Showing papers on "Single-machine scheduling published in 2012"

Single-Machine Sustainable Production Planning to Minimize Total Energy Consumption and Total Completion Time Using a Multiple Objective Genetic Algorithm

Abstract: Energy is an expensive resource that is becoming more scarce with increasing population and demand. In this paper, a mathematical model to minimize energy consumption and reduce total completion time of a single machine is proposed, and a multiobjective genetic algorithm is utilized to obtain an approximate set of nondominated alternatives. Furthermore, dominance rules and a heuristic are proposed to increase the speed of the proposed genetic algorithm. Finally, the analytical hierarchical process is utilized to select a solution with some additional criteria.

Single machine scheduling with general positional deterioration and rate-modifying maintenance

Abstract: We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan We deal with general non-decreasing functions to represent deterioration rates of job processing times Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group

Single-Machine Scheduling With Job-Position-Dependent Learning and Time-Dependent Deterioration

Abstract: Job deterioration and learning co-exist in many realistic scheduling situations. This paper introduces a general scheduling model that considers the effects of position-dependent learning and time-dependent deterioration simultaneously. In the proposed model, the actual processing time of a job depends not only on the total processing time of the jobs already processed but also on its scheduled position. This paper focuses on the single-machine scheduling problems with the objectives of minimizing the makespan, total completion time, total weighted completion time, discounted total weighted completion time, and maximum lateness based on the proposed model, respectively. It shows that they are polynomially solvable and optimal under certain conditions. Additionally, it presents some approximation algorithms based on the optimal schedules for the corresponding single-machine scheduling problems and analyzes their worst case error bound.

Single-machine scheduling with nonlinear deterioration

Abstract: In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.

A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

Abstract: This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors' previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

Abstract: In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of −1 < a < 0, where a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.

Scheduling problems with position dependent job processing times: computational complexity results

Abstract: In this paper, we analyse single machine scheduling problems with learning and aging effects to minimize one of the following objectives: the makespan with release dates, the maximum lateness and the number of late jobs. The phenomena of learning and aging are modeled by job processing times described by non-increasing (learning) or non-decreasing (aging) functions dependent on the number of previously processed jobs, i.e., a job position in a sequence. We prove that the considered problems are strongly NP-hard even if job processing times are described by simple linear functions dependent on a number of processed jobs. Additionally, we show a property of equivalence between problems with learning and aging models. We also prove that if the function describing decrease/increase of a job processing time is the same for each job then the problems with the considered objectives are polynomially solvable even if the function is arbitrary. Therefore, we determine the boundary between polynomially solvable and strongly NP-hard cases.

Reactive scheduling model for the operating theatre

Abstract: This paper addresses the disruption management and rescheduling problem of the day-to-day running of a day surgery unit. The problem is modelled as a single machine scheduling problem with sequence dependent processing times and due dates. The proposed optimisation model sequences both elective and non-elective patients in the online environment. The weighted number of expected surgeries to complete on-time is maximised. We propose a branch and bound algorithm to solve the problem. Computational experiments are conducted illustrating its applicability to the problem of reactive scheduling in the operating theatre.

A bicriteria approach to scheduling a single machine with job rejection and positional penalties

Abstract: Single machine scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed However, in many practical cases, one may wish to reject the processing of some jobs in the shop, which results in a rejection cost A solution for a scheduling problem with rejection is given by partitioning the jobs into a set of accepted and a set of rejected jobs, and by scheduling the set of accepted jobs among the machines The quality of a solution is measured by two criteria: a scheduling criterion, F1, which is dependent on the completion times of the accepted jobs, and the total rejection cost, F2 Problems of scheduling with rejection have been previously studied, but usually within a narrow framework--focusing on one scheduling criterion at a time This paper provides a robust unified bicriteria analysis of a large set of single machine problems sharing a common property, namely, all problems can be represented by or reduced to a scheduling problem with a scheduling criterion which includes positional penalties Among these problems are the minimization of the makespan, the sum of completion times, the sum and variation of completion times, and the total earliness plus tardiness costs where the due dates are assignable Four different problem variations for dealing with the two criteria are studied The variation of minimizing F1+F2 is shown to be solvable in polynomial time, while all other three variations are shown to be $\mathcal{NP}$ -hard For those hard problems we provide a pseudo polynomial time algorithm An FPTAS for obtaining an approximate efficient schedule is provided as well In addition, we present some interesting special cases which are solvable in polynomial time

Group scheduling with independent setup times, ready times, and deteriorating job processing times

Abstract: In this paper we investigate a single machine scheduling problem with deteriorating jobs and group technology assumption. By deteriorating jobs and group technology assumption, we mean that job processing times are simple linear functions of its starting times. The group setup times are assumed to be known and fixed. We attempt to minimize the makespan with ready times of the jobs. For a special case, we show that the problem can be solved in polynomial time when deterioration and group technology are considered simultaneously.

On the performance of smith's rule in single-machine scheduling with nonlinear cost

Abstract: We consider the problem of scheduling jobs on a single machine. Given some continuous cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each individual job is determined by the cost function value at the job's 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 factor of Smith's rule under any particular 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. To overcome unrealistic worst case instances, we also give tight bounds that are parameterized by the minimum, maximum, and total processing time.

Scheduling flexible maintenance activities subject to job-dependent machine deterioration

Abstract: This paper considers single machine scheduling that integrates machine deterioration. The current maintenance state of the machine is determined by a maintenance level which drops by a certain, possibly job-dependent, amount while jobs are processed. A maintenance level of less than zero is associated with the machine's breakdown and is therefore forbidden. Consequently, maintenance activities that raise the maintenance level again may become necessary and have to be scheduled additionally. In what follows, two general types of maintenance activities are distinguished. In the full maintenance case, maintenance activities are always executed until the machine has reached the maximum maintenance level. In contrast to this, the schedule in the partial maintenance case has to additionally determine the duration of maintenance activities. By combining both cases with regular objective functions such as minimization of maximum tardiness, minimization of the sum of completion times, or minimization of the number of tardy jobs, we obtain a new set of specific single-stage scheduling problems. Besides motivating and introducing these problems, we shall also analyze the computational complexity of general and specific cases.

Solving a multiobjective job shop scheduling problem using Pareto Archived Cuckoo Search

Abstract: This paper investigates a new approach for solving the multiobjective job shop scheduling problem, namely the Cuckoo Search (CS) approach The requirement is to schedule jobs on a single machine so that the total material waste is minimised as well as the total tardiness time The material waste is quantified in terms of saving factors to show the reduction in material that can be achieved when producing two jobs with the same materials in sequence The estimated saving factor is used to calculate a cost savings for each job based on its material type A formulation of multiobjective optimisation problems is adopted to generate the set of schedules that maximise the overall cost savings and minimise the total tardiness time, where all trade-offs are considered for the two conflicting objectives A Pareto Archived Multiobjective Cuckoo Search (PAMOCS) is developed to find the set of nondom-inated Pareto optimal solutions The solution accuracy of PAMOCS is shown by comparing the closeness of the obtained solutions to the true Pareto front generated by the complete enumeration method Results show that CS is a very effective and promising technique to solve job shop scheduling problems

Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect

Abstract: Recently, scheduling with learning effects has received growing attention. A well-known learning model is called ‘sum-of processing-times-based learning’ where the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, this paper develops a truncated learning model in which the actual job processing time not only depends on the processing times of the jobs already processed but also depends on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. In this paper, some single-machine scheduling problems can be solved in polynomial time. Besides, the error bounds are also provided for the problems to minimise the maximum lateness and the total weighted completion time.

The symmetric quadratic knapsack problem: approximation and scheduling applications

Abstract: This paper reviews two problems of Boolean non-linear programming: the Symmetric Quadratic Knapsack Problem and the Half-Product Problem. The problems are related since they have a similar quadratic non-separable objective function. For these problems, we focus on the development of fully polynomial-time approximation schemes, especially of those with strongly polynomial time, and on their applications to various scheduling problems.

A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

Abstract: This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the \({1|ST_{sd}|\sum T_{i}}\) scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is to find a schedule with minimum total tardiness. The BB&R algorithm incorporates memory-based dominance rules to reduce the solution search space. The algorithm creates schedules in the reverse direction for problems where fewer than half the jobs are expected to be tardy. In addition, a branch and bound algorithm is used to efficiently compute tighter lower bounds for the problem. This paper also presents a counterexample for a previously reported exact algorithm in Luo and Chu (Appl Math Comput 183(1):575–588, 2006) and Luo et al. (Int J Prod Res 44(17):3367–3378, 2006). Computational experiments demonstrate that the algorithm is two orders of magnitude faster than the fastest exact algorithm that has appeared in the literature. Computational experiments on two sets of benchmark problems demonstrate that the CBFS search exploration strategy can be used as an effective heuristic on problems that are too large to solve to optimality.