Sequence-dependent Setup Times Research Articles

A Q-learning multi-objective grey wolf optimizer for the distributed hybrid flowshop scheduling problem

Most existing research focuses on a single objective for the distributed hybrid flowshop scheduling problem (DHFSP). This article focuses on a multi-objective DHFSP with sequence-dependent set-up time (DHFSP-SDST). A Q-learning multi-objective grey wolf optimizer (QMOGWO) is designed to optimize the makespan, total energy consumption and total tardiness. A mathematical model for DHFSP-SDST is established. Several initialization strategies and a random method are introduced to improve the quality of the initial population. The new individual is developed by the discrete solution updating mechanism of QMOGWO. Based on the Q-learning, local search strategies are designed to avoid local optima. To verify the performance of the proposed QMOGWO, different scales of instances are tested in various factories and at different stages, and the simulation results show that the QMOGWO outperforms the comparison methods.

Considering the peak power consumption problem with learning and deterioration effect in flow shop scheduling

This paper investigates the permutation flow shop scheduling problem with peak power constraints under sequence-dependent setup time, learning, and deterioration effects to minimize the makespan, where the peak power consumption satisfies a given upper bound at any time. We establish relevant mathematical models based on the characteristics of the scheduling environment and set up five setup time-based heuristics, including the earliest start time, the latest setup time based on balance job–machine, latest setup time based on balance machine–job, latest setup time insert based on balance job–machine, and latest setup time insert based on balance machine–job. Similarly, a hybrid genetic algorithm combined with simulated annealing is proposed to prevent premature trapping in local optima. The algorithms are evaluated through a large number of data experiments, and the results show that it can effectively solve this scheduling problem.

A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery

Production and distribution are both crucial components of supply chains. Integrated production and distribution scheduling (IPDS) in the context of flexible assembly flow shop scheduling and batch delivery problems is often overlooked. A realistic problem inspired by the production and distribution processes of a dishwasher factory can be modeled as a resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery (RCFAFSP-BDD). In this problem, order requirements are decomposed into several production tasks processed at different stages of the workshop, and are then delivered in batches via a third-party logistics provider to regional distributors at various locations. Auxiliary resource restrictions, hierarchical coupling constraints, machine eligibility restrictions and sequence-dependent setup times, are incorporated into the problem as operational constraints. To the best of our knowledge, this is the first attempt to solve this problem. This work formulates a mixed-integer linear programming (MIP) model to minimize total costs, including tardiness, inventory, and delivery costs. Given the problem’s strong NP-hard nature, the focus is on developing an efficient solution approach using constraint programming (CP). A CP model is proposed and enhanced with multiple redundant constraints. To reduce runtime, two branching strategies are designed for the CP model. Numerical experiments with varying instance scales reveal that the proposed CP model outperforms the MIP model in accuracy and efficiency within the given time limit. The redundant constraints and search strategy can reduce CP model runtime by up to 263.83%. Compared to manual scheduling at the studied factory, the CP model can cut costs by up to 26.59% for real data, offering viable alternatives for factory planners.

An effective two-stage heuristic for scheduling the distributed assembly flowshops with sequence dependent setup times

This paper studies the Distributed Assembly Permutation Flowshop Scheduling Problem with Sequence Dependent Setup Times (DAPFSP-SDST). The optimization objective is minimization of maximal completion time (makespan), and it is shown that minimizing the sum of Total Setup Times for Assembling Products (TSTAP) and Total Idle Times on Assembly Machine (TITAM) is equivalent to minimizing the makespan. Additionally, minimization of TSTAP and TITAM can be transformed into sequencing problems of products and jobs within critical products, respectively. We also find out that a product sequence essentially explores an area in the solution space, with solutions in the area having the same TSTAP but different TITAMs determined by Critical-Jobs-Sequences (CJSs). Based on the new findings, an effective Two-Stage Heuristic Algorithm (TSHA) is proposed to first obtain promising product sequences and then exploit the corresponding areas for the DAPFSP-SDST. At the first stage of TSHA, high-quality initial product sequences are obtained through a constructive method and two Neighborhood Descent for Product Sequence (NDPS) algorithms are presented for more potential searching areas. At the second stage, a Neighborhood Descent for CJS (NDCJS) is designed to find CJSs with TITAM as small as possible. Evaluations on a benchmark instance set show that TSHA achieves better performance compared to the existing meta-heuristic and hyper-heuristic algorithms on the DAPFSP-SDST. Another impressive advantage of the TSHA is its low computational cost, as it is a heuristic algorithm with some neighborhood search operators.

