Stochastic Scheduling Problem Research Articles

Real-time stochastic flexible flow shop scheduling in a credit factory with model-based reinforcement learning

There has been a significant increase in consumer credit worldwide in recent years. The scheduling of jobs in credit factories is essential for speeding up the loan application process, which can improve the efficiency of credit factories. In this study, we propose a reinforcement learning approach for addressing the scheduling problem in credit factories, which is a stochastic flexible flow shop scheduling problem (SFFSP). First, we propose a mathematical model for the credit factory stochastic flexible flow shop scheduling problem, which abstracts the decision-making process as a semi-Markov process. Then, a reinforcement learning reward mechanism is designed based on the proposed mathematical model. After that, a self-attention neural network is used to extract state information from global and local multidimensional data, enabling each decision to consider the state of the entire process and make a decision that aligns with the global goal. Meanwhile, Monte Carlo Tree Search (MCTS) is utilised to enhance the training effect and sample utilisation of reinforcement learning. Finally, we conduct extensive experiments and demonstrate that our method achieves better performance for SFFSP in credit factories compared to other approaches.

Real-Time Microgrid Energy Scheduling Using Meta-Reinforcement Learning

With the rapid development of renewable energy and the increasing maturity of energy storage technology, microgrids are quickly becoming popular worldwide. The stochastic scheduling problem of microgrids can increase operational costs and resource wastage. In order to reduce operational costs and optimize resource utilization efficiency, the real-time scheduling of microgrids becomes particularly important. After collecting extensive data, reinforcement learning (RL) can provide good strategies. However, it cannot make quick and rational decisions in different environments. As a method with generalization ability, meta-learning can compensate for this deficiency. Therefore, this paper introduces a microgrid scheduling strategy based on RL and meta-learning. This method can quickly adapt to different environments with a small amount of training data, enabling rapid energy scheduling policy generation in the early stages of microgrid operation. This paper first establishes a microgrid model, including components such as energy storage, load, and distributed generation (DG). Then, we use a meta-reinforcement learning framework to train the initial scheduling strategy, considering the various operational constraints of the microgrid. The experimental results show that the MAML-based RL strategy has advantages in improving energy utilization and reducing operational costs in the early stages of microgrid operation. This research provides a new intelligent solution for microgrids’ efficient, stable, and economical operation in their initial stages.

The performance of priority rules for the dynamic stochastic resource-constrained multi-project scheduling problem: an experimental investigation

We consider the problem of a project manager of a matrix organization responsible for the timely completion of projects arriving over time and requiring the usage of a set of resources under his/her purview. A project is defined by a set of activities, precedence relations between activities, resource requirements, a customer due date, and a priority (a weight). Arriving projects are released to a flow control system that monitors the progress of activities and schedules the set of available activities, i.e., activities that are ready to be processed, as appropriate. A critical feature of such control systems is the decision process for choosing the next activity to seize a given resource. This is the focus of this paper. In the past several decades, various heuristic priority rules have been proposed in the literature to support this type of decision in differing settings such as the job shop problem and the deterministic resource-constrained project scheduling problem. A gap exists with respect to testing the various rules all together in the more realistic dynamic-stochastic multi-project environment when the objective is to minimize weighted project tardiness. The purpose of this paper is to fill this gap. Results show that the priority rule “Weighted Critical Ratio and Shortest Processing Time” (W(CR+SPT))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\hbox {W}(\\hbox {CR}+\\hbox {SPT}))$$\\end{document} is the best performing rule with respect to minimizing weighted project tardiness. W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} is shown to be a variant of the family of “Modified Due Date” rules first introduced by Baker and Bertrand (J Oper Manage 1(3):37–42, 1982). Repeated application of Duncan’s Multiple Range test demonstrates the robustness of our findings. For the environmental parameters (due date tightness, variation of expected activity durations, and utilization of resource), the W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} rule is dominant with respect to weighted project tardiness among the eleven priority rules tested. Only when the number of resources is very modest (either 1 or 3 resources) or under a purely parallel resource network is W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} not the dominant rule. In those cases, its variant W(CR+GSPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {GSPT})$$\\end{document} is the best performing rule with respect to weighted project tardiness.

