Showing papers on "Single-machine scheduling published in 2017"

Hybrid evolutionary approaches for the single machine order acceptance and scheduling problem

Abstract: Graphical abstractDisplay Omitted HighlightsTwo evolutionary approaches are proposed for order acceptance and scheduling problem.First approach is based on steady-state genetic algorithm.Second approach is based on evolutionary algorithm with guided mutation.Our approaches are compared with two state-of-the-art approaches.Computational results show the effectiveness of our approaches. This paper presents two hybrid metaheuristic approaches, viz. a hybrid steady-state genetic algorithm (SSGA) and a hybrid evolutionary algorithm with guided mutation (EA/G) for order acceptance and scheduling (OAS) problem in a single machine environment where orders are supposed to have release dates and sequence dependent setup times are incurred in switching from one order to next in the schedule. OAS problem is an NP-hard problem. We have compared our approaches with the state-of-the-art approaches reported in the literature. Computational results show the effectiveness of our approaches.

Minimizing value-at-risk in single-machine scheduling

Abstract: The vast majority of the machine scheduling literature focuses on deterministic problems in which all data is known with certainty a priori. In practice, this assumption implies that the random parameters in the problem are represented by their point estimates in the scheduling model. The resulting schedules may perform well if the variability in the problem parameters is low. However, as variability increases accounting for this randomness explicitly in the model becomes crucial in order to counteract the ill effects of the variability on the system performance. In this paper, we consider single-machine scheduling problems in the presence of uncertain parameters. We impose a probabilistic constraint on the random performance measure of interest, such as the total weighted completion time or the total weighted tardiness, and introduce a generic risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) of the random performance measure at a specified confidence level. We propose a Lagrangian relaxation-based scenario decomposition method to obtain lower bounds on the optimal VaR and provide a stabilized cut generation algorithm to solve the Lagrangian dual problem. Furthermore, we identify promising schedules for the original problem by a simple primal heuristic. An extensive computational study on two selected performance measures is presented to demonstrate the value of the proposed model and the effectiveness of our solution method.

Time-Indexed Formulations for the Runway Scheduling Problem

Abstract: The problem of sequencing and scheduling airplanes landing and taking off on a runway is a major challenge for air traffic management. This difficult real-time task is still carried out by human controllers, with little help from automatic tools. Several methods have been proposed in the literature, including mixed-integer programming (MIP)–based approaches. However, there is an opinion that MIP is unattractive for real-time applications, since computation times are likely to grow too large. In this paper, we reverse this claim, by developing a MIP approach able to solve to optimality real-life instances from congested airports in the stringent times allowed by the application. To achieve this, it was mandatory to identify new classes of strong valid inequalities, along with developing effective fixing and lifting procedures.

A new model for single machine scheduling with uncertain processing time

Abstract: Uncertain single machine scheduling problem for batches of jobs is an important issue for manufacturing systems. In this paper, we use uncertainty theory to study the single machine scheduling problem with deadlines where the processing times are described by uncertain variables with known uncertainty distributions. A new model for this problem is built to maximize expected total weight of batches of jobs. Then the model is transformed into a deterministic integer programming model by using the operational law for inverse uncertainty distributions. In addition, a property of the transformed model is provided and an algorithm is designed to solve this problem. Finally, a numerical example is given to illustrate the effectiveness of the model and the proposed algorithm.

A two-agent single-machine scheduling problem with late work criteria

Abstract: This paper addresses a two-agent scheduling problem where the objective is to minimize the total late work of the first agent, with the restriction that the maximum lateness of the second agent cannot exceed a given value. Two pseudo-polynomial dynamic programming algorithms are presented to find the optimal solutions for small-scale problem instances. For medium- to large-scale problem instances, a branch-and-bound algorithm incorporating the implementation of a lower bounding procedure, some dominance rules and a Tabu Search-based solution initialization, is developed to yield the optimal solution. Computational experiments are designed to examine the efficiency of the proposed algorithms and the impacts of all the relative parameters.

An uncertain single machine scheduling problem with periodic maintenance

Abstract: This paper studies a single machine scheduling problem with periodic maintenance, in which processing time and repair time are nondeterministic. In order to deal with nondeterministic phenomena, uncertainty theory is introduced to minimize the makespan under an uncertain environment. Three uncertain programming models are proposed, which can be converted into deterministic forms based on the uncertainty inverse distribution. List scheduling (LS) and longest processing time (LPT) algorithms are employed to solve the problem. It is proved that the two algorithms have the same worst cast ratio under different confidence levels and the LPT algorithm has a better performance bound. A hybrid intelligent algorithm for the problem is designed and some numerical experiments demonstrate the effectiveness of the proposed models and algorithm.

Single machine scheduling problems with generalised due-dates and job-rejection

Abstract: We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.

