Sequence-dependent Setup Times Research Articles

Simulation-Optimization of Inventory Control of Multiple Products on a Single Machine with Sequence-Dependent Setup Times

Simulation-Optimization of Inventory Control of Multiple Products on a Single Machine with Sequence-Dependent Setup Times

A VNS-IG algorithm for dynamic seru scheduling problem with sequence-dependent setup time and resource constraints

A VNS-IG algorithm for dynamic seru scheduling problem with sequence-dependent setup time and resource constraints

A comparison of different mathematical models for the job sequencing and tool switching problem with non-identical parallel machines

This paper addresses the generalisation of the NP-hard job sequencing and tool switching problem with non-identical parallel machines and sequence-dependent setup times where a set of jobs is to be scheduled on unrelated parallel machines with machine-dependent processing and tool switching times. Three different mathematical models for two different objectives are presented and applied to newly generated test instances. The instances are compared and analysed using a commercial solver and an iterated local search heuristic. Overall, it is shown that the solution quality obtained by the mathematical models depends on the size of the problem instance as well as the tool requirements. The precedence-based formulation is superior in general to the position-based and time-index-based formulation for dense problem instances while the position-based formulation works well for sparse problems. With an increasing problem size, the metaheuristic requires significantly less time to find near-optimal solutions than the mathematical models.

Exact methods for tardiness objectives in production scheduling

Tight deadlines, uncertain release dates and frequent disruptions impose major challenges for manufacturing. Therefore, we take a fresh look at the literature examining tardiness under unrelated machines, sequence-dependent setup times, precedence constraints, job-splitting and multiple resources. Our focus in on exact methods, including integrated methods combining Integer Programming and Constraint Programming. We also present a Bender's approach encompassing most of the above features, augmented with certain inequalities to represent additional problem features or to strengthen the relaxation. We offer computational evidence and discuss possible extensions.

Bi-criteria two-machine flow shop scheduling problem involving sequence-dependent setup times and pieces multiplicity

Bi-criteria two-machine flow shop scheduling problem involving sequence-dependent setup times and pieces multiplicity

Distributed no-wait flow shop problem with sequence dependent setup time: Optimization of makespan and maximum tardiness

This paper investigates a multi-objective optimization distributed no-wait permutation flow shop scheduling problem under the constraint of sequence dependent setup time. Our optimization case is minimizing the makespan and maximum tardiness criteria. Therefore, our main objective will be to find the optimal jobs sequence that minimizes a function representing the two criteria of makespan and maximum tardiness. This function will be linearly dependent of these two criteria via a weighting parameter for each criterion. To solve this industrial problem, we propose the mixed integer linear programming (MILP) and a set of efficient metaheuristics solving different size instances. To this end, we suggest three inspired nature metaheuristics: The genetic algorithm (GA), the artificial bee colony (ABC) algorithm and migratory bird optimization (MBO) algorithm. We suggest a total of six new algorithms based on nature-inspired metaheuristics. Also, two constructive heuristics are used, the greedy randomized adaptive search procedure (GRASP) and Nawaz–Enscore–Ham (NEH) algorithms. It was revealed that GA algorithm with NEH initialization gives the best results comparing to the other metaheuristics.

Exact and metaheuristic approaches for unrelated parallel machine scheduling

In this paper, we study an important real-life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence-dependent setup times, due dates, and machine eligibility constraints. The objective is to minimise total tardiness and makespan. We adapt and extend a mathematical model to find optimal solutions for small instances. Additionally, we propose several variants of simulated annealing to solve very large-scale instances as they appear in practice. We utilise several different search neighbourhoods and additionally investigate the use of innovative heuristic move selection strategies. Further, we provide a set of real-life problem instances as well as a random instance generator that we use to generate a large number of test instances. We perform a thorough evaluation of the proposed techniques and analyse their performance. We also apply our metaheuristics to approach a similar problem from the literature. Experimental results show that our methods are able to improve the results produced with state-of-the-art approaches for a large number of instances.