Multi-objective migrating birds optimization for solving stochastic home health care routing and scheduling problems considering caregiver working time constraints

Currently, many countries are suffering from a heavy burden caused by population aging since the elderly occupy a large number of medical resources. Home health care (HHC) is a prospective approach to relieve and cope with this issue. This study addresses a multi-objective HHC routing and scheduling problem (HHCRSP) considering uncertainties and caregivers’ working time balance. First, a stochastic programming method is employed to formulate the uncertain service time and travel time, and then a chance-constrained programming model is developed to minimize the total operation cost and penalty cost of violating allowable time windows. Second, a multi-objective migrating birds optimization incorporating a stochastic simulation method is proposed. An ensemble of population iteration and external archive search is designed to obtain high-quality solutions. A stochastic simulation strategy is devised to evaluate the feasibility of obtained solutions and calculate their objective values. At last, numerical experiments are implemented for solving an extending benchmark set. The comparisons and discussions verify the better performance of the proposed algorithm compared with its peers.

Biomimicry in Radiation Therapy: Optimizing Patient Scheduling for Improved Treatment Outcomes

In the realm of medical science, the pursuit of enhancing treatment efficacy and patient outcomes continues to drive innovation. This study delves into the integration of biomimicry principles within the domain of Radiation Therapy (RT) to optimize patient scheduling, ultimately aiming to augment treatment results. RT stands as a vital medical technique for eradicating cancer cells and diminishing tumour sizes. Yet, the manual scheduling of patients for RT proves both laborious and intricate. In this research, the focus is on automating patient scheduling for RT through the application of optimization methodologies. Three bio-inspired algorithms are employed for optimization to tackle the complex online stochastic scheduling problem. These algorithms include the Genetic Algorithm (GA), Firefly Optimization (FFO), and Wolf Optimization (WO). These algorithms are harnessed to address the intricate challenges of online stochastic scheduling. Through rigorous evaluation, involving the scrutiny of convergence time, runtime, and objective values, the comparative performance of these algorithms is determined. The results of this study unveil the effectiveness of the applied bio-inspired algorithms in optimizing patient scheduling for RT. Among the algorithms examined, WO emerges as the frontrunner, consistently delivering superior outcomes across various evaluation criteria. The optimization approach showcased in this study holds the potential to streamline processes, reduce manual intervention, and ultimately improve treatment outcomes for patients undergoing RT.

A simulation-based approximate dynamic programming approach to dynamic and stochastic resource-constrained multi-project scheduling problem

We consider the dynamic and stochastic resource-constrained multi-project scheduling problem which allows for the random arrival of projects and stochastic task durations. Completing projects generates rewards, which are reduced by a tardiness cost in the case of late completion. Multiple types of resource are available, and projects consume different amounts of these resources when under processing. The problem is modelled as an infinite-horizon discrete-time Markov decision process and seeks to maximise the expected discounted long-run profit. We use an approximate dynamic programming algorithm (ADP) with a linear approximation model which can be used for online decision making. Our approximation model uses project elements that are easily accessible by a decision-maker, with the model coefficients obtained offline via a combination of Monte Carlo simulation and least squares estimation. Our numerical study shows that ADP often statistically significantly outperforms the optimal reactive baseline algorithm (ORBA). In experiments on smaller problems however, both typically perform suboptimally compared to the optimal scheduler obtained by stochastic dynamic programming. ADP has an advantage over ORBA and dynamic programming in that ADP can be applied to larger problems. We also show that ADP generally produces statistically significantly higher profits than common algorithms used in practice, such as a rule-based algorithm and a reactive genetic algorithm.

Optimising stochastic task allocation and scheduling plans for mission workers subject to learning-forgetting, fatigue-recovery, and stress-recovery effects

This study addresses the stochastic bi-objective task allocation and scheduling problems for mission workers subject to the complex (and joint) effect of learning-forgetting, fatigue-recovery, and stress-recovery processes. The mission consists of work-rest cycles with different types of tasks. Some task types are repetitive, not necessarily back-to-back, with some predecessors for other task types. The workers are multi-skilled, whose experience, learning, fatigue, and stress levels are updated, affecting their performance dynamically. A Markov Decision Process (MDP) is applied to formulate this stochastic problem, considering speed and accuracy as two measures of workforce performance. A decision could be “to repeat a task of a certain type” or “take a rest break till another worker becomes available”. The developed MDP model finds the optimal task allocation and work-break schedule for workers by minimising the sum of the tasks’ completion times and maximising their quality. Completion time is a continuous variable, and the quality index is a binary random variable, i.e., high or moderate, having a continuous probability of occurrence. The model is of a general form with a potential application in similar settings. The paper used the Sequential Greedy Assignment (SGA) and the Monte-Carlo Tree Search (MCTS) to solve the problem with their results compared. Numerical results with those from a sensitivity analysis are discussed.