Constraint Programming Approach for Scheduling Jobs With Release Times, Non-Identical Sizes, and Incompatible Families on Parallel Batching Machines

Abstract: We study a parallel batch-scheduling problem that involves the constraints of different job release times, non-identical job sizes, and incompatible job families, is addressed. Mixed integer programming and constraint programming (CP) models are proposed and tested on a set of common problem instances from a paper in the literature. Then, we compare the performance of the models with that of a variable neighborhood search (VNS) heuristic from the same paper. Computational results show that CP outperforms VNS with respect to solution quality and run time by 3.4%–6.8% and 47%–91%, respectively. When compared to optimal solutions, the results demonstrate CP is capable of generating a near optimal solution in a short amount of time.

Minimizing makespan in a single machine scheduling problem with deteriorating jobs and learning effects

Abstract: This paper considers a single machine scheduling problem with simultaneous deteriorating jobs and learning effects. It is proved in the literature that the single machine scheduling problem with linear deterioration rate and learning effect is NP-hard in strong sense. Therefore, due to complexity of the problem finding the best sequence of jobs with minimum Makespan using Full Enumeration methods is time consuming and costly. Therefore, a new polynomial time heuristic algorithm is proposed to solve the problem in different sizes. The performance of the heuristic algorithm is evaluated against classical Smallest Deterioration Rate and Full Enumeration methods in solving various test problems. For this purpose, different measures including Percentage Relative Error and CPU_Time are considered to demonstrate the superior solution method. In addition, Single Factor ANOVA and Tukey's multiple comparison test are utilized to find significant differences in performance of the solution methods.

Single machine scheduling with slack due dates assignment

Abstract: This paper considers a single machine scheduling problem in which each job is assigned an individual due date based on a common flow allowance (i.e. all jobs have slack due date). The goal is to find a sequence for jobs, together with a due date assignment, that minimizes a non-regular criterion comprising the total weighted absolute lateness value and common flow allowance cost, where the weight is a position-dependent weight. In order to solve this problem, an time algorithm is proposed. Some extensions of the problem are also shown.

Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Abstract: Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.

On single-machine scheduling with workload-dependent maintenance duration

Abstract: In this paper, we consider a single-machine scheduling problem with workload-dependent maintenance duration. The objective is to minimize the total weighted completion time. For the case where the maintenance duration is an arbitrarily non-decreasing function on the workload, we propose a ( 2 + e ) - approximation algorithm and a fully polynomial time approximation scheme, which extends the previous results presented by Xu et al. [Single machine total completion time scheduling problem with workload-dependent maintenance duration. Omega 2015;52:101–6].

A note on resource allocation scheduling with position-dependent workloads

Abstract: In this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.

A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance

Abstract: We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.

Scatter search for minimizing weighted tardiness in a single machine scheduling with setups

Abstract: Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the weighted tardiness. To solve this problem, we propose a scatter search algorithm which uses path relinking in its core. This algorithm is enhanced with some procedures to speed-up the neighbors' evaluation and with some diversification and intensification techniques, the latter taking some elements from iterated local search. We conducted an experimental study across a well-known set of instances to analyze the contribution of each component to the overall performance of the algorithm, as well as to compare our proposal with the state-of-the-art metaheuristics, obtaining competitive results. We also propose a new benchmark with larger and more challenging instances and provide the first results for them.

A single-machine scheduling problem with learning effect, deterioration and non-monotonic time-dependent processing times

Abstract: One of the most common objectives in single-machine scheduling problems is the minimisation of total tardiness. Due to the non-deterministic polynomial-time hard nature of this problem, different heuristic and metaheuristic algorithms have been employed to solve it. In this article, an integer programming model with non-monotonic time-dependent job processing times is developed in which deterioration and learning considerations are incorporated simultaneously. A hybrid genetic algorithm-tabu search GA-TS approach is employed to solve the problem. Also, to improve the performance of the GA, Taguchi method is used for parameter tuning. Lastly, in an attempt to validate the proposed model, different test problems are generated randomly and solved by both the hybrid GA-TS and an optimisation software, and thereafter a comparison is performed between the results obtained by them. According to the results, the developed approach has potential to yield near-optimum solutions in large-sized problems. To the best of our knowledge, this is the first study that considers non-monotonic time-dependent processing times, deterioration and learning effect simultaneously in a single-machine scheduling problem with the objective of total tardiness minimisation.

Unary NP-hardness of minimizing the number of tardy jobs with deadlines

Abstract: For single machine scheduling to minimize the number of tardy jobs with deadlines, Lawler showed in 1983 that the problem is binary NP-hard. But the exact complexity (unary NP-hard or pseudo-polynomial-time solvability) is a long- standing open problem. We show in this paper that the problem is unary NP-hard. Our research also implies that the scheduling problem for finding an optimal schedule to minimize the number of tardy jobs that also satisfies the restriction of deadlines is unary NP-hard. As a consequence, some multi-agent scheduling problems related to minimizing the number of tardy jobs and maximum lateness are unary NP-hard.

Effective dynamic dispatching rule and constructive heuristic for solving single-machine scheduling problems with a common due window

Abstract: This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved.