Algorithm For Single Machine Scheduling Problem Research Articles

Heuristic and exact algorithms for single-machine scheduling problems with general truncated learning effects

Heuristic and exact algorithms for single-machine scheduling problems with general truncated learning effects

Fast solution of single-machine scheduling problem with embedded jobs

We present a fast polynomial-time algorithm for single-machine scheduling problem with release times (rj), processing times (pj) and due dates (dj) with the objective to minimize the maximum job lateness. The general setting is strongly NP-hard. We expose a particular embedded structure that typically possess a subset of jobs in an instance of the problem. We establish useful properties of the problem instances that tolerate this structure, i.e., in such an instance no subset of embedded jobs overlaps in time with the jobs that do not belong to that subset. Relying on these properties, our algorithm finds an optimal solution for the corresponding class of problem instances. Whether a given problem instance is tolerant of the revealed embedded structure becomes known during the execution of the algorithm. Nevertheless, some sufficient conditions in terms of job parameters can a priori be given. One such a condition is that for any pair of jobs j and i with ri>rj and di<dj, dj−rj−pj≤di−ri−pi, and if ri+pi≥rj+pj, then di≥dj. As we show, our setting remains powerful enough to model important real-life applications.

Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.

On exact algorithms for single-machine scheduling problems with a variable maintenance

The aim of this paper is to point out that all mathematical programming models proposed by Ying et al. (2016) are incorrect. We present four revised mathematical programming models and four improved mathematical programming models by adding and revising some constraints and decision variables. Moreover, we show that the first three scheduling problems considered in their paper are equivalent to the problems with the objective of minimizing the sum of completion times or minimizing the maximum lateness, which can be solved by algorithms proposed by Luo et al. (2015) in O(n2) time.

Exact algorithms for single-machine scheduling problems with a variable maintenance

This paper deals with four single-machine scheduling problems (SMSPs) with a variable machine maintenance. The objectives of the four SMSPs are to minimize mean lateness, maximum tardiness, total flow time and mean tardiness, respectively. These four SMSPs are important in the literature and in practice. This study proposes an exact algorithm with the computational complexity O(n2) for each of the four SMSPs. In addition to the given jobs, the machine maintenance activity between two consecutive jobs is optimally scheduled.

Algorithms for single-machine scheduling problem with deterioration depending on a novel model

In this paper, a novel single machine scheduling problem with deterioration depending on waiting times is investigated. Firstly, a new deterioration model for the problem is presented. Secondly, according to characteristics of the problem, dominance properties and lower bounds are proposed and integrated into the Branch and Bound algorithm (B & B) to solve the small-medium scale problems. Thirdly, for solving a large-scale problem, the Rules Guided Nested Partitions method (RGNP) is proposed. The numerical experiments show that when the size of the problem is no more than 17 jobs, the B & B algorithm can obtain the optimal solutions in a reasonable time. The RGNP method can also obtain an average error percentage for near-optimal solutions less than 0.048 within 0.2s. The analysis shows the efficiency of RGNP, and, hence, it can be used for solving large size problems.

On the equivalence of single machine earliness/tardiness problems with job rejection

We present optimal algorithms for single-machine scheduling problems with earliness criteria and job rejection and compare them with the algorithms for the corresponding problems with tardiness objectives. We present an optimal O(nlogn) algorithm for minimizing the maximum earliness on a single machine with job rejection. Our algorithm also solves the bi-criteria scheduling problem is which the objective is to simultaneously minimize the maximum earliness of the scheduled jobs and the total rejection cost of the rejected jobs. We also show that the optimal pseudo-polynomial time algorithm for the total tardiness problem with job rejection can be used to solve the corresponding total earliness problem with job rejection.

Harmony search algorithm for single-machine scheduling problem with planned maintenance

This paper focuses on the single machine scheduling problem, with sequence dependent setup times. Both processing and setup times are deterministic and the objective is to minimize total earliness and tardiness penalties. The novelty of the model can be traced in the fact that the single machine is subjected to breakdowns and that, in order to increase its availability, planned maintenance tasks are also performed. Hence, jobs and maintenance tasks are jointly considered to find the optimal schedule. These features make the problem NP-hard and so, a quasi-optimal solution is searched using a recent metaheuristic, which integrates harmony search and genetic algorithms. In order to validate the proposed metaheuristic, a comprehensive set of scheduling problems was fully investigated. Obtained results, compared with those of exhaustive (for small problems) and standard metaheuristics, confirm both the robustness and the speed of the proposed approach.

A hybrid imperialist competitive algorithm for single-machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we study single-machine scheduling problem when each job is considered with linear earliness and quadratic tardiness penalties with no machine idle time. Here the objective is to find the best sequence of jobs in the reasonable time. This model was studied in several researches, and some algorithms were proposed to solve it such as genetic algorithm. As the size of problem increased, such algorithms were not effective and efficient. Hence, we proposed the hybrid imperialist competitive algorithm. The proposed algorithm is based upon the imperialist competitive algorithm and genetic algorithm concepts. This algorithm was tested in problems with different sizes. The results denoted that the hybrid algorithm can solve different size of problem in reasonable time. This procedure showed its efficiency in medium- and large-sized problems as compared with other available methods.