Stochastic Scheduling Problem Research Articles

Solving a stochastic hierarchical scheduling problem by VNS-based metaheuristic with locally assisted algorithms

High-end equipment manufacture has features of intensive technology, uncertain process, and large scale. Hence, the scheduling of the High-end equipment manufacture is challenging. Large ships are a type of High-end equipment that is tied to national maritime security. In this paper, we study a stochastic hierarchical scheduling problem with serial-batch processing machines and the deterioration effect in ship manufacture. In the studied problem, the job processing time is uncertain and follows a normal probability distribution. Under the deterioration effect, the actual processing time of jobs is formulated as a function of the start time. The first objective is to maximize the robustness of the manufacturing system. The second objective is to minimize the total inventory cost subjected to the optimization of the first objective. The robustness of the manufacturing system is measured by the worst level of completion probability. The total inventory cost is measured by the difference between the job delivery time and the job completion time. The mathematical model for the studied problem is formulated. Some structural properties are derived to solve the problem. Based on the properties, the optimal sequence for the first objective can be obtained and a heuristic algorithm is designed to optimize the second objective. The considered problem is NP-hard involving several non-linearities. Hence, a variable neighborhood search (VNS) algorithm is developed to solve the problem in a reasonable time, which is integrated with three local search strategies and a heuristic algorithm. Various problem instances are generated and extensive computational experiments verify that the proposed VNS algorithm outperforms other compared algorithms and has strong robustness.

Cost-effective stochastic resource placement in edge clouds with horizontal and vertical sharing

To support distributed upper-level services such as those in edge or fog computing, a hierarchical and distributed multicloud architecture is introduced to replace the traditional centralized cloud architecture. The intra-time slot demand fluctuation with corresponding multidimensional resource sharing are neglected for efficiency reasons in the existing algorithms. By considering them, the service provider has the potential to obtain better solution, but also makes the scheduling problem a highly complicated stochastic optimization one. To effectively and efficiently solve the problem containing a nonlinear objective and constraints with heterogeneous nonlinear pricing functions, the general stochastic scheduling problem is formulated and its structure is exploited to obtain the base solution quickly, which is further applied with solution closure for fast convergence in the following configurable metaheuristic searching phrase. The experiments with many different problem settings show its superiority over existing algorithms with more than 30% revenue improvement. Therefore, the proposed algorithm can be used as a good supplement to the existing methods.

Integrating scheduling and routing decisions into home health care operation with skill requirements and uncertainties

ABSTRACT The rapid increase of aging population poses a great challenge on the public medical resources. Home health care (HHC), which provides the care services for the elderly and patients with mild disease, is an emerging approach to cope with such difficulty. This work formulates a stochastic HHC scheduling and routing problem with skill requirements to minimize total operation time. A stochastic programming model is given to mathematically define it. Then, a hybrid approach combining the genetic algorithm (GA) and simulation optimization with an approximated allocation (AA) rule is designed. The GA aims to search candidate solutions, while the simulation optimization method focuses on improving the efficiency of evaluating them. Numerical results show that the AA rule is more effective than equal allocation and proportional to variance rules in guiding the GA to find promising solutions. As a consequence, the designed approach acquires the better solutions for the problem under consideration.

Hyperparameter optimization strategies for machine learning-based stochastic energy efficient scheduling in cyber-physical production systems

