Uncertain Processing Times Research Articles

A Two-Individual-Based Evolutionary Algorithm for Flexible Assembly Job Shop Scheduling Problem with Uncertain Interval Processing Times

The assembly job shop is a prevalent production organization mode in manufacturing enterprises. During the processing and assembly of products, operation processing times are influenced by numerous factors, leading to significant uncertainty. This paper investigates the flexible assembly job shop scheduling problem (FAJSP) with uncertain processing times, where processing times are represented as variable interval numbers. We develop a robust optimization model for the FAJSP, utilizing confidence level estimation to determine the ranges of processing times and reformulating the model based on the chance-constrained method. A two-individual-based master–apprentice evolutionary (MAE) algorithm is proposed. Two effective encoding schemes are designed to prevent the generation of infeasible solutions under assembly sequence constraints. Additionally, a decoding method based on interval scheduling theory is devised to accurately represent interval processing times. Case studies are conducted to validate the effectiveness of the proposed robust optimization model and demonstrate the superiority of the MAE algorithm.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling aims at determining the job sequence with the best desired performance, and provides the basic building block for more advanced scheduling problems. In the present study, a single machine scheduling model with uncertain processing time is considered by incorporating the job release time and due date. The job processing time follows unknown probability distribution, and can be estimated via the historical data. To model the uncertainty, the processing time distribution is defined over a Wasserstein ball ambiguity set, which covers all feasible probability distributions within the confidence radius of the empirical distribution, known as the center of the ball. Then a data-driven distributionally robust scheduling model is constructed with individual chance constraints. In particular, two equivalent reformulations are derived with respect to the ℓ1-norm and ℓ2-norm metrics of the Wasserstein ball, namely, a mixed-integer linear programming and a mixed-integer second order cone programming model, respectively. To accelerate the solving of large-scale instances, a tailored constraint generation algorithm is introduced. In the numerical analysis, the proposed distributionally robust scheduling approach is compared with the state-of-the-art methods in terms of out-of-sample performance.

Analysis of order-of-addition experiments

The order-of-addition (OofA) experiment involves arranging components in a specific order to optimize a certain objective, which is attracting a great deal of attention in many disciplines, especially in the areas of biochemistry, scheduling, and engineering. Recent studies have highlighted its significance, and notable works have aimed to address NP-hard OofA problems from a statistical perspective. However, solving OofA problems presents challenges due to their complex nature and the presence of uncertainty, such as scheduling problems with uncertain processing times. These uncertainties affect processing times, which are not known with certainty in advance. They introduce heteroscedasticity into OofA experiments, where different orders result in varying dispersions. To address these challenges, a unified framework is proposed to analyze scheduling problems without making specific assumptions about the distribution of these certainties. It encompasses model development and optimization, encapsulating existing homoscedastic studies (where different orders produce the same dispersion value) as a specific instance. For heteroscedastic cases, a dual response optimization within an uncertainty set is proposed, aiming to minimize the dispersion of response while keeping the location of response with a predefined target value. However, solving the proposed non-linear minimax optimization is rather challenging. An equivalent optimization formulation with low computational cost is proposed for solving such a challenging problem. Theoretical supports are established to ensure the tractability of the proposed method. Simulation studies are conducted to demonstrate the effectiveness of the proposed approach. With its solid theoretical support, ease of implementation, and ability to find an optimal order, the proposed approach offers a practical and competitive solution to solving general order-of-addition problems.

Minimizing the Total Waiting Time for Fuzzy Two-Machine Flow Shop Scheduling Problem with Uncertain Processing Time

