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Forecasting policies for scheduling a stochastic due date job shop
International Journal of Production Research
Abstract
This work studies the problem of scheduling a production plant subject to uncertain processing times that may arise, e.g. from the variability of human labour or the possibility of machine breakdowns. The problem is modelled as a job shop with random processing times, where the expected total weighted tardiness must be minimized. A heuristic is proposed that amplifies the expected processing times by a selected factor, which are used as input for a deterministic scheduling algorithm. The quality of a particular solution is measured using a risk averse penalty function combining the expected deviation and the worst case deviation from the optimal schedule. Computational tests show that the technique improves the performance of the deterministic algorithm by 25% when compared with using the unscaled expected processing times as inputs.
... In addition to these studies, the total earliness/tardiness problem in the job shop was evaluated by Bollapragada and Sadeh (1996). The idea of minimising total tardiness in a job shop considering uncertain parameters (e.g., processing times) was first applied by Singer (2000). Afterwards, multiple studies have been done in terms of scheduling problem with uncertain parameters. ...
... In this method, the optimisation problem is solved assuming the worst possible outcome for each uncertain data which leads to excessive conservative solution. To overcome the disadvantage of the extremely conservative solution of the RC optimisation with box uncertainty, Ben-Tal and Nemirovski (1998, 2000 proposed the related uncertain linear optimisation problem that consists of collection of linear optimisation problems which is defined as follows: ...
In real world production systems, uncertain events such as random machine breakdown and processing time can occur anytime. These events lead to disruption of normal activities and consequently invalidate the initial schedule. Considering uncertainty in the scheduling process enables organisations to resume their activities effectively after uncertain events occur. The focus of this paper is proactive scheduling approach with an objective of minimising the total cost (lateness/earliness penalty and tooling cost). Robust optimisation is used to solve the scheduling problem considering processing time, setup times and tooling cost as uncertain parameters. Numerous scenarios are solved using data from local job shop. Multiple performance measurement criteria are evaluated to assess the significance of results obtained using robust and deterministic models. Design of experiment (DOE) has been implemented to evaluate the effects of different factors on the total cost and computational times.
... In addition to these studies, the total earliness/tardiness problem in the job shop was evaluated by Bollapragada and Sadeh (1996). The idea of minimising total tardiness in a job shop considering uncertain parameters (e.g., processing times) was first applied by Singer (2000). Afterwards, multiple studies have been done in terms of scheduling problem with uncertain parameters. ...
... In this method, the optimisation problem is solved assuming the worst possible outcome for each uncertain data which leads to excessive conservative solution. To overcome the disadvantage of the extremely conservative solution of the RC optimisation with box uncertainty, Ben-Tal and Nemirovski (1998, 2000 proposed the related uncertain linear optimisation problem that consists of collection of linear optimisation problems which is defined as follows: ...
... Processing times in the JSSP with batching is determined by the number of similar products which are produced simultaneously as part of the same operation (Petrovic et al. 2005; Potts et al. 1998; and Potts and Kovalyov 2000). Minimizing a function of job due dates, as in the JSSP with due dates, indirectly places restrictions on the processing times of jobs (Essafi et al. 2008 and Singer and Pinedo 1998). Operation starting and completion times in an expanded JSSP are restricted by release dates, due dates and technological enabling constraints ( Liang 2001 and Zhao et al. 2005). ...
... The dynamic JSSP and stochastic JSSP belong to the final group since both of these variations allow the scheduler to take into account a certain amount of uncertainty in the scheduling process. The dynamic JSSP incorporates uncertainty with respect to the number of jobs and the release dates associated with the jobs which are to be scheduled (Aydin and Oztemel 2000 and Qi et al. 2000 ), while the stochastic JSSP focuses on incorporating uncertainty into the process time estimates (Lei and Xiong 2007; Singer 2000; and Yoshitomi and Yamaguchi 2003). From the classification inFig. ...
This paper investigates the application of particle swarm optimization (PSO) to the multi-objective flexible job shop scheduling
problem with sequence-dependent set-up times, auxiliary resources and machine down time. To achieve this goal, alternative
particle representations and problem mapping mechanisms were implemented within the PSO paradigm. This resulted in the development
of four PSO-based heuristics. Benchmarking on real customer data indicated that using the priority-based representation resulted
in a significant performance improvement over the existing rule-based algorithms commonly used to solve this problem. Additional
investigation into algorithm scalability led to the development of a priority-based differential evolution algorithm. Apart
from the academic significance of the paper, the benefit of an improved production schedule can be generalized to include
cost reduction, customer satisfaction, improved profitability, and overall competitive advantage.