One of the major challenges faced by system operators in an integrated energy system (IES) is to come up with an optimal schedule of the energy generation units in the presence of uncertainties at both the demand and supply sides. Employing efficient forecasts of the uncertain parameters while ensuring the least possible prediction error is crucial to the overall scheduling of IESs. Long Short-Term Memory (LSTM), a Recurrent Neural Network (RNN) based architecture is widely used in natural language processing and time series forecasting and has reported to be a viable and powerful forecasting technique. The aim of this work is to enhance the autonomy of energy scheduling in cyber-physical production systems (CPPS) through the development of data-driven LSTM based forecast models for the uncertain parameters. However, one of the demanding tasks in time series forecasting methods such as LSTM and the subject that received little attention is the judicious choice/fine-tuning of the hyperparameter values, which significantly impacts the performance of the developed forecasting models. This paper mainly focuses on the performance analysis of various hyperparameter tuning techniques and algorithms used by LSTM networks in forecasting uncertain parameters for stochastic energy scheduling in the context of smart manufacturing. The plant under consideration is the highly energy intensive Model Factory (MF) at the Singapore Institute of Manufacturing Technology (SIMTech), that features an actual production environment supporting both experimentation and learning of digitalisation technologies for Industry 4.0. Three main energy sources installed in an IES framework consisting of solar photo voltaic (PV) system, waste-to-energy (WTE) unit and the main utility grid serves as the energy supply module to meet the requested energy by the industrial facility. Various strategies to tune the LSTM hyperparameters in forecasting the uncertain parameters are examined. Among the four strategies, the first one deals with the traditional manual tuning approach and the second one focuses on automating the traditional manual approach using a FOR loop. While the third one focuses on a tuning strategy using Optuna with a grid search algorithm, the fourth strategy concentrates on adopting Optuna with a Bayesian optimization framework. The overall objective entails generating an optimal day-ahead forecast of the uncertain parameters (in this case solar PV irradiance, temperature, main utility grid energy price and the energy demand of the MF) using LSTM based on the best performing hyperparameter tuning techniques. These forecasts are then utilized to solve a day-ahead stochastic energy scheduling problem that generates an optimal energy dispatch schedule with the overall objectives to minimize the total operational cost and carbon emission.

A Markov decision process approach for managing medical drone deliveries

Drone delivery is a fast and innovative method for delivering parcels, food, and medical supplies. Furthermore, this low-contact delivery mode contributes to reducing the spread of pandemic and vaccine-preventable diseases. Focusing on the delivery of medical supplies, this paper studies optimizing the distribution operations at a drone hub that dispatches drones to hospitals located at different geographic locations. Each hospital generates stochastic demands for medical supplies to be covered. This paper classifies stochastic demands based on the distance between hospitals and the drone hub. Satisfying the demands requires flying over different ranges, which is directly related to the amount of charge of the drone batteries. We develop a stochastic scheduling and allocation problem with multiple classes of demand and model the problem using a finite Markov decision process approach. We provide exact solutions for the modest sizes instances using backward induction and discuss that the problem suffers from the curses of dimensionality. Hence, we provide a reinforcement learning method capable of giving near-optimal solutions. We perform a set of computational tests using realistic data representing a prominent drone delivery company. Finally, we analyze the results to provide insights for managing drone hub operations and show that the reinforcement learning method has high performance compared with the exact and heuristic solution methods.

Stochastic Planning and Scheduling with Logic-Based Benders Decomposition

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple no-good cuts as well as analytic logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method. In particular, a branch-and-check variant of LBBD can be faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classic Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem and the first comparison of LBBD with the integer L-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse. Summary of Contribution: We study an important class of optimization problems, namely, two-stage stochastic programs with integer recourse, which are known to be extremely difficult to solve in general. We focus on an application in which the second-stage problem is a scheduling problem, a first in the literature to the best of our knowledge. Our study exemplifies how one can exploit the combinatorial structure of the scheduling problem to derive novel analytic Benders cuts and use them within a branch-and-check algorithm. The proposed algorithm solves instances that are intractable for commercial solvers and state-of-the-art decomposition-based methods, such as the integer L-shaped method. We believe that our study will inspire further research in the use of hybrid logic-based optimization methods for solving stochastic combinatorial optimization problems.

