Machine-dependent Setup Times Research Articles

Large-scale dynamic surgical scheduling under uncertainty by hierarchical reinforcement learning

Dynamic surgical scheduling within a workday is a complicated decision-making process. The critical challenge is that the actual duration of surgery and the arrival process of emergency patients are uncertain and unknown in advance. In this work, we propose a two-level dynamic scheduling framework based on hierarchical reinforcement learning to solve dynamic surgical scheduling problems considering both elective and emergency patients. Specifically, with the realisation of uncertainty, the upper-level agent (UA) dynamically decides whether to trigger rescheduling to optimise the workday total cost. The lower-level agent (LA) aims at obtaining subscheduling solutions when rescheduling is triggered. The subproblem at the LA can be formulated as a mixed integer programming model, which can be generalised to unrelated parallel machine scheduling with machine eligibility restrictions and sequence- and machine-dependent setup times. Such problems can be solved in small-scale cases and suffers the combinatorial explosion in large scale cases. To address this issue, we propose a heuristic method that is built upon deep reinforcement learning to obtain high-quality solutions. We conduct extensive simulation experiments with real data to test the effective of our framework. The results for different scenarios show that our proposed framework outperforms existing methods in terms of overall performance and has strong generalisation ability.

Minimizing Carbon Emission in Hybrid Flow Shop Scheduling: A Comparative Analysis of Flow-based and Set Partitioning Formulations

This article addresses the Hybrid Flow Shop Green Scheduling Problem with Sequence and Machine Dependent Setup Times (HFSGSP-SMDST) in the context of Industry 4.0. The objective is to minimize carbon emission while optimizing scheduling. Two mathematical formulations, a flow-based positional formulation (FB) and a set partitioning positional formulation (HCG), are proposed to provide tighter lower bounds. The FB formulation is solved using a commercial solver, while the HCG algorithm incorporates an Iterated Local Search (ILS) to generate initial solutions and an upper bound for the problem. Computational experiments demonstrate that HCG achieves better lower bounds, although it requires more time compared to FB. The proposed algorithms offer valuable solutions for carbon emission optimization and scheduling in Industry 4.0, with a trade-off between lower bounds and convergence speed.

Weighted tardiness minimisation for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimisation. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times, and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component – vital to guarantee the non-violation of the problem's constraints – which optimally allocates resources with respect to tardiness minimisation. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure are revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight due dates, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights.

An evolutionary approach comprising tailor-made variation operators for rescue unit allocation and scheduling with fuzzy processing times

This paper addresses the rescue unit allocation and scheduling problem (RUASP) with fuzzy processing times through an evolutionary approach. The goal of RUASP is to efficiently assign and schedule the rescue units to process the incidents in the event of a natural disaster. This problem can be considered as a variant of the unrelated parallel-machine scheduling problem with sequence and machine-dependent setup times. A steady-state grouping genetic algorithm (SSGGA) approach is presented to minimize the total weighted completion time of the incidents, where the weights correspond to the severity levels of the incidents. The crossover and mutation operators used in this approach are designed as per the characteristics of RUASP and its objective. The proposed approach uses a combination of greedy and random heuristics while generating the initial solutions, thereby yielding superior quality diverse initial solutions. The performance of the proposed approach is compared with the state-of-the-art approach available in the literature. The proposed approach always yields better results in much shorter execution times in comparison to the state-of-the-art approach. Moreover, the robustness analysis test demonstrates the proposed approach to be more robust in comparison to the state-of-the-art approach.

Dynamic shop-floor scheduling using real-time information: A case study from the thermoplastic industry

