Single-machine scheduling with truncated sum-of-processing-times-based learning effect including proportional delivery times

Single-machine scheduling problems with past-sequence-dependent delivery times

An improved on-line algorithm for single parallel-batch machine scheduling with delivery times

Impact of learning and fatigue factors on single machine scheduling with penalties for tardy jobs

The research on the theory and method of single machine scheduling is a difficult subject, but it is very important for the companies to improve the production efficiency and effectiveness. The study on single machine scheduling problem has the history of 50 years, but there is still a gap between the classical scheduling theories and practical scheduling problems. According to this characteristic, the problems in practical scheduling area and the various factors need to be concerned are mentioned, and the main methods to solving the single machine scheduling problem and their applications are presented in details. Finally, the directions and suggestions of future work in single machine scheduling problem are summarized.

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.

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.

The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (\( \delta \geqslant 0 \)) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.

Recently, learning scheduling problems have received increasing attention. However, the majority of the research assume that the actual job processing time is a function of its position. This paper deals with the single-machine scheduling problem with a sum-of-processing-time-based learning effect. By the effect of sum-of-processing-time-based learning, we mean that the processing time of a job is defined by total normal processing time of jobs in front of it in the sequence. We show that the single-machine makespan problem remains polynomially solvable under the proposed model. We show that the total completion time minimization problem for a≥1 remains polynomially solvable under the proposed model. For the case of 0<a<1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

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.

An improved approximation algorithm for single machine scheduling with job delivery

Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect

In this paper we consider the single machine scheduling problems with sum-of-logarithm-processing-times based and position based learning effects, i.e., the actual job processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in a sequence. The logarithm function is used to model the phenomenon that learning as a human activity is subject to the law of diminishing return. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable.

Scheduling jobs under decreasing linear deterioration

This paper deals with a single machine scheduling problem with general past-sequence-dependent (psd) setup time and log-linear learning in which the setup times and learning effects are job-dependent. The setup times are unique functions of the length of already processed jobs, and the learning effects show that processing times are unique decreasing functions of job positions. The goal is to find the optimal sequences that minimise objective functions such as the makespan, total completion time, total lateness, total waiting cost, total waiting time, total absolute differences in completion times, and the sum of earliness, tardiness and common due date penalty. Special cases of the resulting problems are solvable in polynomial time; however, the general problems are difficult to solve. We propose branch-and-bound (B&B) methods to derive the optimal sequences for such problems. Computational results show that the proposed methods can solve relatively large problem instances in reasonable amounts of time.