Simheuristic algorithm for a stochastic parallel machine scheduling problem with periodic re-planning assessment

Simheuristic algorithm for a stochastic parallel machine scheduling problem with periodic re-planning assessment

Efficient stochastic scheduling for highly complex resource placement in edge clouds

For the edge cloud-based large-scale distributed systems in wide areas, it is important to quickly adjust the deployed resource in multiple edge clouds to maximize the resource revenue and meet the quality of service requirements. The mean values of demands are usually used in the scheduling algorithms for simplicity, but in the real-world scenarios the resource demands may fluctuate greatly, which cannot be effectively modeled in the mean value-based demand model, resulting in the under-utilization of resources. To address the problem, we investigate a general stochastic scheduling problem in the edge clouds, whose objective is to place the given amount of resources into the edge areas, and to maximize the scheduling revenue like the weighted sum of satisfied demands. We then propose an efficient algorithm by identifying the optimal conditions of nested subproblems. Experiments show that in the scenarios with general settings, the algorithm can achieve at least 97% average revenue of the traditional optimal algorithm with much lower time complexity, which can be further reduced through parallelization. The algorithm has the potential to be an effective supplement to the existing algorithms under the time-tense scheduling scenarios with a large number of resources.

Differential Evolution Algorithm Combined with Uncertainty Handling Techniques for Stochastic Reentrant Job Shop Scheduling Problem

This paper considers two kinds of stochastic reentrant job shop scheduling problems (SRJSSP), i.e., the SRJSSP with the maximum tardiness criterion and the SRJSSP with the makespan criterion. Owing to the NP-complete complexity of the considered RJSSPs, an effective differential evolutionary algorithm (DEA) combined with two uncertainty handling techniques, namely, DEA_UHT, is proposed to address these problems. Firstly, to reasonably control the computation cost, the optimal computing budget allocation technique (OCBAT) is applied for allocating limited computation budgets to assure reliable evaluation and identification for excellent solutions or individuals, and the hypothesis test technique (HTT) is added to execute a statistical comparison to reduce some unnecessary repeated evaluation. Secondly, a reentrant-largest-order-value rule is designed to convert the DEA’s individual (i.e., a continuous vector) to the SRJSSP’s solution (i.e., an operation permutation). Thirdly, a conventional active decoding scheme for the job shop scheduling problem is extended to decode the solution for obtaining the criterion value. Fourthly, an Insert-based exploitation strategy and an Interchange-based exploration strategy are devised to enhance DEA’s exploitation ability and exploration ability, respectively. Finally, the test results and comparisons manifest the effectiveness and robustness of the proposed DEA_UHT.

Scheduling on-site service deliveries to minimise the risk of missing appointment times

This paper studies the stochastic service task scheduling and vehicle routing problem for a telecommunication provider where each vehicle is driven by an engineer who performs service tasks at customer premises. There is an agreed time window for starting each service task. The service times and travel times are subject to uncertainties, e.g., task taking longer or shorter than expected, traffic situation causing delays. The problem is to schedule the tasks and route the vehicles to minimise the risks of missing appointment times. Models are presented to express the risks and describe the problem. Simulated annealing and tabu search are applied for generating an initial schedule of the day and for re-optimisation during the day based on real-time information updates. The study reported is based on the work in an industrial case. The stochastic nature of the travel times and durations of different task types as well as their distribution parameters have been obtained by applying data analytics on large sets of operations data. These are used in calculating the risks and in making scheduling and routing decisions. Real-time data updates sent back from the engineers are used for re-optimisation to adjust the schedule and routes so that the risks are kept at a lower level. Simulation results show that using risk minimisation as objective and re-optimisation during the day help enhance the on-time start of tasks. With this approach organisations can achieve robust task scheduling and improved customer satisfaction, and so become more competitive in the market.

A Monotone Approximate Dynamic Programming Approach for the Stochastic Scheduling, Allocation, and Inventory Replenishment Problem: Applications to Drone and Electric Vehicle Battery Swap Stations

There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to reduce these concerns that allow the swap of depleted for full batteries in minutes. We consider the problem of deriving actions at a battery swap station when explicitly considering the uncertain arrival of swap demand, battery degradation, and replacement. We model the operations at a battery swap station using a finite horizon Markov decision process model for the stochastic scheduling, allocation, and inventory replenishment problem (SAIRP), which determines when and how many batteries are charged, discharged, and replaced over time. We present theoretical proofs for the monotonicity of the value function and monotone structure of an optimal policy for special SAIRP cases. Because of the curses of dimensionality, we develop a new monotone approximate dynamic programming (ADP) method, which intelligently initializes a value function approximation using regression. In computational tests, we demonstrate the superior performance of the new regression-based monotone ADP method compared with exact methods and other monotone ADP methods. Furthermore, with the tests, we deduce policy insights for drone swap stations.