... The general procedure of heuristic decision-making rules is used in situations when several jobs are ready to be served on one machine [4][5][6]. Flow Shop Scheduling (FSS) with random processing times has been studied by Singer [3] to minimize the expected total weighted tardiness. Moreover, a simulation-based genetic algorithm for solving a job shop with random processing times has been proposed by Yoshitomi [7] in order to minimize the expected makespan. ...
In this study, a job shop scheduling optimization model under risk has been developed to minimize the make span. This model has been built using Microsoft Excel spreadsheets and solved using @Risk solver. A set of experiments have been also conducted to examine the accuracy of the model and its effectiveness has been proven.
... Optimal rules have also been developed by Foley and Suresh (1984) and Pinedo (1982) to minimize the expected makespan for the m-machine flow shop problem with stochasticity in processing times. For work in stochastic job shops, see Golenko-Ginzburg et al. (1995, 2002, Singer (2000), Luh et al. (1999), Kutanoglu and Sabuncuoglu, (2001), Yoshitomi (2002), Lai et al. (2004), andTavakkoli-Moghaddam et al. (2005). ...
In this chapter, we address the problem of optimally routing and sequencing a set of jobs over a network of flexible machines for the objective of minimizing the sum of completion times and the cost incurred, assuming stochastic job processing times. This problem is of particular interest for the production control in high investment, low volume manufacturing environments, such as pilot-fabrication of microelectromechanical systems (MEMS) devices. We model this problem as a two-stage stochastic program with recourse, where the first-stage decision variables are binary and the second-stage variables are continuous. This basic formulation lacks relatively complete recourse due to infeasibilities that are caused by the presence of re-entrant flows in the processing routes, and also because of potential deadlocks that result from the first-stage routing and sequencing decisions. We use the expected processing times of operations to enhance the formulation of the first-stage problem, resulting in good linear programming bounds and inducing feasibility for the second-stage problem. In addition, we develop valid inequalities for the first-stage problem to further tighten its formulation. Experimental results are presented to demonstrate the effectiveness of using these strategies within a decomposition algorithm (the L-shaped method) to solve the underlying stochastic program. In addition, we present heuristic methods to handle large-sized instances of this problem and provide related computational results.
... Gourgand et al. (2003) have proposed a recursive algorithm based on a Markov chain to compute the expected makespan in a stochastic flow shop. Singer (2000) has considered a stochastic job shop with random processing times and individual due dates. Tavakkoli-Moghaddam et al. (2005) studied job shop with random operations they develop a hybrid method for solving the problem. ...
In this paper, we study an open shop scheduling (OSS) problem subject to uncertain release dates and processing times. Open shop scheduling problems are one of shop problems in sequence and scheduling problems. The objective is to find the sequence of jobs and machines which minimises total completion times of jobs. We first formulate the problem as a stochastic programming model, and then we employ deterministic mixed binary integer linear programming to solve the linear programming solver. In this paper, we assumed the processing times and release times of jobs to be uncertain, but follow a specific probability function. It is clear that random variables are independent. We use GAMS software to solve it. The superiority and advantages of this study over previous studies are discussed.
... The aim is to find a minimum set of schedules which contains at least one optimal schedule for any realization of the random processing times. Singer [14] presents a heuristic which amplifies the expected processing times by a factor and then applies a deterministic scheduling algorithm. Recently, Lei proposes a genetic algorithm for minimizing makespan in a stochastic job shop with machine breakdowns and non-resumable jobs [15]. ...
Due to the influence of unpredictable random events, the processing time of each operation should be treated as random variables if we aim at a robust production schedule. However, compared with the extensive research on the deterministic model, the stochastic job shop scheduling problem (SJSSP) has not received sufficient attention. In this paper, we propose an artificial bee colony (ABC) algorithm for SJSSP with the objective of minimizing the maximum lateness (which is an index of service quality). First, we propose a performance estimate for preliminary screening of the candidate solutions. Then, the K-armed bandit model is utilized for reducing the computational burden in the exact evaluation (through Monte Carlo simulation) process. Finally, the computational results on different-scale test problems validate the effectiveness and efficiency of the proposed approach.