Practical production planning and scheduling systems must promptly respond to major real-time events and adjust their plans and schedules accordingly. To highlight the importance of concurrency in such systems, this paper addresses the problem of dynamic shop-floor scheduling using real-time information in a case study from the thermoplastic industry. The considered production line is organized as unrelated parallel production cells with a set of identical parallel machines in each cell. Parts are produced in batches using different molds on specific machines. Due to the size and complicated design of the molds, they require extended recovery periods (i.e., maintenance) in case of major failures. Therefore, previously developed plans and schedules need to be revised using real-time information every time a mold’s major failure occurs. The production process is subject to the following constraints: batch processing, safety stocks, dedicated machines, machine-dependent setup times, precedence constraints, mold failures, and real-time updates. The problem is formulated as a mixed-integer programming model to minimize a weighted cost function that includes tardiness and operating costs. To solve the problem, a predictive-reactive scheduling approach is introduced based on a modified simulated annealing (SA) algorithm. The developed approach utilizes an event-driven rescheduling policy. It also embeds a problem-specific neighborhood structure and solution evaluation into the modified SA algorithm. The experimental study indicates that the proposed approach generates better real-life planning and scheduling results than the methods based on dispatching rules. The findings demonstrate that the proposed SA-based predictive-reactive scheduling approach generates the solutions with about a 26.1% less tardiness cost and a 6.99% less total weighted cost (on average). In addition, the results also show the competitiveness of the proposed SA-based predictive-reactive scheduling approach compared to two other approaches based on an iterated greedy (IG) algorithm and a Tabu Search (TS) algorithm from the literature.

An exact decomposition method for unrelated parallel machine scheduling with order acceptance and setup times

In this paper, an unrelated parallel machine scheduling problem is studied, where order acceptance, sequence and machine-dependent setup times and the maximum available times of machines are additionally considered. The objective is to maximize the profit, which is the difference between the total revenues of accepted jobs and the cost associated with makespan. A mixed integer programming (MIP) model is formulated. To tackle this problem efficiently, an exact decomposition method, which is a two-layer logic-based Benders decomposition (LBBD) based (denoted by TL-LBBD) method, is developed, where an inner LBBD is embedded into an outer LBBD. Specifically, in the outer LBBD method, the master problem is used to determine the acceptance of jobs, whereas the subproblem examines the schedule given the accepted jobs from the master problem. The subproblem could be further decomposed into an assignment master problem and a sequencing subproblem by the inner LBBD method as well. Extensive computational experiments are conducted and the results show that the developed TL-LBBD method produce better quality solutions in significantly less computation time than solving the MIP model directly and the classic LBBD method. Moreover, the maximum scales of the problem instances that could be solved to optimality by the developed TL-LBBD method within 30 min are also evaluated.

Learning-Based Grey Wolf Optimizer for Stochastic Flexible Job Shop Scheduling

This work considers a stochastic flexible job shop scheduling with limited extra resources and machine-dependent setup time in a semiconductor manufacturing environment, which is an NP-hard problem. In order to obtain its reliable and high-performance schedule in a reasonable time, a learning-based grey wolf optimizer is proposed. In it, an optimal computing budget allocation-based approach, which is designed for two scenarios from real manufacturing environments, is proposed to intelligently allocate computing budget and improve search efficiency. It extends the application area of optimal computing budget allocation by laying a theoretic foundation. Besides, to obtain proper control parameters iteratively, a reinforcement learning algorithm with a newly designed delay update strategy is used to build a parameter tuning scheme of a grey wolf optimizer. The scheme acts as a guide for balancing global and local search, thereby enhancing effectiveness of the proposed algorithm. The theoretic interpretation of the developed optimal computing budget allocation-based approach and the convergence analysis results of the proposed algorithm are presented. Various experiments with benchmarks and randomly generated cases are performed to compare it with several updated algorithms. The results shows its superiority over them. Note to Practitioners—Meta-heuristic are often deployed to solve semiconductor manufacturing scheduling problems. However, they face to two thorny issues when they face stochastic manufacturing environments. 1) their computational efficiency is quite low, thus requiring substantial improvement, since a stochastic optimization problem requires Monte Carlo sampling to estimate the actual objective function values in a precise manner; and 2) most of them are parameter-sensitive, and choosing their proper parameters is highly challenging in such environments. To address the first issue, we develop an optimal computing budget allocation-based method for deciding the optimal numbers of sampling times based on both prior knowledge and simulation results. To address the second one, we propose a reinforcement learning algorithm to self-adjust the parameters of our proposed method called Learning-based Grey Wolf Optimizer. In addition, we design a delay update strategy to enhance its robustness, and thus, a feasible and high-quality schedule can be founded in a short time for real-time scheduling problems. Theoretic proofs and experimental results show that the proposed method is effective and efficient. Consequently, it can be readily applicable to practical semiconductor manufacturing systems.