Permutation flow shop energy-efficient scheduling with a position-based learning effect

Severe environmental problems have made green scheduling an emerging research hotspot. In this paper, a permutation flow shop energy-efficient scheduling problem that considers multiple criteria is investigated. The aim is to find the optimal job processing sequence and conveyor speed that minimise both the makespan and total energy consumption. In addition to two types of common criteria, namely, machine-based criterion (i.e. sequence-dependent setup time) and energy-based criteria (including both the transportation time control strategy and machine shutdown strategy), a human-based criterion (i.e. a position-based learning effect) is introduced. A bi-objective programming model is developed, and a multi-objective iterated greedy (MOIG) is designed to reach the Pareto front of the model. Considering that there are two types of decisions in the model (i.e. job sequence and conveyor speed), two algorithm alternatives are designed based on the job sequence and conveyor speed, respectively. Meanwhile, an acceptance criterion with advantages in terms of the convergence speed and solution diversity is proposed. Existing algorithms, including NSGA-II and MOEA/D, are introduced to evaluate the performance of the MOIG. The results emphasise the efficiency of the MOIG. Overall, the model and MOIG effectively improve the green efficiency of enterprises and can reasonably control operating costs.

Part-grouping and build-scheduling with sequence-dependent setup time to minimize the makespan for non-identical parallel additive manufacturing machines

Part-grouping and build-scheduling with sequence-dependent setup time to minimize the makespan for non-identical parallel additive manufacturing machines

Introducing preferences in scheduling applications

In some applications like fabric dying, the sequence in which jobs are processed on a single machine can influence product quality, i.e., there is a strong preference to run a certain type of job after another for reasons that do not influence regular scheduling objectives like total completion time. These reasons include minimizing changes in color families on machines (schedule preferences) and reducing the difference in shades between consecutive jobs (shade inconsistency). Nonetheless, the scheduling of jobs on machines must consider sequence-dependent setup times as well. In this paper, a mixed integer linear program has been presented to schedule jobs and account for setup times. The scheduling preferences and shade differences have been modeled as two new objectives, along with traditionally used objectives such as makespan, lateness and total setup time. The MILP is found to be useful only for small problems. To tackle larger problems, several heuristic methods are proposed. In order to obtain solutions quickly, multiple construction heuristics are developed based on SPT/LPT/EDD/LFJ rules and tested on a variety of industrially-inspired data sets. To produce schedules that perform well across multiple objectives at the same time, three additional tailored heuristics are developed. Both the original and tailored heuristics are compared to the optimal solutions for small-sized problems. In addition, a problem size reduction heuristic has been developed which can segment the larger MILP into smaller independently solvable MILPs by reducing the possible machines on which a job can be processed. For these larger problems, the heuristics are compared among themselves as well as against the problem size reduction heuristic.

Single-machine scheduling with energy generation and storage systems

This paper considers a single-machine scheduling problem with sequence-dependent setup times and energy-generation and storage systems. Each job requires a sequence-dependent setup to be processed on the machine, and both setup and processing of the job require job-dependent amounts of energy. The energy consumed by the machine can be bought from an Electric Power Company (EPC) or generated by own Distributed Energy Resource (DER), such as solar photovoltaic or wind, and the energy can be stored in an Energy Storage System (ESS). The objective is to minimise the total cost, the sum of production cost depending on makespan and energy cost by considering energy usage from the EPC, DER and ESS. For the problem, a mathematical programming model is first derived by using period-based indexes. Then, a hybrid genetic algorithm, which adds appropriate idle times between jobs and determines an efficient energy schedule by storing some energy during less expensive periods into the ESS for later use in high-price periods, is developed. Finally, computational experiments show that the proposed algorithm provides effective solutions, and which component of the total cost affects the performance the most, how effective adding idle times between jobs is, and how much cost can be saved by having a DER and ESS.

Branch-and-price approach for robust parallel machine scheduling with sequence-dependent setup times

This paper studies a machine scheduling problem that minimizes the worst-case total tardiness for unrelated parallel machines with sequence-dependent setup and uncertain processing times. We propose a robust optimization reformulation of the related machine scheduling problem and discuss several important properties of the mathematical model and the reformulation approach. The proposed model generalizes robust parallel machine scheduling problems by including sequence-dependent setup times and ellipsoidal uncertainty sets. Another key contribution of the paper is to show that scheduling problems usually have alternative optimal solutions for the worst-case tardiness objective, whose performance under nominal processing times may vary or vice a versa. This issue has been addressed by studying the Pareto efficient extensions of the proposed robust optimization models to provide solutions that are immune to changes in processing times. A branch-and-price algorithm has been developed to solve realistically sized instances in less than one hour, which a commercial solver cannot achieve. Numerical results show the effectiveness of the proposed approach since realistically sized instances such as (4 machines, 32 jobs) and (150 machines, 300 jobs) can be solved to optimality within the time limit, and the (average) objective function value improvement made by the robust approach can get as high as 56% compared with the (nominal) optimal solutions that ignore uncertainty in problem data.