Minimizing the expected maximum lateness for a job shop subject to stochastic machine breakdowns

This paper addresses a stochastic job shop scheduling problem with sequence-dependent setup times, aiming to minimize the expected maximum lateness. The stochastic nature is modeled by considering uncertain times between failures (TBF) and uncertain times to repair (TTR). To tackle this problem, a simheuristic approach is proposed, which combines a tabu search (TS) algorithm with Monte Carlo simulation. A total of 320 instances were used to conduct multiple experiments. Instances were generated with two distributions to study the behavior of stochastic TTR and TBF under log-normal and exponential distributions. Firstly, the performance of the simheuristic was evaluated for small instances by comparing it with the simulation of optimal solutions obtained with a mixed-integer linear programming (MILP) model. The simheuristic approach demonstrated an average improvement of around 7% compared to the simulation of MILP model solutions. Secondly, the simheuristic performance was evaluated for medium and large-size instances by comparing it with the simulation of the solutions obtained by the earliest due date (EDD) and process time plus work in the next queue plus negative slack (PT + WINQ + SL) dispatching rules. The results showed an average improvement of around 11% compared to EDD and 14% compared to PT + WINQ + SL. Furthermore, the results highlight that even when the two distributions have the same expected value and coefficient of variation, they can yield different expected maximum lateness values. This emphasizes the importance of precise distribution fitting when solving real cases to achieve effective scheduling performance.

Bi-Objective Modeling and Optimization for Stochastic Two-Stage Open Shop Scheduling Problems in the Sharing Economy

Nowadays, many manufacturing and service industries prefer to share resources such as facilities and workers to cooperatively perform tasks, which can efficiently improve resource utilization and customer satisfaction. Generally, the decision-makers need to pay more for resource usage, leading to an urgent demand to decrease operational costs. This article proposes a stochastic bi-objective two-stage open shop scheduling problem that models a vehicle maintenance process where tasks are appointed to be completed by multiple third-party companies with professional equipment. We formulate this optimization problem by minimizing the total tardiness and processing cost subject to various resource constraints. A hybrid multiobjective migrating birds optimization combined with a genetic operation and a discrete event system is designed by considering problem characteristics to solve the problem. In this method, the migrating birds optimization with some particular strategies aims at searching candidate solutions from the entire solution domain. Simultaneously, the discrete event system, by using stochastic simulation and discrete event-based simulation approaches, focuses on evaluating the performance of searched solutions. Simulation experiments are performed, and state-of-the-art algorithms are used as competitive approaches. The results confirm that this approach has an excellent performance in handling our considered problem.

Technical Note—Stochastic Scheduling with Abandonment: Necessary and Sufficient Conditions for the Optimality of a Strict Priority Policy

Strict priority policies in a stochastic system with abandonment In the technical note “Stochastic scheduling with abandonment: Necessary and sufficient conditions for the optimality of a strict priority policy,” Chen, Gayon, and Lemaire consider a stochastic scheduling problem in which jobs abandon when their waiting time exceeds their lifetime. Such a problem arises, for example, in call centers or emergency systems. It is known that the optimal policy is a strict priority policy under some sets of conditions. The authors provide the first set of necessary and sufficient conditions for a problem with two types of jobs. They also provide conjectures to guide toward generalizations of the proposed conditions.

A hybrid genetic algorithm for stochastic job-shop scheduling problems

Job-shop scheduling problems are among most studied problems in last years because of their importance for industries and manufacturing processes. They are classified as NP-hard problems in the strong sense. In order to tackle these problems several models and methods have been used. In this paper, we propose a hybrid metaheuristic composed of a genetic algorithm and a tabu search algorithm to solve the stochastic job-shop scheduling problem. Our contribution is based on a study of the perturbations that affect the processing times of the jobs. These perturbations, due to machine failures, occur according to a Poisson process; the results of our approach are validated on a set of instances originating from the OR-Library (Beasley, J. Oper. Res. Soc. 41 (1990) 1069–1072). On the basis of these instances, the hybrid metaheuristic is used to solve the stochastic job-shop scheduling problem with the objective of minimizing the makespan as first objective and the number of critical operations as second objective during the robustness analysis. Indeed, the results show that a high value of the number of critical operations is linked to high variations of the makespan of the perturbed schedules, or in other words to a weak robustness of the relating GA’s best schedule. Consequently, critical operations are not only good targets for optimizing a schedule, but also a clue of its goodness when considering stochastic and robustness aspects: the less critical operations it contains, the better it is.

