The Review of the Single Machine Scheduling Problem and its Solving Methods

In this chapter, we consider some practical scheduling problems under unavailability constraints (breakdown periods, maintenance durations and/or setup times). Such problems can be met in different industrial environments and be associated to numerous real-life applications. This explains why many researchers have become interested in this subject. We aim to present the recent approaches proposed to solve these problems and to discuss their performances. This family of scheduling problems, addressed in this chapter, has been intensively studied (Kacem [8], Lee [17], Schmidt [24]). The studied criteria in this chapter are related to the flowtime minimization (the weighted and unweighted cases). The chapter is organized in two main parts. The first part focuses on the single machine scheduling problem (see Section 2). The second part is devoted to the parallel machine scheduling problem (see Section 3). In each part, we present the main contributions and explain their principles (complexity results, heuristic algorithms and their worstcase performance, existing approximation schemes, exact methods, branch-and-bound algorithms, dynamic programming, integer linear models, lower bounds. . .). Finally, Section 4 concludes the paper.

This paper considers the single machine scheduling problem with cost constraints based on customer driven using noncooperative game theory. The single machine scheduling problem with cost constraints based on customer driven is introduced, and customers bidding strategy is analyzed using noncooperative game method. Then noncooperative game model of single machine scheduling with cost constraints is defined using noncooperative game theory, in which the customer is mapped to the player, customer quotation corresponds to player strategy, and a payoff function of players is defined on condition of two main customer objectives. The satisfactory result of scheduling problem can be achieved by seeking Nash equilibrium solution, and the steps of seeking Nash equilibrium solution for the proposed scheduling game model are given. A single scheduling case is analyzed and solved, and the result verifies the validity of the proposed game model and the solving method.

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.

Scheduling jobs under decreasing linear deterioration

This paper considers the single batch-processing machine scheduling problem with aging effect and multi-maintenance activity concept. Real processing time of jobs increases due to machine’s aging effect. Maintenance time is constant and the machine returns to its initial condition after each maintenance activity and the aging effect starts anew. Our scheduling problem is under assumptions: non identical job sizes and dynamic job arrivals. We have to determine jointly (1) the maintenance frequencies, (2) the position of the maintenance activities on the machine, (3) the grouping of the jobs into the batches, and (4) the sequence of the batches on the machine, to minimize makespan. At first, we formulate the problem as a mathematical model. Since this problem has been proved to be NP-hard; therefore, a heuristic and two meta-heuristic algorithms are offered for the real-sized problems. The performance of the proposed algorithms is analyzed on the various test problems based on the considered measures.

This paper is concerned with single machine scheduling problem with fuzzy due dates where satisfaction based benefit are relevant. It gives an analysis and proof to the character of optimal solution for the scheduling problem. A property is proposed based on the analysis and it is also extended to some special cases.

Motivated by a real-life scheduling problem in a steel wire factory in China,this paper considers the single machine scheduling problem with sequence-dependent family setup times to minimize maximum lateness. In view of the NP-hard nature of the problem, structural (dominance and neighbourhood)properties of the problem are described and used in the tabu search algorithms to find optimal or near-optimal schedules. These proposed structural properties quickly exclude unpromising and/or non-improving neighbours from further search.Empirical results on the randomly generated and real-life problem instances from a factory in China show that the proposed heuristic algorithms utilizing the structural properties can obtain optimal or near optimal solutions with a reasonable computational effort.

Single machine scheduling (SMS) problems seem to have received substantial attention because of several reasons. These type of problems are important both because of their own intrinsic value, as well as their role as building blocks for more generalized and complex problems. In a multi-processor environment single processor schedules may be used in bottlenecks, or to organize task assignment to an expensive processor; sometimes an entire production line may be treated as a single processor for scheduling purposes. Also, compared to multiple processor scheduling, SMS problems are mathematically more tractable. Hence more problem classes can be solved in polynomial time, and a larger variety of model parameters, such as various types of cost functions, or an introduction of change-over cost, can be analyzed. Single processor problems are thus of rather fundamental character and allow for some insight and development of ideas when treating more general scheduling problems.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

This study considers a single machine scheduling problem with the objective of minimizing the total weighted tardiness of the jobs. This problem is one of the most famous problems in single machine scheduling theory and it is NP-hard. In this paper, we propose a hybrid heuristic which combines GRASP with Path Relinking to find good quality solutions for the considered problem. The performance of the hybrid GRASP heuristic is tested over multiple benchmark problems from the OR-Library with up to 100 jobs and experimental results show that it is very competitive with the existing good performing algorithms.

A grasp for single machine scheduling with sequence dependent setup costs and linear delay penalties

This paper studies an energy-efficient parallel packaging machine scheduling problem in the global logistics distribution centre considering a dominant job and the linear deterioration effect. The objective is to minimise total energy costs. First, we discuss the structural properties of the single-machine scheduling problem without a dominant job. Then, for the single-machine scheduling problem with a dominant job, we divide the problem into three situations depending on the time window requirement of the special customer. Based on the structural properties, two heuristic algorithms are designed to solve the single machine scheduling problem with or without a dominant job. For the parallel-machine scheduling problem, we develop four neighbourhood structures and propose a variable neighbourhood search (VNS) algorithm to find the near-optimal solution in a reasonable time. Finally, computational experiments are conducted, with the results validating the effectiveness of the designed neighbourhood structures and the VNS algorithm.

Complexity and approximation of single machine scheduling with an operator non-availability period to minimize total completion time

We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear form f(t) = a+bt with a ≥ 0 and b > 1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem with b ≥ 0 unless P = NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the case b > 1 and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the case b ≤ 1 both from the worst-case bound point of view.

In this paper, the authors consider a single machine scheduling problem with rejection. In traditional research, it is assumed all jobs must be processed. However, in the real-world situation, certain jobs can be rejected. In this study, the jobs can be either accepted and scheduled or be rejected at the cost of a penalty. Two objective functions are considered simultaneously: (1) minimization of the sum of weighted completion times for the accepted jobs, and (2) minimization of the sum of penalties for the rejected jobs. The authors apply two-phase method (TPM), which is a general technique to solve bi-objective combinatorial optimization problems, to find all supported and non-supported solutions for small-sized problems. The authors present a mathematical model for implementing both phases. On the other hand, three different bi-objective simulated annealing algorithms have also been developed to find a good estimation of Pareto-optimal solutions for large-sized problems. Finally the authors discuss the results obtained from each of these algorithms.