Advanced discrete firefly algorithm with adaptive mutation‐based neighborhood search for scheduling unrelated parallel machines with sequence‐dependent setup times

The unrelated parallel machine scheduling problem with sequence-dependent setup times is addressed in this paper with the objective of minimizing the elapsed time between the start and finish of a sequence of operations in a set of unrelated machines. The machines are considered unrelated because the processing speed is dependent on the job being executed and not on the individual machines. Generally, the problem is considered NP-hard, as it presents additional complexity to find an optimal solution in terms of minimum makespan. An advanced firefly metaheuristic optimization algorithm is introduced to solve this problem. The proposed method, called the FAII algorithm, aims to improve the standard firefly algorithm's performance by incorporating an enhanced global best solution update mechanism and adaptive mutation-based local and global neighborhood search scheme to improve the quality of the proposed algorithm's generated solution. Several experiments were conducted to compare and validate the proposed algorithms' performance on small and large-scale benchmarked problem instances with up to 12 machines and 120 job combinations. Moreover, the performance of the FAII was also compared with eight other metaheuristic algorithms, which were implemented in parallel with the FAII method. Furthermore, the numerical results of the FAII algorithm were compared with the scheduling results of six other well-known metaheuristics from the literature. The comparison results backed with a comprehensive statistical analysis showed the superiority of the enhanced FA-style scheduling optimization over other metaheuristic methods to find good quality solutions or minimum average makespan.

Clustering-based solution approach for a capacitated lot-sizing problem on parallel machines with sequence-dependent setups*

This paper studies an industrial lot-sizing and scheduling problem coming from the food-industry that extends the multi-item capacitated lot-sizing and includes lost sales, overtimes, safety stock and non-uniform sequence-dependent setups on parallel machines. We introduce two different formulations and adapt the well-known Relax-and-Fix and Fix-and-Optimise heuristics in order to quickly obtain feasible solutions on large industrial instances. The complexity of our problem prevents the procedure to obtain good solutions within the time allocated by practitioners on real-life cases, hence we propose to use a clustering approach to approximate the sequence-dependent setup times. The resulting problem is significantly smaller to solve and experimental results suggest that this transformation effectively improves the solutions found on industrial instances. In particular, the combination of this clustering method and Relax-and-Fix and Fix-and-Optimise procedure turns out to be a promising approach to obtain good solutions in the given time-limit.

Auxiliary resource planning in a flexible flow shop scheduling problem considering stage skipping

This paper investigates a flexible flow shop scheduling problem wherein there are some unrelated parallel machines with different technology levels in the first stage. Some of these machines are multifunctional that can do several processes on jobs. Therefore, the jobs assigned to these machines do not require processing in some of the next stages. Although the majority of the traditional scheduling problems deal with machines as the only resource, there are usually unavailability constraints to auxiliary resources such as labor, tools, pallets, industrial robots, and so on. This challenge with inspiration from a spring manufacturing plant is tackled in the considered problem with machine eligibility and sequence-dependent setup times. This problem is described with a numeric example, and its parameters and decision variables are defined. Then, to formulate the problem, a mixed-integer linear programming model is developed to minimize the makespan and determine the number of required auxiliary resources. Then the genetic algorithm is calibrated for all aforementioned features of the problem at hand as the main solution approach. Furthermore, two other well-known metaheuristics i.e., simulated annealing and enhanced particle swarm optimization are modified and employed for computational comparisons. The result shows that the proposed algorithm provides accurate results regarding the number of required auxiliary resources to achieve the minimum makespan. Moreover, supplementary analysis is presented considering practical constraints such as budget and desired efficiency of machines. The result indicates that the solution approach could provide proper alternatives for managers in various conditions.

Agent-based approach integrating deep reinforcement learning and hybrid genetic algorithm for dynamic scheduling for Industry 3.5 smart production

Dynamic scheduling is crucial for semiconductor manufacturing as product-mix is increasing with shortening product life cycle. However, the present problem is challenging owing to complicated constraints and short time for decision making. Focusing on realistic needs, this research aims to develop a novel agent-based approach that integrates deep reinforcement learning and hybrid genetic algorithm for the unrelated parallel machine scheduling problem with sequence-dependent setup time. In particular, deep Q network (DQN), a combination of deep learning and Q learning, is employed to train a scheduling agent. A trained agent could perform job allocation tasks in short computation time for addressing the dynamic scheduling problem. Furthermore, the proposed hybrid genetic algorithm is employed to enhance searching effectiveness and efficiency during the training process. To estimate the validity, scenarios are designed to compare the developed solution with a number of dispatching rules and other knowledge-based approaches. The experimental results have shown practical viability of the developed solution. Indeed, the developed solution is implemented in a semiconductor manufacturing company.