تتضمن الجدولة تخصيص الموارد للوظائف ضمن قيود محددة مع مرور الوقت. تقليديا، كان وقت المعالجة لكل مهمة يعتبر قيمة ثابتة. ومع ذلك، في السيناريوهات العملية، يمكن أن تتقلب أوقات معالجة الوظائف ديناميكيًا بناءً على الظروف السائدة. في هذه المقالة، يتم تقديم أسلوب جديد لمشكلة جدولة متجر التدفق الضبابي (FSSP) في بيئة غامضة، حيث يتم تمثيل أوقات معالجة الوظيفة بأرقام غامضة شبه منحرفة. بالإضافة إلى ذلك، تم اقتراح وتطوير خوارزمية جديدة تعتمد على نهج جويال لـ FSSP المكون من جهازين مع أوقات معالجة غامضة. وفي الوقت نفسه، تم تعزيز الخوارزمية الموجودة لتحسين أدائها في هذا السياق المحدد. تهدف الدراسة إلى تقليل إجمالي وقت الانتظار للوظائف. يتم استخدام وظيفة إزالة الضبابية لترتيب الأرقام الغامضة، بهدف نهائي هو تقليل إجمالي وقت الانتظار. علاوة على ذلك، يقوم المقال بتقييم أداء هذه الأساليب من حيث جودة الحلول، وذلك باستخدام مشاكل الاختبار مع 10، 20، 30، 40، 50، 60، 80، 90، 100، 120، 200، 250، 300، و 500 وظيفة، جنبا إلى جنب مع 2 آلات. تتم مقارنة متوسط ​​إجمالي وقت الانتظار بالخوارزميات الموجودة، بما في ذلك خوارزمية NEH، وطريقة Palmer، وطريقة Johnson، وB. Goyal وB. Kaur، والخوارزمية المقترحة. بالإضافة إلى ذلك، فإن النتائج التي تم الحصول عليها، إلى جانب اختبار ANOVA جيد التنظيم، تسلط الضوء على فعالية الطريقة المقترحة في معالجة مشكلة الجدولة قيد التحقيق. توضح النتائج التجريبية أن الخوارزمية المقترحة يمكنها تقليل وقت الانتظار بشكل فعال في FSSP ثنائي الجهاز وتحقيق نتائج متفوقة بالمقارنة مع الخوارزميات المختلفة الموجودة.

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

Co-Evolutionary Algorithm for Two-Stage Hybrid Flow Shop Scheduling Problem with Suspension Shifts

Demand fluctuates in actual production. When manufacturers face demand under their maximum capacity, suspension shifts are crucial for cost reduction and on-time delivery. In this case, suspension shifts are needed to minimize idle time and prevent inventory buildup. Thus, it is essential to integrate suspension shifts with scheduling under an uncertain production environment. This paper addresses the two-stage hybrid flow shop scheduling problem (THFSP) with suspension shifts under uncertain processing times, aiming to minimize the weighted sum of earliness and tardiness. We develop a stochastic integer programming model and validate it using the Gurobi solver. Additionally, we propose a dual-space co-evolutionary biased random key genetic algorithm (DCE-BRKGA) with parallel evolution of solutions and scenarios. Considering decision-makers’ risk preferences, we use both average and pessimistic criteria for fitness evaluation, generating two types of solutions and scenario populations. Testing with 28 datasets, we use the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) to quantify benefits. Compared to the average scenario, the VSS shows that the proposed algorithm achieves additional value gains of 0.9% to 69.9%. Furthermore, the EVPI indicates that after eliminating uncertainty, the algorithm yields potential improvements of 2.4% to 20.3%. These findings indicate that DCE-BRKGA effectively supports varying decision-making risk preferences, providing robust solutions even without known processing time distributions.

A distributionally robust approach for the parallel machine scheduling problem with optional machines and job tardiness

This paper investigates a parallel machine scheduling problem with uncertain job processing time, where the job tardiness and optional machines are considered. To address the factor of energy saving, only a subset of all available machines are turned on, which is referred to as not-all-machine (NAM). To depict the uncertain processing time, a mean–mean absolute deviation (MAD) ambiguity set is utilized, and the cost of job tardiness is minimized under the worst-case distribution scenario over the ambiguity set. After building a distributionally robust optimization (DRO) model, theoretical bounds of the optimal number of machines are obtained. Since the model is not computationally scalable, an upper bound on its inner minimization problem is employed, and a mixed integer linear programming (MILP) approximation is obtained based on McCormick inequalities. For the DRO model, tailored speedup techniques are employed, significantly enhancing the computational performance. To evaluate the validity of the proposed DRO model, we compare it with its stochastic programming (SP) counterpart under various parameter settings. Numerical experiments demonstrate that the DRO model exhibits strong performance in the worst-case scenarios. As the problem size increases, the DRO model casts clear advantages over the SP model in terms of computational efficiency and reliability. It is observed that the performance of the DRO model is more stable than that of the nominal sequence, especially with loose due dates. Furthermore, the out-of-sample performance under various decision making preferences shed new lights into the trade-off between energy saving and production efficiency.