Scheduling unrelated machines with job splitting, setup resources and sequence dependency

ABSTRACT We examine the parallel machine scheduling problem where a set of jobs are to be processed by a set of unrelated parallel machines. We examine the most general among the variations for which an exact method has been proposed regarding makespan minimisation. This is because, apart from unrelated machines, we allow for (i) job splitting: each job's quantity can be split and processed by multiple machines simultaneously; (ii) sequence- and machine-dependent setup times: the setup time when job j succeeds k is different than the time when k succeeds j and varies also per machine m; and (iii) setup resource constraints: the number of setups that can be performed simultaneously on different machines is restricted. We present novel lower bound formulations and a heuristic that solves instances of up to 1000 jobs in a few minutes at an average gap of less than . Then, we propose a logic-based Benders decomposition, which, coupled with our heuristic, solves instances of up to 200 jobs and 20 machines to near optimality in less than two hours. Our method is used for a broad range of instances from textile manufacturing, thus yielding valuable managerial insights on makespan's versatility under varying machines or resources.

A hybrid genetic algorithm for parallel machine scheduling with setup times

This paper addresses the unrelated parallel machine scheduling problem with sequence and machine dependent setup times and machine eligibility constraints. The objective is to minimize the maximum completion time (makespan). Instances of more than 500 jobs and 50 machines are not uncommon in industry. Such large instances become increasingly challenging to provide high-quality solutions within limited amount of computational time, but so far, have not been adequately addressed in recent literature. A hybrid genetic algorithm is developed, which is lean in the sense that is equipped with a minimal number of parameters and operators, and which is enhanced with an effective local search operator, specifically targeted to solve large instances. For evaluation purposes a new set of larger problems is generated, consisting of up to 800 jobs and 60 machines. An extensive comparative study shows that the proposed method performs significantly better compared to other state-of-the-art algorithms, especially for the new larger instances. Also, it is demonstrated that calibration is crucial and in practice it should be targeted at a narrower set of representative instances.

Agent Scheduling in Unrelated Parallel Machines with Sequence- and Agent–Machine–Dependent Setup Time Problem

Assignation-sequencing models have played a critical role in the competitiveness of manufacturing companies since the mid-1950s. The historic and constant evolution of these models, from simple assignations to complex constrained formulations, shows the need for, and increased interest in, more robust models. Thus, this paper presents a model to schedule agents in unrelated parallel machines that includes sequence and agent–machine-dependent setup times (ASUPM), considers an agent-to-machine relationship, and seeks to minimize the maximum makespan criteria. By depicting a more realistic scenario and to address this NP-hard problem, six mixed-integer linear formulations are proposed, and due to its ease of diversification and construct solutions, two multi-start heuristics, composed of seven algorithms, are divided into two categories: Construction of initial solution (designed algorithm) and improvement by intra (tabu search) and inter perturbation (insertions and interchanges). Three different solvers are used and compared, and heuristics algorithms are tested using randomly generated instances. It was found that models that linearizing the objective function by both job completion time and machine time is faster and related to the heuristics, and presents an outstanding level of performance in a small number of instances, since it can find the optimal value for almost every instance, has very good behavior in a medium level of instances, and decent performance in a large number of instances, where the relative deviations tend to increase concerning the small and medium instances. Additionally, two real-world applications of the problem are presented: scheduling in the automotive industry and healthcare.

Unrelated parallel machine scheduling with new criteria: Complexity and models

In this paper, a scheduling problem on non-identical parallel machines with auxiliary resources and sequence-dependent and machine-dependent setup times is studied. This problem can be found in various manufacturing contexts, and in particular in workshops of wafer manufacturing facilities. Three different criteria are defined and analyzed: The number of products completed before the end of a given time horizon, the weighted sum of completion times and the number of auxiliary resource moves. The first criterion is maximized, while the two others are minimized. The first and the third criteria are not classical in scheduling theory, but are justified in industrial settings. The complexity of the problem with each of the new criteria is characterized. Integer linear programming models are also proposed and numerical experiments are conducted to analyze their behavior.