... McKay et al. (2000) introduce a dynamic rescheduling approach that sub-optimizes for a period of time to allow the manufacturing situation a chance to re-stabilize and then progressively optimizes. Singer (2000) applies this idea to minimizing total tardiness in a job shop with uncertain processing times, obtaining similar results. ...
We review the literature on executing production schedules in the presence of unforeseen disruptions on the shop floor. We discuss a number of issues related to problem formulation, and discuss the functions of the production schedule in the organization and provide a taxonomy of the different types of uncertainty faced by scheduling algorithms. We then review previous research relative to these issues, and suggest a number of directions for future work in this area.
... McKay et al. [6] developed an aversion dynamics heuristic that prevents scheduling of expensive jobs after a machine repair. Singer [10] solved a job shop problem with uncertain processing times caused by variability of human labour or machine breakdowns. Leon et al. [5] analysed job shop schedule delays caused by disruptions and proposed surrogate measures for delay estimation. ...
In this paper, a new fuzzy logic-based approach to production scheduling in the presence of uncertain disruptions is presented.
The approach is applied to a real-life problem of a pottery company where the uncertain disruption considered is glaze shortage.
This disruption is defined by two parameters that are specified imprecisely: number of glaze shortage occurrences and glaze
delivery time. They are modelled and combined using standard fuzzy sets and level 2 fuzzy sets, respectively. A predictive
schedule is generated in such a way as to absorb the impact of the fuzzy glaze shortage disruption. The schedule performance
measure used is makespan. Two measures of predictability are defined: the average deviation and the standard deviation of
the completion time of the last job produced on each machine. In order to analyse the performance of the predictive schedule,
a new simulation tool FPSSIM is developed and implemented. Various tests carried out show that the predictive schedules have
good performance in the presence of uncertain disruptions.
In dual-resource constrained job shop scheduling, jobs have to be assigned to workers and machines. While the problem is notoriously hard in terms of computational complexity, additional practical difficulties arise from data uncertainty and worker efficiency variation. In this paper, we propose a methodological pipeline combining mathematical optimization, simulation, and data analysis to cope with these aspects over time. Accounting for uncertain worker processing times, we employ an iterative two-stage optimization-simulation approach: A first-stage optimization model determines an assignment of workers to jobs; in the second stage, the scheduling of this assignment is evaluated operationally using sampled realizations of worker processing times. Both stages are executed in an alternating fashion until no further improvement is possible in the average realized makespan. At the end of a work day, realized worker efficiencies are then measured in a slacks-based data envelopment analysis on the operations level. Workers learn about their individual efficiency and are prompted to reduce inefficiencies. The resulting overall methodology not only provides robustified schedules for dual-resource constrained job shops under uncertainty, but also reduces the impact of uncertainty over time by motivating workers to operate on the efficient frontier. Computational results are conducted in several settings with both heuristic and exact solution procedures for the second-stage dual-resource constrained job shop scheduling problem. The results demonstrate the versatility of the outline with respect to addressing uncertainty and worker inefficiency.
The Job shop scheduling problems with stochastic processing times under machine-worker dual resource constraints is studied. Considering the difference in worker proficiency and the insufficient number of workers, a robust scheduling approach is adopted, and then the machine-worker dual-resource constrained robust Job shop scheduling problems model (DR-RJSSP) is formulated. Because of the requirements of DR-RJSSP for workers' rational assignment and bi-objective optimization, a heuristic based on a two-stage assignment strategy is proposed, which can minimize the random disturbances of the processing times as well as its impact on scheduling efficiency. Thereafter, a multi-objective hybrid estimation of distribution algorithm is employed to solve the DR-RJSSP. Thereby, the solution set considers both the performance and the robustness of the schedule can be obtained. At last, the proposed two-stage assignment strategy(TSAS) is compared with the proficiency-based assignment strategy as well as the machine-worker randomly assigned strategy through simulation experiments. Finally, eight standard instances and a problem instance obtained from a manufacturing company are employed. According to the simulation results, the Pareto optimization performance of the proposed TSAS and its effectiveness to solve the Job shop scheduling problem of the actual manufacturing system are verified. Key words：dual-resource；robust job shop scheduling problems；two-stage assignment strategy；robustness 0 前言 *
Job shop scheduling problem is very important one in real application of many kind of industries. In the real world applications, there exists many different kinds of disruptions with different sizes. In this situation, beyond the optimality of the final solution, its ability to absorb disruptions is vital, so that the final solution remains feasible in the case of occurring predicted disruptions. In this paper a robust job shop scheduling problem under disruptions is considered. It is intended to generate robust schedules which are able to absorb a predefined range of disruptions. For this reason, two robustness indices are proposed and the related formulas for computing the required buffer times to reach the desired robustness level are proposed. For this purpose, four methods are proposed to solve the variant defined robust job shop scheduling problem, including (1) a mathematical model, (2) a branch and bound algorithm, (3) a beam search algorithm, and (4) a meta-heuristic algorithm based on the particle swarm optimization (PSO) method. The first and second methods result in optimum solution. As the size of the problem increases, the required time to find the optimum solutions raises, so that no solutions can be achieved in rational amount of time, e.g. one hour. Therefore, the third and fourth methods are proposed to find good solutions even for large-scale problem in a limited amount of time. Finally, the algorithms are compared using some randomly generated instances. The results show that each algorithm can outperform the others in different conditions.
In real-world manufacturing systems, the processing of jobs is frequently affected by various unpredictable events. However, compared with the extensive research for the deterministic model, study on the random factors in job shop scheduling has not received sufficient attention. In this paper, we propose a hybrid differential evolution (DE) algorithm for the job shop scheduling problem with random processing times under the objective of minimizing the expected total tardiness (a measure for service quality). First, we propose a performance estimate for roughly comparing the quality of candidate solutions. Then, a parameter perturbation algorithm is applied as a local search module for accelerating the convergence of DE. Finally, the K-armed bandit model is utilized for reducing the computational burden in the exact evaluation of solutions based on simulation. The computational results on different-scale test problems validate the effectiveness and efficiency of the proposed approach.
Real-world manufacturing systems are influenced by various random factors, which must be taken into consideration in order to obtain an effective schedule. However, compared with the extensive research on the deterministic model, the stochastic job shop scheduling problem (SJSSP) has not been sufficiently studied. In this paper, we propose a two-stage particle swarm optimization (PSO) algorithm for SJSSP with the objective of minimizing the expected total weighted tardiness. In the first-stage PSO, a performance estimate is used for quick evaluation of the solutions, and a local search procedure is embedded for accelerating the convergence to promising regions in the solution space. The second-stage PSO continues the search process, but applies a more accurate solution evaluation policy, i.e. the Monte Carlo simulation. In order to reduce the computational burden, the optimal computing budget allocation (OCBA) method is used in this stage. Finally, the computational results on different-scale test problems validate the effectiveness of the proposed approach.
Effective manpower allocation is among the most vital and complicated decisions for most companies on account of imprecise nature of input information of the problem. This paper presents a novel combination of the chance-constrained programming and the global criterion model for manpower allocation problem that is called chance-constrained global criterion. The proposed model is a deterministic equivalent for the multi-objective stochastic problem of manpower allocation. To illustrate the model, a tri-objective stochastic manpower allocation case problem for determining optimal number of manpower in a job-shop manufacturing system is formulated and solved, and then the competitive advantages of the model are discussed. To have a better judgment on the validity and performance efficiency of the model, 20 different problems are generated and solved. The results show that increasing the size of problem do not have much effect on the number of iterations required for finding the optimal solution, and this model decreases complicacy in modeling the problem.
This paper addresses the problem of scheduling stochastic job shop subject to breakdown. A relative good and efficient genetic algorithm (GA) is proposed for the problem with normal processing time, resumable jobs and the objective of minimizing makespan. Some operations of normal processing times are defined to build the schedule. In the GA, an operation-based representation is used, a discrete event driven decoding method is presented to deal with breakdown and repair, and generalized order crossover and swap are applied to produce new solutions. Genetic operators are separate from the handling of random breakdown. The GA is applied to some test problems and compared with a simulated annealing (SA) and a particle swarm optimization (PSO). The computational results show the GA performs better than PSO and SA for stochastic job shop scheduling problems considered.
