Processing Time Uncertainty Research Articles

Multi-level job scheduling under processing time uncertainty

Abstract This study deals with a multi-level job scheduling problem in a single machine under processing time uncertainty. For the objectives of minimizing the total weighted tardiness of orders and the schedule deviation of the realized schedule from the baseline schedule, two surrogate measures for each of the two objectives are proposed to cope with the processing time uncertainty in the baseline scheduling phase. For the suggested surrogate measures, several optimal solution properties are developed to reduce the size of the solution space. Then, by using the solution properties a heuristic algorithm with two different order prioritization rules and a metaheuristic algorithm based on the discrete particle swarm optimization are developed for the order sequencing problem. Also, an iterative job sequencing algorithm is developed for the job sequencing problem that can be used for a given order sequence. From a series of computational experiments with a number of randomly generated problem instances with multiple bills of materials and normally distributed processing times of items, it is identified that the suggested metaheuristic algorithm with or without the iterative job sequencing algorithm shows good performance compared with the heuristic algorithm.

Minimizing the weighted sum of completion times under processing time uncertainty

We address the robust counterpart of a classical single machine scheduling problem by considering a budgeted uncertainty and an ellipsoidal uncertainty. We prove that the problem is NP-hard for arbitrary ellipsoidal uncertainty sets. Then, a mixed-integer linear programming reformulations and a second order cone programming reformulations are provided. We assess the reformulations on randomly generated instances, comparing them with branch-and-cut algorithms.

Profit-oriented partial disassembly line design: dealing with hazardous parts and task processing times uncertainty

This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature.

Multistage Adaptive Optimization for Steelmaking and Continuous Casting Scheduling under Processing Time Uncertainty

The scheduling of steelmaking and continuous casting process is an important exercise for the steel industry. Uncertain processing time can significantly affect the schedule performance. To tackle this uncertainty, a multistage adaptive optimization method is proposed in this work. The proposed method can effectively handle a large number of uncertain parameters and generate an adjustable scheduling policy for online use. The method is flexible in choosing a robust objective or an expectation objective. Results demonstrate that the stochastic adaptive solution is less conservative and can be employed for optimal scheduling of the steelmaking process.

Simulation-based optimization approach for simultaneous scheduling of vehicles and machines with processing time uncertainty in FMS

Many stochastic factors, such as vehicle congestion, deadlock or conflict, or stochastic processing time have significant effects on performance in scheduling problem in flexible manufacturing system (FMS). This paper proposed a simulation-based optimization, L-GAOCBA, to address the simultaneous scheduling of vehicles and machines in FMS. The simulation model is constructed to evaluate the performance of scheduling decision, and includes stochastic elements, such as vehicle congestion, deadlock, and uncertain processing time. Genetic algorithm (GA) combined with local search, L-GA, plays important role in exploring the good design alternative based on simulation output. Optimal computing budget allocation (OCBA) embedded with L-GA is used to allocate the number of replications for reducing simulation replications. The design of experiments is used to analyze and set the parameters of L-GA and OCBA. This study shows that L-GAOCBA is superior for enhancing solution quality and search efficiency.

Congestion game scheduling for virtual drug screening optimization.

In virtual drug screening, the chemical diversity of hits is an important factor, along with their predicted activity. Moreover, interim results are of interest for directing the further research, and their diversity is also desirable. In this paper, we consider a problem of obtaining a diverse set of virtual screening hits in a short time. To this end, we propose a mathematical model of task scheduling for virtual drug screening in high-performance computational systems as a congestion game between computational nodes to find the equilibrium solutions for best balancing the number of interim hits with their chemical diversity. The model considers the heterogeneous environment with workload uncertainty, processing time uncertainty, and limited knowledge about the input dataset structure. We perform computational experiments and evaluate the performance of the developed approach considering organic molecules database GDB-9. The used set of molecules is rich enough to demonstrate the feasibility and practicability of proposed solutions. We compare the algorithm with two known heuristics used in practice and observe that game-based scheduling outperforms them by the hit discovery rate and chemical diversity at earlier steps. Based on these results, we use a social utility metric for assessing the efficiency of our equilibrium solutions and show that they reach greatest values.