Machine Learning based Algorithm Selection and Genetic Algorithms for serial-batch scheduling

Whenever combinatorial optimization problems cannot be solved by exact solution methods in reasonable time, tailor-made algorithms (heuristics, meta-heuristics) are developed. Often, these heuristics exploit structural properties and perform well on selected subsets of the problem space. For example, this is how the two best-known construction heuristics solve the scheduling problem investigated in this study (i.e., the scheduling of parallel serial-batch processing machines with incompatible job families, restricted batch capacities, arbitrary batch capacity demands, and sequence-dependent setup times). However, when the properties change, the performance of one algorithm might decrease, and another algorithm might have been the better choice. To resolve this issue, we propose using Machine Learning to exploit the strengths of different algorithms and to select the probably best-performing algorithm for each problem instance individually. To that, we investigate a variety of methods from the “learning-to-rank” literature and propose several adaptations. Furthermore, because there is no algorithm for the considered scheduling problem that is capable to explore the entire solution space, we developed two Genetic Algorithms for the improvement of initial solutions computed by the selected algorithms. Here, we put special emphasis on ensuring that the solution representation (encoding) reflects the entire solution space and that the operators (e.g., for recombination and mutation) are appropriate to explore and exploit this space completely. Our computational experiments show an average increase of 39.19% in solution quality.

Parallel branch-and-price algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times

Scheduling problems occur in a broad range of real-world application fields and have attracted a huge set of research articles. However, there is only little research on exact algorithms for scheduling problems, many of which are NP-hard in the strong sense. We investigate the problem on a single machine with a total weighted tardiness objective function and sequence-dependent setup times. First, we adopt a serial branch-and-price algorithm from the literature and present a modified branching strategy and a primal heuristic. Second, we use the potential of parallel computing architectures by presenting two parallel versions of the branch-and-price algorithm. Third, we conduct extensive computational experiments to show that our parallelization approaches provide substantial parallel speedups on well-known benchmark instances from the literature. We further observe that the parallel speedups achieved by our parallel algorithms are very robust among all tested instances.

Integrated Working-Age Maintenance to the Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

Integrated Working-Age Maintenance to the Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

Energy-aware production lot-sizing and parallel machine scheduling with the product-specific machining tools and power requirements

This study addresses a multi-product lot-sizing and scheduling problem with sequence-dependent setup times, considering that the machining operations cause energy consumption. The production facility comprises identical parallel machines under which the production of each product requires a certain set of tools. The energy requirement of production depends on the product-specific machining tools. The problem deals with determining the minimum cost lot-sizing and scheduling plan considering the energy capacity of the production facility. We formulate the problem as a mixed integer linear programming model by introducing energy consumption-related costs and constraints. We perform a case study on CNC milling and turning workshops. Further, we propose an heuristic approach combining a decomposition-based Simulated Annealing heuristic and Fix&Optimise algorithms to handle larger-sized problem instances. The computational performance of the proposed heuristic approach is evaluated against the proposed mixed integer linear programming model on a numerical study. Our numerical experiments reveal that the proposed heuristic approach is capable of providing cost-efficient solutions without compromising time efficiency.

