Showing papers on "Single-machine scheduling published in 2015"
TL;DR: A joint model for integrating run-based preventive maintenance into the production scheduling problem is proposed, in which the sequence of jobs, the PM times and the planned completion times of jobs are proactively determined simultaneously.
88 citations
TL;DR: The recently-developed sequential quadratic programming (SQP), is used by solve the single machine scheduling problem and results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error.
Abstract: Article history: Received January 20, 2015 Received in revised format 6 February 2015 Accepted 25 March 2015 Available online March 25 2015 The single machine scheduling problem aims at obtaining the best sequence for a set of jobs in a manufacturing system with a single machine. In this paper, we optimize rewards in single machine scheduling in rewards-driven systems such that total reward is maximized while the constraints contains of limitation in total rewards for earliness and learning, independent of earliness and learning and etc. are satisfied. In mentioned systems as for earliness and learning the bonus is awarded to operators, we consider only rewards in mentioned systems and it will not be penalized under any circumstances. Our objective is to optimize total rewards in mentioned system by taking the rewards in the form of quadratic for both learning and earliness. The recently-developed sequential quadratic programming (SQP), is used by solve the problem. Results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error. Finally, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the “amount of earliness for jobs (Ei parameter)”. Growing Science Ltd. All rights reserved. 5 © 201
59 citations
TL;DR: This study introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position, and shows that both problems are solvable in O(n log n) time.
Abstract: In many real-life scheduling situations, the jobs deteriorate at a certain rate while waiting to be processed. This study introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The objective is to find the optimal schedule such that the makespan or total completion time is minimised. This study first shows that both problems are solvable in On log n time. This study further shows that in both cases there exists an optimal schedule that is the shortest processing time, longest processing time, or V-shaped with respect to the job normal processing times, depending on the relationships between problem parameters.
54 citations
TL;DR: This work provides polynomial-time algorithms to solve the problems to minimize the makespan, sum of completion times, maximum lateness, and number of tardy jobs in a maintenance activity and jobs on a single machine.
49 citations
TL;DR: It is proved that there exists a subset of problems for which the computational complexity remains NP-hard, and pseudo-polynomial time algorithms are presented for these problems.
45 citations
TL;DR: This work considers several two-agent single-machine scheduling problems with deteriorating jobs, and considers six scheduling problems associated with different combinations of the two agents' objective functions, which include the maximum cost, total weighted completion time, discounted total weighted completed time, maximum earliness cost,total earliness, and total weighted earliness.
39 citations
TL;DR: A solution method is proposed that decomposes each CSP into three instances of a one machine sequencing problem with variable capacity and shows clearly that the proposed algorithm is efficient and that it outperforms a classic dispatching rule.
37 citations
TL;DR: It is proved that both scheduling problems arising when two agents compete to perform their respective jobs on a common machine are NP -hard in the strong sense and develop polynomial or pseudo-polynomial solutions for some important special cases.
36 citations
TL;DR: It turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial, and it is shown that this approximation ratio is asymptotically equal to k(k − 1)/(k + 1), denoting by k the degree of the cost function.
Abstract: We consider a single-machine scheduling problem. Given some continuous, nondecreasing cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each job is determined by the cost function value at its completion time. This problem is closely related to scheduling a single machine with nonuniform processing speed. We show that for piecewise linear cost functions it is strongly NP-hard. The main contribution of this article is a tight analysis of the approximation guarantee of Smith’s rule under any convex or concave cost function. More specifically, for these wide classes of cost functions we reduce the task of determining a worst-case problem instance to a continuous optimization problem, which can be solved by standard algebraic or numerical methods. For polynomial cost functions with positive coefficients, it turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial. We show that this approximation ratio is asymptotically equal to k(k − 1)s(k p 1), denoting by k the degree of the cost function. To overcome unrealistic worst-case instances, we also give tight bounds for the case of integral processing times that are parameterized by the maximum and total processing time.
36 citations
TL;DR: This analysis informs companies about how much it would be worthwhile to invest in measures to reduce or encourage multitasking, and develops optimal algorithms for some fundamental and practical single machine scheduling problems with multitasking.
Abstract: This study considers a typical scheduling environment that is influenced by the behavioral phenomenon of multitasking. Under multitasking, the processing of a selected job suffers from interruption by other jobs that are available but unfinished. This situation arises in a wide variety of applications; for example, administration, manufacturing, and process and project management. Several classical solution methods for scheduling problems no longer apply in the presence of multitasking. The solvability of any scheduling problem under multitasking is no easier than that of the corresponding classical problem. We develop optimal algorithms for some fundamental and practical single machine scheduling problems with multitasking. For other problems, we show that they are computationally intractable, even though in some cases the corresponding problem in classical scheduling is efficiently solvable. We also study the cost increase and value gained due to multitasking. This analysis informs companies about how much it would be worthwhile to invest in measures to reduce or encourage multitasking
35 citations
TL;DR: In this article, the authors considered single machine scheduling problems with simple linear deterioration in which the processing time of a job is a simple linear function of its execution starting time and the objective is to determine the optimal schedule to minimize the weighted sum of the θ th ( θ is a positive integer number) power of waiting times.
TL;DR: This work designs a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized.
Abstract: We study single machine scheduling problems with linear time-dependent deterioration effects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration effects, that is, all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional effects.
TL;DR: This paper constructs three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur, and examines the problem of identifying a set of worst-case processing times with respect to a fixed schedule.
Abstract: In this paper, we study a robust single-machine scheduling problem under four alternative optimization criteria: minimizing total completion time, minimizing total weighted completion time, minimizing maximum lateness, and minimizing the number of late jobs. We assume that job processing times are subject to uncertainty. Accordingly, we construct three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur. The robust optimization framework assumes that, given a job schedule, a worst-case set of processing times will be realized from among those allowed by the uncertainty set under consideration. For each combination of objective function and uncertainty set, we first analyze the problem of identifying a set of worst-case processing times with respect to a fixed schedule, and then investigate the problem of selecting a schedule whose worst-case objective is minimal.
TL;DR: Several theoretical results which can be ranked in a series of similar investigations of NP-hardness of equal-processing-time single-machine scheduling problems without precedence relations are obtained.
01 Dec 2015
TL;DR: A memetic algorithm that combines and extends several ideas from the literature, including a crossover operator that respects both the absolute and relative position of the tasks, a replacement strategy that improves the diversity of the population, and an effective but computationally expensive neighborhood structure is proposed.
Abstract: Graphical abstractDisplay Omitted HighlightsA replacement strategy that improves the diversity of the population is proposed.A decomposition of a computationally expensive neighborhood is defined.Some methods to speed-up the evaluation of the neighbors are proposed and extended.The resulting hybrid algorithm is significantly better than the state-of the-art. The single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the total weighted tardiness is a challenging problem due to its complexity, and has a huge number of applications in real production environments. In this paper, we propose a memetic algorithm that combines and extends several ideas from the literature, including a crossover operator that respects both the absolute and relative position of the tasks, a replacement strategy that improves the diversity of the population, and an effective but computationally expensive neighborhood structure. We propose a new decomposition of this neighborhood that can be used by a variable neighborhood descent framework, and also some speed-up methods for evaluating the neighbors. In this way we can obtain competitive running times. We conduct an experimental study to analyze the proposed algorithm and prove that it is significantly better than the state-of-the-art in standard benchmarks.
TL;DR: This paper proves APX-hardness of the problem when the number of resources is part of the input, and new polynomial time approximation schemes are devised for some variants.
Abstract: The paper presents new approximability results for single machine scheduling problems with jobs requiring some non-renewable resources (like raw materials, energy, or money) beside the machine. Each resource has an initial stock and additional supplies over time. A feasible schedule specifies a starting time for each job such that no two jobs overlap in time, and when a job is started, enough resources are available to cover its requirements. The goal is to find a feasible schedule of minimum makespan. This problem is strongly NP-hard. Recently, the authors of this paper have proposed a PTAS for the special case with a single non-renewable resource and with a constant number of supply dates, as well as an FPTAS for the special case with two supply dates and one resource only. In this paper we prove APX-hardness of the problem when the number of resources is part of the input, and new polynomial time approximation schemes are devised for some variants, including (1) job release dates, and more than one, but constant number of resources and resource supply dates, and (2) only one resource, arbitrary number of supply dates and job release dates, but with resource requirements proportional to job processing times. © 2015 Springer Science+Business Media New York
TL;DR: A single machine scheduling problem in which the processing time of a job is a linear function of its starting time and a variable maintenance on the machine must be performed prior to a given deadline is investigated, it is proved that both problems are NP-hard.
TL;DR: This paper presents heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound.
TL;DR: It is shown that some single machine scheduling problems are still polynomially solvable under the proposed model and that some special cases of the flow shop scheduling problems can be solved in polynomial time.
Abstract: The note deals with machine scheduling problems with a more general learning effect model, i.e., the actual job processing time is a function of the sum of the function of the processing times of the jobs already processed and job position. We show that some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.
TL;DR: This paper proves that the single machine scheduling problem with the total weighted completion time objective is NP-hard in the strong sense, and provides an FPTAS for a special case with two supply dates.
TL;DR: Wang et al. (2008) showed that an optimal schedule for the number of tardy jobs minimization problem could be obtained by Moores algorithm for some special cases, but these results are incorrect by two counterexamples.
TL;DR: In this article, a single-machine scheduling problem with an exponentially time-dependent learning effect is introduced, where the processing time of a job is assumed to be an exponential function of the total normal processing times of jobs already processed before it, and the upper bound for the maximum lateness and for the total weighted completion time is provided.
TL;DR: The proposed algorithm has been used to solve the single machine scheduling problem and the results show that the proposed SAC and HCA-BA outperformed the basic BA in almost all the considered instances, in particular when the complexity of the problem increases.
Abstract: This paper focuses on improvements to the Bees Algorithm (BA) with slope angle computation and Hill Climbing Algorithm (SACHCA) during the local search process. First, the SAC was employed to determine the inclination of the current sites. Second, according to the slope angle, the HCA was utilised to guide the algorithm to converge to the local optima. This enabled the global optimum of the given problem to be found faster and more precisely by focusing on finding the available local optima first before turning the attention on the global optimum. The proposed enhancements to the BA have been tested on continuous-type benchmark functions and compared with other optimisation techniques. The results show that the proposed algorithm performed better than other algorithms on most of the benchmark functions. The enhanced BA performs better than the basic BA, in particular on higher dimensional and complex optimisation problems. Finally, the proposed algorithm has been used to solve the single machine scheduling problem and the results show that the proposed SAC and HCA-BA outperformed the basic BA in almost all the considered instances, in particular when the complexity of the problem increases.
17 Oct 2015
TL;DR: This paper considers the problem of rate allocation when jobs of unknown size arrive online (non-clairvoyant setting), with the goal of minimizing weighted delay or flow time, and develops the first constant competitive algorithm with constant speed augmentation for single-sink flow routing, routing multicast trees, and multidimensional resource allocation with substitutes resources.
Abstract: Many scheduling problems can be viewed as allocating rates to jobs, subject to convex packing constraints on the rates. In this paper, we consider the problem of rate allocation when jobs of unknown size arrive online (non-clairvoyant setting), with the goal of minimizing weighted delay or flow time. Though this problem has strong lower bounds on competitive ratio in its full generality, we show positive results for natural and fairly broad sub-classes. More specifically, the subclasses we consider not only generalize several well-studied models such as scheduling with speedup curves and related machine scheduling, but also capture as special cases hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We establish several first positive results by making connections with two disparate disciplines: Economics and Queueing theory. First, we view the instantaneous allocation of rates as a resource allocation problem. We analyze the natural proportional fairness algorithm from economics. To do this, we extend results from market clearing literature, particularly the Eisenberg-Gale markets and the notions of Walrasian equilibria and Gross Substitutes. This yields the first constant competitive algorithm with constant speed augmentation for single-sink flow routing, routing multicast trees, and multidimensional resource allocation with substitutes resources. Next, we consider the general scheduling problem with packing constraints on rates, but with the restriction that the number of different job types is fixed. We model this problem as a non-stochastic queueing problem. We generalize a natural algorithm from queueing literature and analyze it by extending queueing theoretic ideas. We show that the competitive ratio, for any constant speed, depends polynomially only on the number of job types. Further, such a dependence on the number of job types is unavoidable for non-clairvoyant algorithms. This yields the first algorithm for scheduling multicommodity flows whose competitive ratio depends polynomially on the size of the underlying graph, and not on the number of jobs.
TL;DR: A two-step approach embedding a Recovering Beam Search algorithm is proposed to get a good-quality initial solution reachable in short time and a more time consuming matheuristic algorithm to take into account the maximum lateness constraints.
TL;DR: A robust model is presented to tackle the single machine scheduling problem, based on goal programming and a stochastic programming model named E-model, which not only obtains optimal operating systems, but also considers the variance of the objective functions and the correlation between them.
Abstract: In this study, a static single machine scheduling problem is investigated, where processing times are stochastic, due dates are deterministic and inserted idle time is allowed. Two objective functions are simultaneously taken into account, minimization of mean completion time and minimization of earliness and tardiness costs. A robust model is presented to tackle the problem, based on goal programming and a stochastic programming model named E-model. The proposed model not only obtains optimal operating systems, but also considers the variance of the objective functions and the correlation between them. Moreover, chance-constrained programming model is used to take into account the randomness in the constraints of the model. The model is presented with general distribution of processing times and the normal case is explored in experiments. Two sets of computational experiments are presented to test the efficiency of the proposed model. In the first set, the performance obtained by the bi-objective formulation is measured, where in the second set the performance obtained by incorporating robustness is measured. Results confirm the effectiveness of the proposed model, in both directions.
TL;DR: It is proved that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimizationProblem, and the total lateness minimizationproblem, respectively.
Abstract: In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.
TL;DR: This article provides a branch-and-bound algorithm to search for the optimal solution and a genetic algorithm equipped with a local search to obtain near-optimal solutions for a single-machine scheduling problem with learning effects.
Abstract: Scheduling with learning effects or scheduling with two competing agents has been widely studied in recent years. However, they are seldom discussed at the same time. In this article, we consider a...
TL;DR: This paper considers scheduling of deteriorating jobs on a single machine with slack (SLK) due date assignment, resource allocation, and a rate-modifying activity to minimize a total penalty function comprising the earliness, tardiness, common flow allowance, and resource allocation costs.
TL;DR: This paper studies systems that can be modeled by single-machine scheduling problems with due date assignment with polynomial-time dynamic programming algorithms to find the optimal jobs sequence, respectively.