A combinatorial evolutionary algorithm for unrelated parallel machine scheduling problem with sequence and machine-dependent setup times, limited worker resources and learning effect

The existing papers on unrelated parallel machine scheduling problem with sequence and machine-dependent setup times (UPMSP-SMDST) ignore the worker resources and learning effect. Given the influence and potential of human factors and learning effect in real production systems to improve production efficiency and decrease production cost, we propose a UPMSP-SMDST with limited worker resources and learning effect (NUPMSP). In the NUPMSP, the workers have learning ability and are categorized to different skill levels, i.e., a worker’s skill level for a machine is changing with his accumulating operation times on the same machine. A combinatorial evolutionary algorithm (CEA) which integrates a list scheduling (LS) heuristic, the shortest setup time first (SST) rule and an earliest completion time first (ECT) rule is presented to solve the NUPMSP. In the experimental phase, 72 benchmark instances of NUPMSP are constructed to test the performance of the CEA and facilitate future study. The Taguchi method is used to obtain the best combination of key parameters of the CEA. The effectiveness of the LS, SST and ECT is verified based on 15 benchmark instances. Extensive experiments conducted to compare the CEA with some well-known algorithms confirm that the proposed CEA is superior to these algorithms in terms of solving accuracy and efficiency.

Sine-Cosine Algorithm to Enhance Simulated Annealing for Unrelated Parallel Machine Scheduling with Setup Times

This paper presents a hybrid method of Simulated Annealing (SA) algorithm and Sine Cosine Algorithm (SCA) to solve unrelated parallel machine scheduling problems (UPMSPs) with sequence-dependent and machine-dependent setup times. The proposed method, called SASCA, aims to improve the SA algorithm using the SCA as a local search method. The SCA provides a good tool for the SA to avoid getting stuck in a focal point and improving the convergence to an efficient solution. SASCA algorithm is used to solve UPMSPs by minimizing makespan. To evaluate the performance of SASCA, a set of experiments were performed using 30 tests for 4 problems. Moreover, the performance of the proposed method was compared with other meta-heuristic algorithms. The comparison results showed the superiority of SASCA over other methods in terms of performance dimensions.

A meta-heuristic based on the Imperialist Competitive Algorithm (ICA) for solving Hybrid Flow Shop (HFS) scheduling problem with unrelated parallel machines

ABSTRACTThis paper addresses the hybrid flow shop (HFS) scheduling problem with unrelated parallel machines considering sequence and machine dependent setup times. The performance measurement used in this study is based on minimizing maximum completion time (makespan). Because of the complexity of the problem, a meta-heuristic based on the imperialist competitive algorithm (ICA) and the genetic algorithm (GA) has been used. To achieve reliable results, an experimental design has been developed to determine the incidence of the factors in the objective function which is applied in twelve instances. The efficiency of the meta-heuristic is compared with a model of mixed-integer programming validated in GAMS. The results of the study reveal that the meta-heuristic obtains equal or better solutions than those of the exact method for half of the instances.

작업자 1명이 내부 및 외부 셋업을 수행하는 이종병렬기계의 일정계획

This research deals with a scheduling problem that minimizes makespan in a single setup-operator and non-identical parallel machine system, in which the machine dependent setup time of each job is divided into internal and external setup times. The internal setup refers to those setup actions that inevitably require that the machine be stopped, and the external setup refers to actions that can be taken while the machine is operating. We first present a mixed integer linear programming formulation for the problem, and using this formulation, the optimal solutions for relatively small problems can be easily found. However, since the problem is NP-hard and the size of a real problem can be large, we propose a genetic algorithm based heuristic to solve the practical big-size problems in a reasonable computational time. To assess the performance of the algorithm, we conduct a computational experiment, from which we found the heuristic algorithm shows very good performances.