A learning-driven multi-objective cooperative artificial bee colony algorithm for distributed flexible job shop scheduling problems with preventive maintenance and transportation operations

In recent years, distributed production scheduling problems receive much attention from both scholars and practicers. Nevertheless, existing research on such problems commonly ignores machine maintenance and job transportation operations. This work proposes a distributed flexible job shop scheduling problem with preventative maintenance and transportation operations in consideration of sequence-dependent setup time. First, a mixed integer programming model is formulated to minimize maximum completion time of jobs and maximum workload of factories. Second, a learning-driven multi-objective cooperative artificial bee colony algorithm is developed to deal with the model. A Q-learning-based cooperation strategy between population and obtained non-dominated individuals is devised to strengthen the exploration and exploitation performance. Furthermore, heuristic-based population initialization, crossover operations in employed bee phase and iterated local search methods in onlooker bee phase are specially developed considering the problem characteristics. Finally, the proposed method is compared against three well-known meta-heuristics from existing literature and an exact solver CPLEX by using a set of benchmark instances. The results confirm the competitive performance of the developed model and algorithm for addressing the studied problems.

Optimising distributed heterogeneous flowshop group scheduling arising from PCB mounting: integrating construction and improvement heuristics

ABSTRACT In real-world manufacturing systems for processing printed circuit boards (PCBs), the workshops integrating various flowline-based cells are common in large-scale enterprises. The scheduling problem within the systems is modelled as the distributed heterogeneous flowshop group scheduling problem (DHFGSP) in this study. Departing from practical requirements and considering the grouping characteristics among PCB components, we account for carryover sequence-dependent setup time (CSDST). Moreover, recognising the critical importance of just-in-time production in semiconductor manufacturing, the total tardiness, a previously unexplored objective within the DHFGSP context, is addressed. To tackle this problem, a mixed-integer linear programming (MILP) model, capable of obtaining optimal solutions for small-scale instances, is proposed. Due to the NP-hard nature of the problem, obtaining high-quality solutions in a reasonable time using the MILP model becomes challenging for large-scale instances. Therefore, a solution algorithm, comprising construction and improvement heuristics, is developed. Capitalising on the problem’s characteristics, the construction heuristic efficiently generates high-quality feasible solutions in a very short time. Built primarily around artificial bee colony (ABC) optimisation, the improvement heuristic can significantly further enhance solutions by integrating the collaborative and restart operators. Comprehensive experiments on instances of varying scales demonstrate the effectiveness of the proposed algorithm for the problem under investigation.

A self-learning particle swarm optimization for bi-level assembly scheduling of material-sensitive orders

In modern assembly production, maximizing fulfillment becomes challenging amid resource scarcity and process unpredictability. This study addresses such issues with an effective approach to solving the integrated problem. This confluence presents a scenario where resource allocation mirrors a multidimensional knapsack and job sequencing corresponds to distributed assembly permutation flowshop scheduling, factoring in sequence-dependent setup times. Employing a mixed-integer mathematical model, we capture the configurations and objectives of the integrated problem. A special dual-level cooperative self-learning particle swarm optimization (SLPSO) metaheuristic is developed for improved hierarchical decision-making. Adaptive learning is harnessed to guide dynamic job selection under uncertainty, aiming for the highest total value. To minimize tardiness, a neighborhood search operator customizes sequences for each shop, considering changing setup times between jobs. Benchmark tests have been performed, showing that SLPSO surpasses established genetic algorithms and swarm techniques by 8%–15%. When implemented in an operational traditional pharmaceutical manufacturer, significant improvements were observed. The integrated structure harmonizes planning and scheduling stages, enhancing the algorithm via bidirectional feedback between decisions at various levels under uncertainty, thus providing guidance for real-world production.