An efficient scenario penalization matheuristic for a stochastic scheduling problem

An efficient scenario penalization matheuristic for a stochastic scheduling problem

Maximizing the service level on the makespan in the stochastic flexible job-shop scheduling problem

This paper considers the flexible job-shop scheduling problem with stochastic processing times. To find a sequence insensitive to shop floor disturbances, the available probabilistic information related to the variability of processing times is taken into account by maximizing the makespan service level for a given deadline. This corresponds to the probability of the makespan to be smaller than a given threshold. After showing why this criterion makes sense compared to minimizing the average makespan, a solution approach relying on a tabu search and a Monte Carlo sampling-based approximation is presented. Then, new instances are generated by extending the deterministic benchmark instances. Extensive computational experiments are conducted to evaluate the relevance of the makespan service level and the performance of the proposed solution method. The drawbacks of a number of reference scenarios, including worst-case and best-case scenarios, in addressing effectively the problem under study are presented. A numerical analysis is also performed to compare the scope of the proposed criterion against the minimization of the expected makespan. The accuracy of the proposed solutions induced by the hyper-parameters of the Monte Carlo approximation is explicitly analyzed.

Two-Stage Genetic Algorithm for Scheduling Stochastic Unrelated Parallel Machines in a Just-in-Time Manufacturing Context

This paper considers a stochastic parallel machine scheduling problem in a just-in-time manufacturing context, in which its processing time can be described by a gamma or log-normal distribution. In order to obtain a high-performance schedule in a reasonable time, this work proposes a two-stage genetic algorithm with optimal computing budget allocation (OCBA) and improved Monte-Carlo Policy Evaluation (MCPE). In it, a genetic algorithm is selected as a main optimizer. An OCBA-based approach is developed to improve search efficiency, which is designed for two scenarios in a just-in-time manufacturing context. Different from most prior OCBA studies, this work considers that the stochastic processing time of jobs does not obey normal distribution. It extends the application area of OCBA by laying a theoretical foundation. A parameter control scheme based on MCPE is proposed, which aims to balance the global and local search in GA. To further enhance the efficiency and effectiveness of the proposed method, a two-stage framework is constructed. In the first stage, the performance is estimated roughly aiming at locating satisfactory solution regions. In the second stage, OCBA is incorporated to provide the reliable evaluation of excellent individuals. The theoretic interpretation of the proposed OCBA, and the convergence analysis results of the proposed method are presented. Various simulation results with benchmark and randomly generated cases validate that the proposed algorithm is more efficient and effective than several existing optimization algorithms. Note to Practitioners—A parallel machine scheduling problem under stochastic processing time is usually solved via meta-heuristic algorithms. However, their computational efficiency requires substantial improvement, especially for a stochastic optimization case that requires Monte Carlo sampling to estimate the actual objective function values in a precise manner. Most of them are parameter-sensitive, and choosing their proper parameters is highly challenging. For the first thorny issue, we develop an OCBA-based approach for determining the optimal numbers of simulations according to both prior knowledge and simulation results. In order to select proper control parameters of the proposed algorithm iteratively, we introduce a parameter control scheme based on MCPE. The combination of a meta-heuristic algorithm, OCBA and MCPE makes it possible to find high-quality solutions for the concerned scheduling problems in a short time. Theoretic analysis and numerical simulation results suggest that the proposed framework is valid and efficient. Hence, it can be readily applicable to practical systems, e.g., semiconductor manufacturing.

A Secure and Adaptive Hierarchical Multi-Timescale Framework for Resilient Load Restoration Using a Community Microgrid

Distribution system integrated community microgrids (CMGs) can partake in restoring loads during extended duration outages. At such times, the CMGs are challenged with limited resource availability, absence of robust grid support, and heightened demand-supply uncertainty. This paper proposes a secure and adaptive three-stage hierarchical multi-timescale framework for scheduling and real-time (RT) dispatch of CMGs with hybrid PV systems to address these challenges. The framework enables the CMG to dynamically expand its boundary to support the neighboring grid sections and is adaptive to the changing forecast error impacts. The first stage solves a stochastic extended duration scheduling (EDS) problem to obtain referral plans for optimal resource rationing. The intermediate near-real-time (NRT) scheduling stage updates the EDS schedule closer to the dispatch time using new obtained forecasts, followed by the RT dispatch stage. To make the decisions more secure and robust against forecast errors, a novel concept called delayed recourse is designed. The approach is evaluated via numerical simulations on a modified IEEE 123-bus system and validated using OpenDSS and hardware-in-loop simulations. The results show superior performance in maximizing load supply and continuous secure distribution network operation under different operating scenarios.