Three-way decision based island harmony search algorithm for robust flow-shop scheduling with uncertain processing times depicted by big data

This paper discusses an uncertain two-machine permutation flow-shop scheduling problem (2PFSP) with total weighted tardiness and common due date. Uncertain processing times are described by a large set of discrete scenarios, which is a type of big data. The objective is to minimize the schedule performance under the worst-case scenario. Identifying the worst-case scenario for each evaluated schedule is quite time-consuming in the situation that the scenario set size is large so that the objective evaluation might be computationally expensive. To handle this difficulty, three-way decision is used to preprocess the large-size scenario set to get a reduced scenario set so that the concept of surrogate worst-case scenario is adopted. A hybrid harmony search algorithm of combining three-island framework and the scenario-based local search is developed to solve the discussed problem. Based on the single-scenario knowledge of 2PFSP, a problem-specific scenario-dependent neighborhood structure is constructed under the surrogate worst-case scenario. An extensive experiment was carried out. The computational results show that the application of surrogate worst-case scenario based on three-way decision is effective in reducing the time consuming while keeping schedule performance evaluation. Being compared to the worst-case scenario objective evaluation, for an example in the case of the middle bad-scenario ratio, the surrogate worst-case scenario objective evaluation made the solution algorithm save 12.95 % in average CPU time for all instances while the relative performance difference is only 1.809 % in average. Being compared to possible alternative algorithms derived from the state-of-the-art algorithms, the developed algorithm is advantageous for the addressed problems.

Rescheduling optimisation of sustainable multi-objective fuzzy flexible job shop under uncertain environment

ABSTRACT The fourth industrial revolution has necessitated the integration of sustainability and customer centricity into modern manufacturing systems, thereby emphasising their significance. However, the production process itself is characterised by inherent uncertainties. Hence, this paper primarily focuses on the multi-objective flexible job shop rescheduling problem with uncertain processing time and new job insertions. Two fuzzy constraints are incorporated: fuzzy processing time and fuzzy due date, which aim to model the uncertainty of processing time and ensure flexibility in meeting deadlines. The objective function aims to optimise both customer satisfaction and energy consumption. To address two types of rescheduling problems: time delay caused by fuzzy features and new job insertions, this paper is dedicated to providing a hybrid adaptative rescheduling strategy that combines a satisfaction-driven policy with two specific rescheduling methods. Moreover, an enhanced version of the non-dominated sorting genetic algorithm II (NSGA-II) is developed, incorporating population initialisation rules and multiple genetic operators to obtain solutions of superior quality. Experimental studies have demonstrated the impact of time delay caused by fuzzy features on customer satisfaction. The proposed hybrid adaptative rescheduling strategy and methods exhibit significant improvements in rescheduling plan performance under uncertain environments.

Probabilistic Task Offloading with Uncertain Processing Times in Device-to-Device Edge Networks

D2D edge computing is a promising solution to address the conflict between limited network capacity and increasing application demands, where mobile devices can offload their tasks to other peer devices/servers for better performance. Task offloading is critical to the performance of D2D edge computing. Most existing works on task offloading assume the task processing time is known or can be accurately estimated. However, the processing time is often uncertain until it is finished. Moreover, the same task can have largely different execution times under different scenarios, which leads to inaccurate offloading decisions and degraded performance. To address this problem, we propose a game-based probabilistic task offloading scheme with an uncertain processing time in D2D edge networks. First, we characterize the uncertainty of the task processing time using a probabilistic model. Second, we incorporate the proposed probabilistic model into an offloading decision game. We also analyze the structural properties of the game and prove that it can reach a Nash equilibrium. We evaluate the proposed work using real-world applications and datasets. The experimental results show that the proposed probabilistic model can accurately characterize the uncertainty of completion time, and the offloading algorithm can effectively improve the overall task completion rate in D2D networks.