A cooperative learning-aware dynamic hierarchical hyper-heuristic for distributed heterogeneous mixed no-wait flow-shop scheduling

The distributed heterogeneous mixed scheduling mode in the manufacturing systems emphasizes the cooperation between factories for the entire production cycle, which poses enormous challenges to the processing and assignment of jobs. Discrepancies in the processing environment and types of machines of each factory during various production stages cause diverse processing paths and scheduling. The distributed heterogeneous mixed no-wait flow-shop scheduling problem with sequence-dependent setup time (DHMNWFSP-SDST), abstracted from the industrial scenarios, is addressed in this paper. The mathematical model of DHMNWFSP-SDST is established. A cooperative learning-aware dynamic hierarchical hyper-heuristic (CLDHH) is proposed to solve the DHMNWFSP-SDST. In CLDHH, a cooperative initialization method is developed to promote diversity and quality of solutions. A hierarchical hyper-heuristic framework with reinforcement learning (RL) is designed to select the algorithm component automatically. Estimation of Distribution Algorithm (EDA) guides the upper-layer RL to select four neighborhood structures. A dynamic adaptive neighborhood switching constructs the lower-layer RL to accelerate exploitation with the dominant sub-neighborhoods. An elite-guided hybrid path relinking achieves local enhancement. The experimental results of CLDHH and six state-of-the-art algorithms on instances indicate that the proposed CLDHH is superior to the state-of-the-art algorithms in solution quality, robustness, and efficiency.

A novel fuzzy finite-horizon economic lot and delivery scheduling model with sequence-dependent setups

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.

Optimizing Mixed-Model Synchronous Assembly Lines with Bipartite Sequence-Dependent Setup Times in Advanced Manufacturing

In advanced manufacturing, optimizing mixed-model synchronous assembly lines (MMALs) is crucial for enhancing productivity and adhering to sustainability principles, particularly in terms of energy consumption and energy-efficient sequencing. This paper introduces a novel approach by categorizing sequence-dependent setup times into bipartite categories: workpiece-independent and workpiece-dependent. This strategic division streamlines assembly processes, reduces idle times, and decreases energy consumption through more efficient machine usage. A new mathematical model is proposed to minimize the intervals at which workpieces are launched on an MMAL, aiming to reduce operational downtime that typically leads to excessive energy use. Given the Non-deterministic Polynomial-time hard (NP-hard) nature of this problem, a genetic algorithm (GA) is developed to efficiently find solutions, with performance compared against the traditional branch and bound technique (B&B). This method enhances the responsiveness of MMALs to variable production demands and contributes to energy conservation by optimizing the sequence of operations to align with energy-saving objectives. Computational experiments conducted on small and large-sized problems demonstrate that the proposed GA outperforms the conventional B&B method regarding solution quality, diversity level, and computational time, leading to energy reductions and enhanced cost-effectiveness in manufacturing settings.

Novel integer L-shaped method for parallel machine scheduling problem under uncertain sequence-dependent setups

We study scheduling problems on unrelated parallel machines with uncertainty in job processing and sequence-dependent setup times. We first formulate this problem as a two-stage stochastic program using a scenario-based approach, in which the first-stage decisions involve job-machine assignments, and the second-stage deals with job sequencing. We then propose an innovative modified integer L-shaped method, uniquely designed to decompose the primary problem into independent subproblems at both the scenario and machine levels. We have augmented this method with a specialized integer optimality cut, which is further strengthened using a sequential lifting procedure. To broaden the applicability of our model and solution, we have adapted it to a distributionally robust optimization (DRO) framework under Wasserstein ambiguity. This process involves reformulating the DRO model into a mixed-integer linear program (MILP) using conic duality theory. Additionally, we integrate a distribution separation program to define the worst-case probability distribution during each iteration of the proposed integer L-shaped method, enhancing the computational speed for solving the DRO model. We conducted a series of numerical experiments to illustrate the effectiveness and scalability of the proposed solution methodology, which demonstrated highly promising results. Our innovative decomposition algorithms showed superior performance, achieving solution times that are significantly faster (up to two orders of magnitude) compared to the traditional integer L-shaped method for the stochastic scheduling model and the direct MILP reformulation of the DRO model. These results were obtained for problem instances solved to the exactness within the time limit. Moreover, the solution derived from the DRO model exhibited greater robustness in out-of-sample analysis with simulated data compared to the solution obtained from the stochastic model.

