Single-machine two-agent scheduling involving a just-in-time criterion

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.

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.

Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work

In this paper, we investigate the job scheduling problems with human multitasking and asymmetric switching costs. It is shown that the makespan problem is binary NP-hard. Both the total completion time and the due date assignment problems are unary NP-hard. We then consider a special case in which the cost of switching from job A (interrupted job) to job B (interrupting job) is in a form of κ 1 ƒp A + κ 2 ƒw B , where κ 1 and κ 2 are constants and ƒp A and ƒw B are costs depending on job A and B respectively. With this special form of switching cost, we show that the makespan, the total completion time and the due date assignment problems can be formulated as linear assignment problems and thus be solved in polynomial time. Even if stress effect is introduced, these three scheduling problems with the special form of asymmetric switching costs are polynomial time solvable.

Two-agent scheduling problems under rejection budget constraints

Single-machine scheduling against due dates with past-sequence-dependent setup times

In this paper we consider a single machine preemptive scheduling problem to minimize the weighted number of late jobs. There are given n jobs and for each job we have a release date, a processing time and a due date. It is assumed that certain specified jobs have to be completed on time. The due dates for these jobs are considered as deadlines. while for the other jobs due dates may be violated. For the case of similarly ordered release and due dates (when there is no advantage to preemption) as well as for the case of embedded release and due date intervals and preemption allowed, we transform the initial problem into a reduced problem, where all jobs with deadlines are eliminated. It gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.

Scheduling with controllable release dates and processing times: Total completion time minimization

Optimal restricted due date assignment in scheduling

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Execution times are crucial for effectiveness of tasks or jobs scheduling. It is very hard to accurately estimate execution times because they are influenced by many factors. Though there are some models for traditional machine scheduling problems, no attention has been paid on virtual machine scheduling in cloud computing. Based on cloud agent (VM administrator, scheduler or intelligent procedure) experiences, we develop integrated learning effects models to obtain accurate execution times. Based on the constructed learning effects model for single virtual machine scheduling, optimal schedule rules are proposed for minimizing makespan, the total completion time and the sum of (square) completion times. Problems with the total weighted completion time and the maximum lateness minimization are proved to be optimally solvable in polynomial time only for certain assumptions. Furthermore, we adapt the developed learning effects model to two special m-virtual machine MapReduce scenarios, for which optimal schedule rules are introduced correspondingly. Optimal solutions are demonstrated by examples of the problems under study using the constructed rules.

Different variants of the multi-agent scheduling have been studied in the literature due to its wide applications in artificial intelligence, decision theory, operations research, etc. Most of previous research focused on the single-machine environment and two-agent scheduling. In this paper, we address a multi-agent scheduling problem on a set of m machines in a proportionate flow shop system, where the job processing times are machine independent. Each agent desires to maximize its total gains of JIT jobs which are completed exactly at the due dates. The goal is to find a feasible schedule in which each agent’s cost function value does not less than a given lower bound. When the number of agents is part of the input, we use the reduction method to show that the general problem is strongly $$\mathcal {NP}$$ -complete even if all jobs have unit processing times. When the number of agents is fixed, we first develop a dynamic programming algorithm that runs in pseudo-polynomial time, then we design a fully polynomial time approximation scheme by exploiting the technique of trimming-the-state-space. The results presented in this paper imply that by relaxing each agent’s desired cost function value a small fraction, we can obtain an efficient approximate schedule for the problem with fixed number of agents in polynomial time, while when the number of agents is part of the input, the problem become much intractable, and it needs more sophisticated methods to solve in future research.

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

Energy-efficient bi-objective single-machine scheduling with power-down mechanism

Single machine scheduling and due date assignment with positionally dependent processing times