A deep reinforcement learning model for dynamic job-shop scheduling problem with uncertain processing time

The dynamic job-shop scheduling problem (DJSP) is a type of scheduling tasks where rescheduling is performed when encountering the uncertainties such as the uncertain operation processing time. However, the current deep reinforcement learning (DRL) scheduling approaches are hard to train convergent scheduling policies as the problem scale increases, which is very important for rescheduling under uncertainty. In this paper, we propose a DRL scheduling method for DJSP based on the proximal policy optimization (PPO) with hybrid prioritized experience replay. The job shop scheduling problem is formulated as a sequential decision-making problem based on Markov Decision Process (MDP) where a novel state representation is designed based on the feasible solution matrix which depicts the scheduling order of a scheduling task, a set of paired priority dispatching rules (PDR) are used as the actions and a new intuitive reward function is established based on the machine idle time. Moreover, a new hybrid prioritized experience replay method for PPO is proposed to reduce the training time where samples with positive temporal-difference (TD) error are replayed. Static experiments on classic benchmark instances show that the make-span obtained by our scheduling agent has been reduced by 1.59% on average than the best known DRL methods. In addition, dynamic experiments demonstrate that the training time of the reused scheduling policy is reduced by 27% compared with the retrained policy when encountering uncertainties such as uncertain operation processing time.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

Assembly line balancing and capacity evaluation based on interval grey processing time

PurposeAssembly line is a common production form and has been effectively used in many industries, but the imprecise processing time of each process makes production line balancing and capacity forecasting the most troublesome problems for production managers. In this paper, uncertain man-hours are represented as interval grey numbers, and the optimization problem of production line balance in the case of interval grey man-hours is studied to better evaluate the production line capacity.Design/methodology/approachFirst, this paper constructs the basic model of assembly line balance optimization for the single-product scenario, and on this basis constructs an assembly line balance optimization model under the multi-product scenario with the objective function of maximizing the weighted greyscale production line balance rate, second, this paper designs a simulated annealing algorithm to solve problem. A neighborhood search strategy is proposed, based on assembly line balance optimization, an assembly line capacity evaluation method with interval grey man-hour characteristics is designed.FindingsThis paper provides a production line balance optimization scheme with uncertain processing time for multi-product scenarios and designs a capacity evaluation method to provide managers with scientific management strategies so that decision-makers can scientifically solve the problems that the company's design production line is quite different from the actual production situation.Originality/valueThere are few literary studies on combining interval grey number with assembly line balance optimization. Therefore, this paper makes an important contribution in this regard.

Energy aware semi-automatic assembly line balancing problem considering ergonomic risk and uncertain processing time

The semiautomated assembly line balancing problem (SAALBP) is a complex planning problem in which the production process comprises human workers, robots, and human-robot collaboration. With increasing awareness of sustainable practices in the manufacturing environment, this study addresses a sustainable SSALBP, where a mixed integer linear programming (MILP) model is formulated for the first time for this type of assembly systems. The model consists of three objectives and each of the objectives represents the three pillars of sustainability. The problem becomes more realistic by considering uncertainty in processing time and the influence of human workers’ age and skill in processing time. The uncertainty is adopted in the MILP model by using a chance-constraint programing approach. Since the problem is complex, Q-learning and Monte-Carlo simulation-assisted based genetic algorithm (GA) based memetic algorithm (MA) are proposed to solve the problem. The performance of MA is evaluated against the well-known non-dominated sorting GA-III (NSGA-III) and state-of-the-art algorithms for solving the problem. The experimental results show that MA surpasses its contest significantly in finding better Pareto-fronts.

Single machine scheduling with uncertain processing times and carbon emission constraint in the shared manufacturing environment

Single machine scheduling with uncertain processing times and carbon emission constraint in the shared manufacturing environment

Scheduling wagons to unload in bulk cargo ports with uncertain processing times

Optimising operations in bulk cargo ports is of great relevance due to their major participation in international trade. In inbound operations, which are critical to meet due dates, the product typically arrives by train and must be transferred to the stockyard. This process requires several machines and is subject to frequent disruptions leading to uncertain processing times. This work focuses on the scheduling problem of unloading the wagons to the stockyard, approaching both the deterministic and the stochastic versions. For the deterministic problem, we compare three solution approaches: a Mixed Integer Programming model, a Constraint Programming model and a Greedy Randomised algorithm. The selection rule of the latter is evolved by Genetic Programming. The stochastic version is tackled by dispatching rules, also evolved via Genetic Programming. The proposed approaches are validated using real data from a leading company in the mining sector. Results show that the new heuristic presents similar results to the company’s algorithm in a considerably shorter computational time. Moreover, we perform extensive computational experiments to validate the methods on a wide spectrum of randomly generated instances. Finally, as managing uncertainty is fundamental for the effectiveness of these operations, distinct strategies are compared, ranging from purely predictive to completely reactive scheduling. We conclude that re-scheduling with high frequency is the best approach to avoid performance deterioration under schedule disruptions, and using the evolved dispatching rules incur fewer deviations from the original schedule.