Optimization of the production planning process in a nuts and dried fruits industry

A resource-constrained machine scheduling problem is addressed in this paper. The problem arises in an industry located in the Canary Islands (Spain) and is characterized by a set of jobs to be completed on multiple processing lines, where each job has a specific processing time and a sequence-dependent setup time. The objective is to maximize the productivity of the processing lines, subject to constraints such as availability of personnel and processing lines, due dates, precedence order, and setup times, among others.In order to solve this problem, an optimization model that represents the problem as a mixed-integer program is proposed. The paper also introduces a constraint satisfaction heuristic to find near-optimal solutions of the problem. The effectiveness of the proposal is demonstrated through computational experiments on a set of real and synthetic instances, showing that the proposed technique is able to find solutions that are close to the optimal ones within a reasonable amount of time.

Accelerated evaluation of blocking flowshop scheduling with total flow time criteria using a generalized critical machine-based approach

Despite the considerable advances in the research of the blocking flowshop scheduling problem (BFSP), several unresolved challenges persist. Algorithmic complexity presents hurdles. Although the insertion-based method is considered to generate superior solutions, its high computational demand diminishes the efficiency of algorithms, especially within large-scale sequences. The existing accelerated evaluation methods cannot utilize the existing information to quickly calculate the total flow time or the total tardiness time of the changed sequence after the job insertion, but recalculates it from scratch. This does not significantly reduce computational effort and needs to be further improved.In this paper, we delve into the intrinsic features of these challenges, proposing a generalized accelerated critical machine-based evaluation tailored for the total flow time and tardiness criteria of the BFSP with and without sequence-dependent setup times. First, we propose three theorems, one corollary, and their proofs based on the critical machine. Second, we propose the accelerated evaluation procedure based on these theorems to calculate the objectives related to the total flow time. Third, we also extend the proposed accelerated evaluation method to the BFSP with sequence-dependent setup times, aiming to significantly reduce the time complexity. Finally, we conduct four experiments on five well-known benchmarks (a total of 3540 test instances). Through statistical analysis, it becomes evident that our computational efforts have significantly decreased in computing both the total flow time and the total tardiness time. This performance enhancement is superior to the effectiveness of existing acceleration techniques.

Neighborhood Combination Search for Single-Machine Scheduling with Sequence-Dependent Setup Time

Neighborhood Combination Search for Single-Machine Scheduling with Sequence-Dependent Setup Time

A hybrid genetic programming algorithm for the distributed assembly scheduling problems with transportation and sequence-dependent setup times

This paper investigates a distributed assembly permutation flow-shop scheduling problem with transportation and sequence-dependent set-up times (DAPFSP-TSDST). A hybrid genetic programming (HGP) algorithm is proposed to optimize the makespan of the assembly stage, which inherits the merits of genetic programming (GP) and neighbourhood search operators. In HGP, a hybrid problem-specific initialization heuristic is developed to make populations more diverse. Multiple neighbourhood search operators are employed as the leaf nodes, which are vital for the success of GP. A product shift strategy is proposed to strengthen its exploitability. In addition, a simulated annealing criterion is adopted to make the HGP explore more thoroughly. Finally, statistical and computational experiments are carried out on the benchmark instances. The results exhaustively identify the notable competitiveness of the HGP algorithm in coping with the DAPFSP-TSDST.

A cooperative grey wolf optimizer for the joint flowshop scheduling problem with sequence-dependent set-up time

With the complexity involved in manufacturing products, many companies use multiple processes to complete product processing. Most studies have been concerned with single production but have neglected the widespread joint flowshop scheduling problem (JFSP). In this article, a cooperative grey wolf optimizer (CGWO) is developed to solve the JFSP. First, according to the features of the JFSP, a corresponding mathematical model is constructed, and three collaborative strategies and random generation are proposed to initialize the population. In the process of searching for prey, a discretized search for prey update mechanism is proposed, which is conducive to balancing exploration and exploitation. An energy-saving strategy is proposed to decrease energy consumption. Moreover, four local search mechanisms are developed for different optimization objectives to enhance the performance of the method in attacking the prey. The results show that the CGWO is effective in solving the JFSP.