Flow shop scheduling with human–robot collaboration: a joint chance-constrained programming approach

ABSTRACT Human–robot collaboration has been incorporated into production and assembly processes to promote system flexibility, changeability and adaptability. However, it poses new challenges to resource allocation and production scheduling due to its intrinsic uncertainty and also the increasing complexity of resources. This paper investigates a stochastic flow shop scheduling problem in the context of human–robot collaboration. The goal is to achieve efficient utilisation of flexible resources including human workers and cobots and take full advantage of human–robot collaboration in production scheduling. A stochastic Cobb–Douglas production function is utilised to evaluate the production efficiency of human–robot collaboration considering instabilities of human performance. A joint chance-constrained programming model is formulated to ensure that the required system performance can be achieved. A CVaR approximation-based approach is proposed to solve the formulated model with mixed-integer variables and a nonconvex constraint. The effectiveness of the formulated model and the efficiency of the proposed solution approach are evaluated via numerical experiments. Computational results show the superiority of our solution approach over three other approaches including Bonferroni approximation, scenario approach and individual chance-constrained programming.

RETRACTED ARTICLE: A nonanticipatory policy for stochastic seru scheduling problems

We, the Editors and Publisher of Journal of the Operational Research Society, have retracted the following article: Zhang, Z., Gong, X., Song, X., Yin, Y., Lev, B., & Zhou, X. (2023). A nonanticipatory policy for stochastic seru scheduling problems. Journal of the Operational Research Society, 1–12. https://doi.org/10.1080/01605682.2023.2182723. Since publication, significant concerns have been raised about the fact that this article appears to have substantial overlap with the following articles, which were not cited or referenced. Skutella, M., Sviridenko, M., & Uetz, M. (2016). Unrelated Machine Scheduling with Stochastic Processing Times, Mathematics of Operations Research, 41(3), 851–864. https://doi.org/10.1287/moor.2015.0757. Uetz, M. (2003). When greediness fails: examples from stochastic scheduling, Operations Research Letters, 31(6), 413–419. https://doi.org/10.1016/S0167-6377(03)00047-6 Subsequent to investigation, and communication with the authors, we have also been informed by the first corresponding author that the co-authors were not consulted on the decision to submit to the Journal of the Operational Research Society, nor on the submission of the revised manuscript. The first corresponding author also highlighted inaccuracies in the methodology, specifically the omission of the Worker element extension and the improper application of the model’s extension from discrete to continuous time, both of which were important to the claimed contribution of the article. The authors have agreed with the decision to retract the article. We have been informed in our decision-making by our Editorial Policies and the COPE guidelines. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as “Retracted”.

A Formulation for the Stochastic Multi-Mode Resource-Constrained Project Scheduling Problem Solved with a Multi-Start Iterated Local Search Metaheuristic

This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. Furthermore, we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it. In this approach, the multi-verse optimization is adopted to find favorable solutions from the huge solution domain, while the stochastic simulation method is employed to assess them. By conducting comparison experiments on test problems, it can be verified that the developed approach has better performance in coping with the considered problem, compared to two classic multi-objective evolutionary algorithms.

Decomposing Two-Stage Stochastic Scheduling Problems on a continuous-time basis via Slot Similarity

Incorporating uncertainty into process scheduling by explicitly considering future forecasts is crucial for achieving optimal and feasible solutions in practice. However, the complexity of two-stage stochastic scheduling formulations increases exponentially with the number of scenarios, making it difficult to solve large-scale problems in real-time using mathematical programming, which is often necessary for production-maintenance scheduling. This is where decomposition strategies on a scenario basis can be advantageous. Recently, the authors developed a method for decomposing two-stage scheduling problems (TSSPs) formulated on a discrete-time basis using the Similarity Index. This paper extends this concept to TSSPs formulated on a continuous-time basis by fuzzifying discrete decisions among slots instead of time periods, and incorporating the progressive-hedging algorithm to manage non-anticipativity in continuous decisions. The proposed algorithm is tested in a case study of a multiproduct plant consisting of a single processing unit from the literature. Results show that the proposed decomposition algorithm solves the problem faster than the monolithic formulation.