorter periods, the production volume of each product is determined for each of these shorter periods to maintain a constant rate of parts usage and meet the delivery date to distributors. Next, a production schedule is established for each period to realise smoother production on the assembly line.