MODELING, OPTIMISATION AND ANALYSIS OF RE-ENTRANT FLOWSHOP JOB SCHEDULING WITH FUZZY PROCESSING TIMES

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

Extending the boundaries between scheduling and dispatching: hedging and rescheduling techniques

While deterministic scheduling models have been well studied, the use of these models is not well documented in manufacturing environments. Previous research has indicated that deterministic scheduling approaches quickly lose their advantage compared to dispatching rules when processing time uncertainty is present. This research presents the case of a Printed Wiring Board Manufacturer’s drilling operation, which is a group of unrelated parallel machines. The manufacturer wishes to minimise makespan, number of late jobs, total overtime, average machine finishing time and machine utilisation when stochastic uncertainty is present. While deterministic scheduling has been shown to be a good solution approach when processing time variability is low, this research attempts to extend the boundaries in which scheduling is useful by investigating job and machine hedges as well as periodic and event driven rescheduling policies. The success of the approach is evaluated using a simulation model to evaluate the performance over a number of sequential schedules under various distributional assumptions.

A Two-Phase Soft Optimization Method for the Uncertain Scheduling Problem in the Steelmaking Industry

In this paper, an uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) production system is investigated. For the practical SCC production system, it is difficult to obtain a schedule with better performance using traditional deterministic scheduling methods since there exists uncertainty in processing times. According to the analysis on characteristics of the uncertain SCC scheduling problem (SCCSP), we construct a soft-form schedule which includes slack ratios as characteristic indexes and the job sequence at the casting stage as key decision variables to cope with the uncertainty in processing times, and propose a two-phase soft optimization method to solve the uncertain SCCSP with the just-in-time and the waiting time objectives under the break probability. In the first phase, the continuous estimation distribution algorithm (EDA) with the ordinal optimization policy is proposed to optimize slack ratios under the chance constraint, in which the optimal computing budget allocation with constrained optimization is applied to reduce the computational burden. In the second phase, based on the above optimized characteristic indexes, the discrete EDA with a local search procedure is proposed to optimize the job sequence at the casting stage. Finally, computational experiments with various scales and noise levels are performed to validate the effectiveness of the proposed algorithm.

A hybrid multi-objective evolutionary algorithm approach for handling sequence- and machine-dependent set-up times in unrelated parallel machine scheduling problem

This paper addresses a fuzzy mixed-integer non-linear programming (FMINLP) model by considering machine-dependent and job-sequence-dependent set-up times that minimize the total completion time, the number of tardy jobs, the total flow time and the machine load variation in the context of unrelated parallel machine scheduling (UPMS) problem. The above-mentioned multi-objectives were considered based on non-zero ready times, machine- and sequence-dependent set-up times and secondary resource constraints for jobs. The proposed approach considers unrelated parallel machines with inherent uncertainty in processing times and due dates. Since the problem is shown to be NP-hard in nature, it is a challenging task to find the optimal/near-optimal solutions for conflicting objectives simultaneously in a reasonable time. Therefore, we introduced a new multi-objective-based evolutionary artificial immune non-dominated sorting genetic algorithm (AI-NSGA-II) to resolve the above-mentioned complex problem. The performance of the proposed multi-objective AI-NSGA-II algorithm has been compared to that of multi-objective particle swarm optimization (MOPSO) and conventional non-dominated sorting genetic algorithm (CNSGA-II), and it is found that the proposed multi-objective-based hybrid meta-heuristic produces high-quality solutions. Finally, the results obtained from benchmark instances and randomly generated instances as test problems evince the robust performance of the proposed multi-objective algorithm.

Minimizing energy consumption and tardiness penalty for fuzzy flow shop scheduling with state-dependent setup time

This paper addresses a flow shop scheduling problem in a production system where the machine setup times depend on their prior states. State-dependent setup times exist widely in thermal facilities such as boilers and furnaces. The fuzzy set theory is introduced to describe the uncertainty of processing times and due dates in this study. The goal of the proposed fuzzy flow shop scheduling problem is to dispatch jobs to the machines and to determine the job sequence and state transition of each machine to minimize energy consumption and tardiness. To most efficiently determine the impact of uncertainty, the problem is formulated based on accurate operations of fuzzy numbers, which differ from approximate calculations in the existing literature on scheduling. To solve the problem, two common pattern matching schemes and heuristics are proposed to be combined with the classical genetic algorithm. Computational experiments show that the proposed GA performs better than the random key GA method, especially for large problems. The numerical results also provide practical implications for the proposed problem. The state-dependent setup time constraint significantly influences the scheduling results. In addition, the objective can be improved by reducing the uncertainty of processing times and due dates.