The effect of few historical data on the performance of sample average approximation method for operating room scheduling

AbstractWe model the scheduling problem of a single operating room for outpatient surgery, with uncertain case durations and an objective function comprising waiting time, idle time, and overtime costs. This stochastic scheduling problem has been studied in diverse forms. One of the most common approaches used is the sample average approximation (SAA). Our contribution is to study the use of SAA to solve this problem under few historical data using families of log t distributions with varying degrees of freedom. We analyze the results of the SAA method in terms of optimality convergence, the effect of the number of scenarios, and average computational time. Given the case sequence, computational results demonstrate that SAA with an adequate number of scenarios performs close to the exact method. For example, we find that the optimality gap, in units of proportional weighted time, is relatively small when 500 scenarios are used: 99% of the instances have an optimality gap of less than 2.6 7% (1.74%, 1.23%) when there are 3 (9, many) historical samples. Increasing the number of SAA scenarios improves performance, but is not critical when the case sequence is given. However, choosing the number of SAA scenarios becomes critical when the same method is used to choose among sequencing heuristics when there are few historical data. For example, when there are only three (nine, many) historical samples, 99% of the instances have less than 25.38% (13.15%, 6.87%) penalty in using SAA with 500 scenarios to choose the best sequencing heuristic.

Integrated stochastic bicriteria flow shop scheduling problem with preventive maintenance

In this paper, the concept of flexible and multiple preventive maintenance activities is introduced by reformulating classical bicriteria permutation flow shop scheduling problem into stochastic scheduling with objective to minimise system utilisation time with minimum makespan. The mathematical model is formulated to handle the uncertainties in job processing time and the time interval for machine maintenance. The problem of stochastic flow shop scheduling environment with maintenance activities, is NP-hard. Therefore, the advanced metaheuristic is implemented to solve large scale instances of referred problem. Extensive computational analysis is carried out to depict the superiority of proposed metaheuristic in terms of effectiveness and efficacy.

Effective Proactive Policies for the Stochastic Resource-Constrained Project Scheduling Problem with Inventory Consideration

Effective Proactive Policies for the Stochastic Resource-Constrained Project Scheduling Problem with Inventory Consideration

The Similarity Index to Decompose Two-Stage Stochastic Scheduling Problems

Two-stage stochastic scheduling problems often involve a large number of continuous and discrete variables, so fnding solutions in short time periods is challenging and computationally expensive. However, for online or closed-loop scheduling implementations, optimal or near-optimal solutions are required in real-time. We propose a decomposition method based on the so-called Similarity Index (SI). An iterative procedure is set up so that each sub-problem (corresponding to a scenario) is solved independently, aiming to optimize the original cost function while maximizing the similarity of the frst-stage variables among the scenarios solutions. The SI is incorporated into each subproblem cost function, multiplied by a penalty parameter that is updated in each iteration until reaching complete similarity in the frst-stage variables among all subproblems. The method is applied to schedule production and maintenance tasks in an evaporation network. The tests show that signifcant benefts are expected in terms of computational demands as the number of scenarios increases.

A simulation-optimization framework for generating dynamic dispatching rules for stochastic job shop with earliness and tardiness penalties

Most of real-world problems regarding production and manufacturing contain stochastic parameters. In this research, job shop scheduling problem with stochastic process times and weighted earliness-tardiness objective function is considered. When machines are freed in the course of manufacturing, a job has to be selected from the line and passed on the machine. In deterministic job shop scheduling, the selection process is static. In the stochastic variants however, dynamic or real-time dispatching rules may be used. The goal of this paper is to develop a solution method for stochastic job shop scheduling problem that delivers dynamic and global dispatching rules that use information pertaining to the entire shop floor. In order to achieve this, the problem is converted to a near-Markov decision process that comprises an alternate sequence of states (machines becoming free) and actions (selecting a job). Using simulation and ant colony, a database of states is generated and a meaningful pheromone trail for each state is formed gradually. The pheromones act as a memory mechanism and, in combination with a heuristic based on the Central Limit Theorem, comprise the dispatching rule. Efficiency of this approach is investigated through extensive simulation. Results show an average of 92% cost reduction in comparison with the random dispatching rule. Moreover, the approach yields better results in congested scheduling systems.

