Single-machine scheduling with accelerating deterioration effects

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.

Scheduling with learning effects has been widely studied. However, there are situations where the learning effect might accelerate. In this paper, we propose a new model where the learning effect accelerates as time goes by. We derive the optimal solutions for the single-machine problems to minimize the makespan, total completion time, total weighted completion time, maximum lateness, maximum tardiness, and total tardiness.

A note on single-machine scheduling with general learning effect and past-sequence-dependent setup time

Some scheduling problems with deteriorating jobs and learning effects

This article introduces a general single-machine setup times scheduling model with learning effect and deteriorating jobs simultaneously which is a generalisation of some existing models in the literature. 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). By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The article shows that the problems to minimise the makespan, sum of the kth power of completion times, total lateness and sum of earliness penalties (with common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimise total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with common due date) are polynomially solvable under certain conditions.

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.

This paper considers the multi-criteria scheduling problem with total completion time, maximum lateness, and maximum earliness as the objectives. The problem is a minimisation problem; the total completion time, a MIN-SUM problem, the maximum earliness, a MIN-MAX problem, and the maximum lateness, a MIN-MAX problem. Though, the problem is NP-hard, shortest processing time (SPT) rule, yields optimal for total completion time while early due date rule (EDD) is the optimal solution for maximum lateness and maximum earliness if each criterion were to be considered separately. Two heuristics, named SOL I and SOL II were proposed and the results for each of the criteria were compared to the optimal of the sub-problems. Results of the computational experiment on small job-sizes (5 ≤ n ≤ 30) and large job-sizes (40 ≤ n ≤ 100) show that the two heuristics results are not significantly different from the optimal at 99% significant level for total completion time and maximum lateness performance measures. However, for maximum earliness, the optimal solutions are significantly better than the two proposed heuristics.

Single-machine scheduling problems with deteriorating jobs and learning effects

Complexity of single machine scheduling subject to nonnegative inventory constraints

In this paper, we develop branch-and-bound algorithms for several hard, two-agent scheduling problems, i.e., problems in which each agent has an objective function which depends on the completion times of its jobs only. Our bounding approach is based on the fact that, for all problems considered, the Lagrangian dual gives a good bound and can be solved exactly in strongly polynomial time. The problems addressed here consist in minimizing the total weighted completion time of the jobs of agent A, subject to a bound on the cost function of agent B, which may be: (i) total weighted completion time, (ii) maximum lateness, (iii) maximum completion time. An extensive computational experience shows the effectiveness of the approach.

This paper studies a single-machine bicriterion scheduling in which both group setup times and job-processing times are deterioration (increasing) functions of their starting times. Two objectives are considered, i.e., the primary criterion is the total weighted completion time, the secondary criterion is the maximum cost. We show that this bicriterion group scheduling problem can be solved in polynomial time.

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing times, some special flow shop scheduling problems remain polynomially solvable.

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

This paper studies the problem of scheduling three-operation jobs in a two-machine flowshop subject to a predetermined job processing sequence. Each job has two preassigned operations, which are to be performed on their respective dedicated machines, and a flexible operation, which may be processed on either of the two machines subject to the processing order as specified. Five standard objective functions, including the makespan, the maximum lateness, the total weighted completion time, the total weighted tardiness, and the weighted number of tardy jobs are considered. We show that the studied problem for either of the five considered objective functions is ordinary NP-hard, even if the processing times of the preassigned operations are zero for all jobs. A pseudo-polynomial time dynamic programming framework, coupled with brief numerical experiments, is then developed for all the addressed performance metrics with different run times.