A worm optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times

This paper addresses the unrelated parallel machine scheduling problem with setup times, with an objective of minimizing the makespan. The machines are unrelated in the sense that the processing speed depends on the job being executed and not the machine. Each job will have different processing times for each of the available machines, is available at the beginning of the scheduling horizon, and can be processed on any of the machines but needs to be processed by one machine only. Sequence-dependent and machine-dependent setup times are also considered. A Worm Optimization (WO) algorithm is introduced and is applied to this NP-hard problem. The novel WO is based on the behaviors of the worm, which is a nematode with only 302 neurons. Nevertheless, these neurons allow worms to achieve several intricate behaviors including finding food, interchanging between solitary and social foraging styles, alternating between dwelling and roaming, and entering a type of stasis/declining stage. WO’s performance is evaluated by comparing its solutions to solutions of six other known metaheuristics for the problem under study, and the extensive computational results indicated that the proposed WO performs best.

Using high performance computing for unrelated parallel machine scheduling with sequence-dependent setup times: Development and computational evaluation of a parallel branch-and-price algorithm

Scheduling problems are essential for decision making in many academic disciplines, including operations management, computer science, and information systems. Since many scheduling problems are NP-hard in the strong sense, there is only limited research on exact algorithms and how their efficiency scales when implemented on parallel computing architectures. We address this gap by (1) adapting an exact branch-and-price algorithm to a parallel machine scheduling problem on unrelated machines with sequence- and machine-dependent setup times, (2) parallelizing the adapted algorithm by implementing a distributed-memory parallelization with a master/worker approach, and (3) conducting extensive computational experiments using up to 960 MPI processes on a modern high performance computing cluster. With our experiments, we show that the efficiency of our parallelization approach can lead to superlinear speedup but can vary substantially between instances. We further show that the wall time of serial execution can be substantially reduced through our parallelization, in some cases from 94 h to less than 6 min when our algorithm is executed on 960 processes.

<b>A genetic algorithm and variable neighborhood search for the unrelated parallel machine scheduling problem with sequence dependent setup time

This paper presents the evaluation of two metaheuristics to solve the Unrelated Parallel Machine Scheduling Problem with Sequence Machine Dependent Setup Time. Considering such a problem, there is no relation between the time to process each task and the machine; and this is why the machines are referred to as unrelated. Furthermore, the setup time between the executions of two tasks depends on both, the task sequence and its associated machine. A metaheuristic genetic algorithm and a variable neighborhood search were used in order to solve the problem due to the difference among their characteristics. The maximal time for the schedule to be completed, also called makespan, was the performance measure used to evaluate the solutions. The results obtained by both metaheuristics were directly compared according to their performance to try to reduce this makespan. The results showed that the variable neighborhood algorithm search outperformed the genetic algorithm regarding the solutions quality and execution time.

A Hybrid Genetic Algorithm for Parallel Machine Scheduling at Semiconductor Back-End Production

This paper addresses batch scheduling at a back-end semiconductor plant of Nexperia. This complex manufacturing environment is characterized by a large product and batch size variety, numerous parallel machines with large capacity differences, sequence and machine dependent setup times and machine eligibility constraints. A hybrid genetic algorithm is proposed to improve the scheduling process, the main features of which are a local search enhanced crossover mechanism, two additional fast local search procedures and a user-controlled multi-objective fitness function. Testing with real-life production data shows that this multi-objective approach can strike the desired balance between production time, setup time and tardiness, yielding high-quality practically feasible production schedules.

A constraint programming approach for solving unrelated parallel machine scheduling problem

Abstract This paper addresses the non-preemptive unrelated parallel machine scheduling problem (PMSP) with job sequence and machine dependent setup times. This is a widely seen NP-hard (non-deterministic polynomial-time) problem with the objective to minimize the makespan. This study provides a noval constraint programming (CP) model with two customized branching strategies that utilize CP’s global constraints, interval decision variables, and domain filtering algorithms. The performance of the CP model is evaluated against the state-of-art algorithms. In addition, we compare the performance of the default branching method in the CP solver against the two customized variants. In terms of average solution quality, the computational results indicate that the CP model slightly outperforms all of the state-of-art algorithms in solving small problem instances, is able to prove the optimality of 283 currently best-known solutions. It is also effective in finding good quality feasible solutions for the larger problem instances.