Industrial systems are constantly subject to random events with inevitable uncertainties in production factors, especially in processing times. Due to this stochastic nature, selecting appropriate dispatching rules has become a major issue in practical problems. However, previous research implies that using one dispatching rule does not necessarily yield an optimal schedule. Therefore, a new algorithm is proposed based on computer simulation and artificial neural networks (ANNs) to select the optimal dispatching rule for each machine from a set of rules in order to minimise the makespan in stochastic job shop scheduling problems (SJSSPs). The algorithm contributes to the previous work on job shop scheduling in three significant ways: (1) to the best of our knowledge it is the first time that an approach based on computer simulation and ANNs is proposed to select dispatching rules; (2) non-identical dispatching rules are considered for machines under stochastic environment; and (3) the algorithm is capable of finding the optimal solution of SJSSPs since it evaluates all possible solutions. The performance of the proposed algorithm is compared with computer simulation methods by replicating comprehensive simulation experiments. Extensive computational results for job shops with five and six machines indicate the superiority of the new algorithm compared to previous studies in the literature.
This paper studies a dynamic production system where multiple products must visit stations where inventories are constrained
by maximum and minimum sojourn times with neither negative flow nor backlog being allowed. A resource availability constraint
limits the aggregate throughput of the stations. The objective is to minimize the sum of flow and inventory cost. The problem
is broken down into several single-product serial systems that serve as subroutines of a Lagrangian relaxation routine. This
model is implemented in a spreadsheet so that it can be used by the officials of a Chilean institution for planning the operations
and defining the optimal allocation of resources.
We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.
With the Simulation based Job Shop Production Analyser a powerful analysis tool has been developed by use of modern Java and database technology. This straight forward approach offers the possibility to model the production flow of even complex job shop production systems efficiently. It provides a professional decision base for the daily operative production business. System integration, automated modelling from the database and very fast simulation runs are key features of this approach. As an industrial application for the Job Shop Production Analyser the simulation of a complex semiconductor production plant is shown.
In the recent past, a great deal of time and effort has been devoted to the development of job shop schedules. These schedules
are able to cope with the dynamic and stochastic nature of job shops that consist of the uncertainties both at the planning
stages and on on-line execution. Deviations from predictive schedules occur when the job shop experiences both external disturbances
(e.g. urgent job arrivals) and internal disruptions (e.g. machine breakdowns). To avoid complete rescheduling of the job shop
a repair and recovery strategy for the schedule becomes essential. This paper provides a comprehensive review of the literature
on the reactive recovery of job shop schedules and proposes further research work in this area.
In this paper, we study a group shop scheduling (GSS) problem subject to uncertain release dates and processing times. The
GSS problem is a general formulation including the other shop scheduling problems such as the flow shop, the job shop, and
the open shop scheduling problems. The objective is to find a job schedule which minimizes the total weighted completion time.
We solve this problem based on the chance-constrained programming. First, the problem is formulated in a form of stochastic
programming and then prepared in a form of deterministic mixed binary integer linear programming such that it can be solved
by a linear programming solver. To solve the problem efficiently, we develop an efficient hybrid method. Exploiting a heuristic
algorithm in order to satisfy the constraints, an ant colony optimization algorithm is applied to construct high-quality solutions
to the problem. The proposed approach is tested on instances where the random variables are normally, uniformly, or exponentially
distributed.
The problem of scheduling stochastic job shop subject to breakdown is seldom considered. This paper proposes an efficient
genetic algorithm (GA) for the problem with exponential processing time and non-resumable jobs. The objective is to minimize the stochastic makespan itself. In the proposed GA, a novel random key representation
is suggested to represent the schedule of the problem and a discrete event-driven decoding method is applied to build the
schedule and handle breakdown. Probability stochastic order and the addition operation of exponential random variables are
also used to calculate the objective value. The proposed GA is applied to some test problems and compared with a simulated annealing and a particle swarm optimization. The computational results show the effectiveness of the GA and its promising advantage on stochastic scheduling.
KeywordsStochastic job shop scheduling–Breakdown–Stochastic order–Random key representation–Discrete event driven
This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.
For a container terminal system, efficient berth and quay crane (QC) schedules have great impact on the improvement of both operation efficiency and customer satisfaction. In this paper we address both berth and quay crane scheduling problems in a simultaneous way, with uncertainty of container handling time. The berth is of discrete type and vessels arrive dynamically with different service priorities. Besides we assume QCs can move to other berths before finishing processing on currently assigned vessels, adding more flexibility to the terminal system. A mixed integer programming model is established, and a simulation based Genetic Algorithm (GA) search procedure is applied to generate robust berth and QC schedule proactively. Computational experiment shows the satisfied performance of our developed algorithm.
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