Wen-Hung Wu

A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations

Scheduling with learning effects has received a lot of research attention lately. By learning effect, we mean that job processing times can be shortened through the repeated processing of similar tasks. On the other hand, different entities (agents) interact to perform their respective tasks, negotiating among one another for the usage of common resources over time. However, research in the multi-agent setting is relatively limited. Meanwhile, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of jobs increases or a job with a long processing time exists. Motivated by these observations, we consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and three simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.

Single-machine scheduling with time-dependent and position-dependent deteriorating jobs

In many real-life scheduling situations, the jobs deteriorate at a certain rate while waiting to be processed. This study introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The objective is to find the optimal schedule such that the makespan or total completion time is minimised. This study first shows that both problems are solvable in O(n log n) time. This study further shows that in both cases there exists an optimal schedule that is the shortest processing time, longest processing time, or V-shaped with respect to the job normal processing times, depending on the relationships between problem parameters.

Due-date assignment and single-machine scheduling with generalised position-dependent deteriorating jobs and deteriorating multi-maintenance activities

This paper addresses a single-machine scheduling problem with simultaneous consideration of due-date assignment, generalised position-dependent deteriorating jobs, and deteriorating maintenance activities. It is assumed that the actual processing time of a job is a general non-decreasing function depending on the number of maintenance activities performed before it and its position in a sequence. Moreover, the machine may be subject to several maintenance activities up to a limit over the scheduling horizon. The maintenance activities do not necessarily restore the machine fully to its original perfect state and the duration of a maintenance activity depends on its start time. The objective is to find jointly the optimal job sequence, maintenance frequency and maintenance positions to minimise an objective function that includes the cost of due-date assignment, the cost of discarding jobs that cannot be completed by their due dates and the earliness of the scheduled jobs under the popular CON and SLK due-date assignment methods. We provide polynomial-time solution algorithms for various versions of the problem.

A study of the single-machine two-agent scheduling problem with release times

In many management situations, multiple agents compete on the usage of common processing resources. On the other hand, the importance of the ready times can be shown in Wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. However, research on scheduling with two-agent and ready time simultaneously is relatively unexplored. This paper addresses a single-machine two-agent scheduling problem with ready times. The aim is to find an optimal schedule to minimize the total completion time of the jobs of the first agent with the restriction that total completion time is allowed an upper bound for the second agent. To the best of our knowledge, the problem under study has not been considered. Firstly, we show that the proposed problem is strongly NP-hard. Following that, we then develop a branch-and-bound, an ant colony, and four genetic algorithms for an optimal and near-optimal solution, respectively. In addition, the extensive computational experiments are also given.

A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents

This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.

A tabu method for a two-agent single-machine scheduling with deterioration jobs

In recent 10 years, the multi-agent idea applied in scheduling issues has received continuing attention. However, the study of the multi-agent scheduling with deteriorating jobs is relatively limited. In light of this, this paper deliberates upon a two-agent single-machine scheduling problem with deteriorating jobs. Taking the proposed model, the actual processing time of a job from both the first agent and the second agent is modeled as a linearly increasing function of its starting time. The goal of this paper is to minimize the total weighted number of tardy jobs of the first agent subject to the condition that the maximum lateness of the second agent is allowed to have an upper bound. The complexity of the model concerned in the paper is claimed as an NP-hard one. Following that, several dominance rules and a lower bound are proposed to be applied in a branch-and-bound algorithm for the optimal solution, and a tabu algorithm is applied to find near-optimal solutions for the problem. The simulation results obtained from all the proposed algorithms are also reported.

A branch-and-bound algorithm for a single machine sequencing to minimize the total tardiness with arbitrary release dates and position-dependent learning effects

This study considers an NP-hard problem of minimizing the total tardiness on a single machine with arbitrary release dates and position-dependent learning effects. A mixed-integer programming (MIP ) model is first formulated to find the optimal solution for small-size problem instances. Some new dominance rules are then presented which provide a sufficient condition for finding local optimality. The branch-and-bound (B& B) strategy incorporating with several dominance properties and a lower bound is proposed to derive the optimal solution for medium- to-large-size problem instances, and four marriage-in-honey-bees optimization algorithms (MBO) are developed to derive near-optimal solutions for the problem. To show the effectiveness of the proposed algorithms, 3600 situations with 20 and 25 jobs, are randomly generated for experiments.

Solving a two-agent single-machine learning scheduling problem

Scheduling with learning effects has been widely studied. However, there has been little work done on multi-agent scheduling with learning effects. This article investigates a two-agent single-machine scheduling problem with learning effects via an objective function which minimises the weighted completion time of all the jobs subject to a constraint that one agent makespan cannot exceed a prescribed upper bound. This article develops a branch-and-bound algorithm along with three simulated-annealing (SA) algorithms searching for an optimal and near-optimal solution. The computational results show that all the average error percentages of combined SA algorithms are less than 0.076%.

The single-machine total tardiness problem with unequal release times and a linear deterioration

Recently, machine scheduling problems with deteriorating jobs have received more attention from the scheduling research community. In this paper we consider a single-machine scheduling problem with a linear deteriorating effect and unequal release times. The objective is to minimize the total tardiness. We propose a branch-and-bound algorithm incorporating with several dominance properties and two lower bounds to search for the optimal solution. In addition, we propose a marriage in honey-bees optimization algorithm (MBO) to provide a near-optimal solution. The computational experiment is also conducted to evaluate the impacts of the parameters over the performances of the proposed algorithms.

A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect

This paper considers a scheduling model involving two agents, job release times, and the sum-of-processing-times-based learning effect. The sum-of-processing-times-based learning effect means that the actual processing time of a job of either agent is a decreasing function of the sum of the processing times of the jobs already scheduled in a given schedule. The goal is to seek for an optimal schedule that minimizes the total weighted completion time of the first agent, subject to no tardy job for the second agent. We first provide a branch-and-bound method to solve the problem. We then develop an approach that combines genetic algorithm and simulated annealing to seek for approximate solutions for the problem. We carry on extensive computational tests to assess the performance of the proposed algorithms.