Single machine scheduling with interval grey processing time

PurposeThis paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval grey number and its related definitions, properties, and theorems, the single machine scheduling with uncertain processing time and its general forms are studied as the research object. Then several single machine scheduling models are reconstructed, and an actual production case is developed to illustrate the rationality of the research.Design/methodology/approachIn this paper, the authors first summarize the definitions and properties related to interval grey numbers, especially the transitivity of the partial order of interval grey numbers, and give an example to illustrate that the transitivity has a positive effect on the computational time complexity of multiple interval grey number comparisons. Second, the authors redefine the general form of the single machine scheduling problem with uncertain processing time according to the definitions and theorems of interval grey numbers. The authors then reconstruct three single machine scheduling models with uncertain processing time, give the corresponding heuristic algorithms based on the interval grey numbers and prove them. Finally, the authors develop a case study based on the engine test shop of K Company, the results show that the proposed single machine scheduling models and algorithms with uncertain processing time can provide effective guidance for actual production in an uncertain environment.FindingsThe main findings of this paper are as follows: (1) summarize the definitions and theorems related to interval grey numbers and prove the transitivity of the partial order of interval grey numbers; (2) define the general form of the single machine scheduling problem with interval grey processing time; (3) reconstruct three single machine scheduling models with uncertain processing time and give the corresponding heuristic algorithms; (4) develop a case study to illustrate the rationality of the research.Research limitations/implicationsIn the further research, the authors will continue to summarize more advanced general forms of grey scheduling, improve the theory of grey scheduling and prove it, and further explore the application of grey scheduling in the real world. In general, grey scheduling needs to be further combined with grey system theory to form a complete theoretical system.Originality/valueIt is a fundamental work to define the general form of single machine scheduling with uncertain processing time used the interval grey number. However, it can be seen as an important theoretical basis for the grey scheduling, and it is also beneficial to expand the application of grey system theory in real world.

Algorithms for three-machine flowshop scheduling problem to minimize makespan with uncertain processing times

We address the three-machine flowshop scheduling problem to minimize makespan where processing times are uncertain within some lower and upper bounds. We propose sixteen algorithms based on Johnson’s algorithm, which is known to yield the optimal solution for the three-machine flowshop problem under certain cases. The proposed algorithms are computationally evaluated based on randomly generated data. Computational experiments indicate that one of the proposed algorithms, algorithm AL-7, significantly performs better than the rest. Tests of hypotheses were performed to statistically confirm the results. In algorithm AL-7, more weight is given to the processing times of jobs on the first and the third machines compared to those of the second machine. Moreover, both the lower and upper bounds of job processing times on all three machines are utilized. Furthermore, algorithm AL-7 is shown to perform the best regardless of the extreme distributions considered. Hence, it is recommended as the best algorithm.

A cooperative iterated greedy algorithm for the distributed flowshop group robust scheduling problem with uncertain processing times

A cooperative iterated greedy algorithm for the distributed flowshop group robust scheduling problem with uncertain processing times

Scenario-Based Robust Remanufacturing Scheduling Problem Using Improved Biogeography-Based Optimization Algorithm

As a promising method for organizing remanufacturing production activities, remanufacturing scheduling has attracted increasing attention in recent years. However, extant studies have primarily focused on solving remanufacturing scheduling problems in a deterministic environment, while neglecting the impact of uncertainties on remanufacturing. Therefore, a new scenario-based robust remanufacturing scheduling problem was investigated in this study, and a robust optimization model for this problem was established. In the proposed model, a discrete scenario set is used to describe the uncertain arrival time and uncertain processing time of end-of-life products, and the variable start-up batch size constraint is considered to improve the practicality and flexibility of the model. To solve this model, an improved biogeography-based optimization algorithm with a new three-dimensional unequal-length representation scheme is proposed, in which, new migration and mutation operators, a local search strategy, and a new batch promotion mechanism are designed to improve the algorithmic performance. The results of the experiments demonstrate the feasibility of the proposed model and the superiority of the presented algorithm in solving the proposed model.