On the optimality of the earliest due date rule in stochastic scheduling and in queueing

We consider an environment with m servers in parallel and n jobs. The n jobs have i.i.d. exponentially distributed processing requirements. The servers operate at different speeds and preemptions are allowed. The jobs have random release times that are not known in advance, but whenever a job is released, its due date is fixed and becomes known to the scheduler. We first consider three stochastic scheduling problems with three due date related objective functions and consider variations of the Earliest Due Date (EDD) rule, including the preemptive policy that at any point in time assigns the job with the Earliest Due Date to the Fastest Server (EDD-FS). Our optimality results turn out to be examples of stochastic scheduling problems that have relatively simple priority rules that are optimal while their deterministic counterparts do not allow such simple priority rules to be optimal. We furthermore extend our results to include a priority queueing model with m exponential servers that operate at different speeds and preemptions being allowed. The jobs arrive according to an arbitrary renewal process, and we assume that the utilization factor of the system is less than 1. Upon a job’s release the time difference between its due date and release time is set by the draw of a random variable from a given distribution. At a job’s release time, its due date is then immediately fixed and known while its actual processing time only becomes known upon its service completion. We show that for this priority queueing model the preemptive EDD-FS rule also minimizes the limit of several due date related objective functions as the number of jobs converges to infinity.

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.

Solving real-size stochastic railway rapid transit network construction scheduling problems

We propose an iterated greedy matheuristic for efficiently solving stochastic railway rapid transit transportation network construction scheduling problems, where both the construction duration of the segments and the passenger demand rate of increase are stochastic. The network construction scheduling problem consists of sequencing the construction of lines of a urban transportation network with the aim of maximizing the discounted long-term profit of the project. This problem can be described as a resource-constrained project scheduling problem, where both the budget and the available construction equipment act as resources influencing the schedule. We consider that partial lines can be put into operation as soon as they are finished, thus benefiting users with a partial and quick usage of the network infrastructure. This assumption makes both the costs and the revenues dependent on the schedule. After analyzing some characteristics of the best solutions, we propose an iterated greedy matheuristic for solving the stochastic version of real-size network construction scheduling problems. To illustrate our methodology we apply the algorithm to the construction of the full metro network of the city of Seville.

A simulation-based modified backtracking search algorithm for multi-objective stochastic flexible job shop scheduling problem with worker flexibility

The flexible shop scheduling problem (FJSSP) has been an extensively studied and applied manufacturing systems in recent years. However, research has mostly focused on addressing the FJSSP in its basic form by relaxing several practical constraints. In this work, we consider FJSSP with worker flexibility and uncertain processing times. A simheuristic approach addresses the multi-objective stochastic FJSSP with worker flexibility, minimizing the expected makespan and standard deviation of makespan. This approach integrates the Monte Carlo simulation (MCS) into the proposed multi-objective modified Backtracking Search Algorithm (MBSA) framework. MBSA employs an effective population initialization strategy, dynamic mutation and crossover operators, and a transfer criterion. MCS evaluates’ promising’ solutions generated by MBSA to guide the search process. Extensive experiments are performed considering three FJSSP benchmark data sets. At first, the best parameters for the MBSA are identified using the Taguchi method. Then, for the deterministic variant of the problem, MBSA is compared with two other metaheuristics to demonstrate its effectiveness. Finally, the stochastic variant is investigated considering two factors: variation level and the probability distribution of the processing times. Computational results statistically show a significant effect of these factors on the objectives, demonstrating the importance of selecting an appropriate probability distribution in an uncertain environment.