Analysis of Integrated Preventive Maintenance and Machine Failure in Stochastic Flexible Job Shop Scheduling with Sequence-dependent Setup Time

ABSTRACT When we consider the real-time situation in scheduling problems, it always helps to enhance the manufacturing system and increases the system performance. In this study, the effect of five input parameters, i.e., reliability-centered preventive maintenance, percentage of machine failure (PMF), mean time to repair for random machine breakdown, due date tightness factor, and routing flexibility (RF) on stochastic flexible job shop scheduling problem (SFJSSP) under simultaneously reliability-centered preventive maintenance and random machine breakdown environment with sequence-dependent setup time is evaluated. The effects of input parameters are measured using four different performance measures, i.e., mean flow time (MFT), makespan (Cmax), mean tardiness (MT), and total setups (TS). A statistical response surface methodology is used to assess the performance measures. ANOVA analysis is used to determine the model’s suitability. The results show that PMF and RF are found as the most common significant input factors for all the performance measures. Multi-objective optimization is performed using the desirability function approach to optimize the system performance measures. It is found that the minimum value of MFT, Cmax, MT, and TS performance measures for optimum performance of the SFJSSP are predicted as 123.432, 220,561, 103.399, and 102,171, respectively, with composite desirability, D of 0.916. The confirmatory results show that the error between the predicted and experimental results is less than 5%. Moreover, considering both uncertainties with dynamic jobs arrival environment shows the study’s real-time scheduling scenario and novelty.

A differential evolution algorithm for the customer order scheduling problem with sequence-dependent setup times

Although the customer order scheduling problem to minimize the total completion time has received a lot of attention from researchers, the literature has not considered so far the case where there are sequence-dependent setups between jobs belonging to different orders, a case that may occurs in real-life scenarios. For this NP-hard problem we develop a novel efficient approximate solution procedure. More specifically, we develop an innovative discrete differential evolution algorithm where differential mutations are performed directly in the permutation space and that uses a novel, parameter-free, restart procedure. The so-obtained solutions are improved by two proposed local search mechanisms that employ problem-specific, heuristic dominance relations. We carry out an extensive computational experience with randomly generated test instances to compare our proposal with existing algorithms from related problems. In these experiments, the proposed algorithm obtains the best results in terms of their average relative percentage deviation and success rate. Furthermore, an analysis of variance test, followed by a Tukey’s test, confirms the excellent performance of the algorithm proposed.

Optimizing distributed no-wait flow shop scheduling problem with setup times and maintenance operations via iterated greedy algorithm

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given to the distributed flow shop scheduling problem and the addition of constraints to the problem. This article introduces the distributed no-wait flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is to mathematically describe the problem and heuristic procedures to incorporate maintenance operations to job scheduling are proposed. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with size of 4,800 and 13,200 problems, respectively. Computational experiments were conducted to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.

A multi-objective flexible job-shop cell scheduling problem with sequence-dependent family setup times and intercellular transportation by improved NSGA-II

With the development of Industry 4.0 and requirement of smart factory, cellular manufacturing system (CMS) has been widely concerned in recent years, which may leads to reducing production cost and wip inventory due to its flexibility production with groups. Intercellular transportation consumption, sequence-dependent setup times, and batch issue in CMS are taken into consideration simultaneously in this paper. Afterwards, a multi-objective flexible job-shop cell scheduling problem (FJSCP) optimization model is established to minimize makespan, total energy consumption, and total costs. Additionally, an improved non-dominated sorting genetic algorithm is adopted to solve the problem. Meanwhile, for improving local search ability, hybrid variable neighborhood (HVNS) is adopted in selection, crossover, and mutation operations to further improve algorithm performance. Finally, the validity of proposed algorithm is demonstrated by datasets of benchmark scheduling instances from literature. The statistical result illustrates that improved method has a better or an equivalent performance when compared with some heuristic algorithms with similar types of instances. Besides, it is also compared with one type scalarization method, the proposed algorithm exhibits better performance based on hypervolume analysis under different instances.