A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs

We consider a single-machine scheduling problem with an outsourcing option in an environment where the processing time and outsourcing cost are uncertain. The performance measure is the total cost of processing some jobs in-house and outsourcing the rest. The cost of processing in-house jobs is measured as the total weighted completion time, which can be considered the operating cost. The uncertainty is described through either an interval or a discrete scenario. The objective is to minimize the maximum deviation from the optimal cost of each scenario. Since the deterministic version is known to be NP-hard, we focus on two special cases, one in which all jobs have identical weights and the other in which all jobs have identical processing times. We analyze the computational complexity of each case and present the conditions that make them polynomially solvable.

A Cardinality-constrained Approach for Robust Machine Loading Problems

The Machine Loading Problem (MLP) refers to the allocation of operative tasks and tools to machines for the production of parts. Since the uncertainty of processing times might affect the quality of the solution, this paper proposes a robust formulation of an MLP, based on the cardinality-constrained approach, to evaluate the optimal solution in the presence of a given number of fluctuations of the actual processing time with respect to the nominal one. The applicability of the model in the practice has been tested on a case study.

Research on scheduling and optimization under uncertain conditions in panel block production line in shipbuilding

Based on non-completely hybrid flow line scheduling of panel block in shipbuilding, several uncertain factors influencing the problem were analyzed in a real environment, and a nonlinear integer programming model was built for each sub-scheduling problem. To narrow the difference between theory and application, rolling horizon and rescheduling methods are proposed. Moreover, with respect to the uncertainty of processing time, arriving time and due time, we take the minimizing of the early and delayed delivery costs as the objective, and establish an evaluation with a global penalty function. Finally, numerical experiments and a simulation analysis were undertaken to demonstrate the effectiveness of the model and algorithm.

Artificial bee colony algorithm for scheduling and rescheduling fuzzy flexible job shop problem with new job insertion

This study addresses flexible job shop scheduling problem (FJSP) with two constraints, namely fuzzy processing time and new job insertion. The uncertainty of processing time and new job insertion are two scheduling related characteristics in remanufacturing. Fuzzy processing time is used to describe the uncertainty in processing time. Rescheduling operator is executed when new job(s) is (are) inserted into the schedule currently being executed. A two-stage artificial bee colony (TABC) algorithm with several improvements is proposed to solve FJSP with fuzzy processing time and new job insertion constraints. Also, several new solution generation methods and improvement strategies are proposed and compared with each other. The objective is to minimize maximum fuzzy completion time. Eight instances from remanufacturing are solved using the proposed TABC algorithm. The proposed improvement strategies are compared and discussed in detail. Two proposed ABC algorithms with the best performances are compared against seven existing algorithms over by five benchmark cases. The optimization results and comparisons show the competitiveness of the proposed TABC algorithm for solving FJSP.

Mathematical modeling and a memetic algorithm for the integration of process planning and scheduling considering uncertain processing times

The integration of process planning and scheduling is important for an efficient utilization of manufacturing resources. However, the focus of existing works is mainly on deterministic constraints of jobs. This article proposes a novel memetic algorithm for the integrated process planning and scheduling problem with processing time uncertainty based on processing time scenarios. First, a mathematical model for the stochastic integrated process planning and scheduling problem based on the network graph is established. Due to the nonlinearity in the model and the complexity of the problem, a memetic algorithm is then suggested for this problem. A novel local search (variable neighborhood search) algorithm is incorporated into the memetic algorithm. Two effective neighborhood structures are employed in the variable neighborhood search algorithm to improve the overall performance of the population. Furthermore, for the uncertainty in processing times, a set of scenarios have been generated to evaluate each individual. Finally, two performance measures—the expected performance measure and the worst-case deviation measure—are introduced and compared. In the experimental studies, the proposed memetic algorithm is tested on typical benchmark instances. Computational results show that the expected makespan measure performs better than the worst-case deviation measure and the proposed method exhibits high performance especially for large-scale instances. In addition, the results obtained by the proposed memetic algorithm are more satisfactory than those obtained by the algorithm that considers deterministic processing times only.

Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty

We consider the min-max regret version of a single-machine scheduling problem to determine which jobs are processed by outsourcing under processing time uncertainty. The performance measure is expressed as the total cost for processing some jobs in-house and outsourcing the rest. Processing time uncertainty is described through two types of scenarios: either an interval scenario or a discrete scenario. The objective is to minimize the maximum deviation from optimality over all scenarios. We show that when the cost for in-house jobs is expressed as the makespan, the problem with an interval scenario is polynomially solvable, while the one with a discrete scenario is NP-hard. Thus, for the discrete scenario case, we develop a 2-approximation algorithm and investigate when the problem is polynomially solvable. Since the problem minimizing the total completion time as a performance measure for in-house jobs is known to be NP-hard for both scenarios, we consider the problem with a special structure for the processing time uncertainty and develop a polynomial-time algorithm for both scenarios.

A hybrid estimation of distribution algorithm for simulation-based scheduling in a stochastic permutation flowshop

The permutation flowshop scheduling problem (PFSP) is NP-complete and tends to be more complicated when considering stochastic uncertainties in the real-world manufacturing environments. In this paper, a two-stage simulation-based hybrid estimation of distribution algorithm (TSSB-HEDA) is presented to schedule the permutation flowshop under stochastic processing times. To deal with processing time uncertainty, TSSB-HEDA evaluates candidate solutions using a novel two-stage simulation model (TSSM). This model first adopts the regression-based meta-modelling technique to determine a number of promising candidate solutions with less computation cost, and then uses a more accurate but time-consuming simulator to evaluate the performance of these selected ones. In addition, to avoid getting trapped into premature convergence, TSSB-HEDA employs both the probabilistic model of EDA and genetic operators of genetic algorithm (GA) to generate the offspring individuals. Enlightened by the weight training process of neural networks, a self-adaptive learning mechanism (SALM) is employed to dynamically adjust the ratio of offspring individuals generated by the probabilistic model. Computational experiments on Taillard’s benchmarks show that TSSB-HEDA is competitive in terms of both solution quality and computational performance.

Scheduling the two-machine flowshop to hedge against processing time uncertainty

This paper addresses the two-machine flowshop scheduling problem with uncertain job processing times. It is assumed that in the realization of a schedule, job processing times may take any values from their corresponding intervals given before scheduling. The objective is to determine a robust schedule with the minimum makespan of the restricted worst-case scenario among all possible scenarios to hedge against processing time uncertainty for a given number of jobs. We formulate the problem of interest as a robust counterpart optimization model, and apply a simulated annealing (SA) algorithm and an iterated greedy (IG) algorithm to solve it. The experimental results show that both algorithms are effective in determining robust schedules for small-size problems, while the IG algorithm is more effective than the SA algorithm for large-size problems, albeit at the expense of more computational time.

A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines

In this study, a robust optimization approach is developed for a new integrated mixed-integer linear programming (MILP) model to solve a dynamic cellular manufacturing system (DCMS) with unreliable machines and a production planning problem simultaneously. This model is incorporated with dynamic cell formation, inter-cell layout, machine reliability, operator assignment, alternative process routings and production planning concepts. To cope with the parts processing time uncertainty, a robust optimization approach immunized against even worst-case is adopted. In fact, this approach enables the system’s planner to assess different levels of uncertainty and conservation throughout planning horizon. This study minimizes the costs of machine breakdown and relocation, operator training and hiring, inter-intra cell part trip, and shortage and inventory. To verify the performance of the presented model and proposed approach, some numerical examples are solved in hypothetical limits using the CPLEX solver. The experimental results demonstrate the validity of the presented model and the performance of the developed approach in finding an optimal solution. Finally, the conclusion is presented.