Chin-Chia Wu

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.

Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the jobs scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.

Minimizing total completion time in a two-machine flowshop with a learning effect

Abstract In many situations, a workers ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the “learning effect”. In this paper, the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes the total completion time. Several dominance properties and the lower bounds are derived to speed up the elimination process of the branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. In the simulation, the proposed heuristic algorithm is shown to perform consistently better than the previous one.

A bi-criterion single-machine scheduling problem with learning considerations

Abstract.Conventionally, job processing times are assumed to be constant from the first job to be processed until the last job to be completed. However, recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the “learning effect.” This paper focuses on a bi-criterion single-machine scheduling problem with a learning effect. The objective is to find a sequence that minimizes a linear combination of the total completion time and the maximum tardiness. A branch-and-bound and a heuristic algorithm are proposed to search for optimal and near-optimal solutions, respectively. Computational results are also provided for the problem.

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.

Scheduling problems with deteriorating jobs and learning effects including proportional setup times

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered setup times. We introduce a new scheduling model in which job deterioration and learning, and setup times are considered simultaneously. In the proposed model, the actual processing time of a job is defined as a function of the setup and processing times of the jobs already processed and the jobs own scheduled position in a sequence. In addition, the setup times are assumed to be proportional to the actual processing times of the already scheduled jobs. We derive polynomial-time optimal solutions for some single-machine problems with or without the presence of certain conditions.

Single-machine and flowshop scheduling with a general learning effect model

Learning effects in scheduling problems have received growing attention recently. Biskup [Biskup, D. (2008). A state-of-the-art review on scheduling with learning effect. European Journal of Operational Research, 188, 315-329] classified the learning effect scheduling models into two diverse approaches. The position-based learning model seems to be a realistic assumption for the case that the actual processing of the job is mainly machine driven, while the sum-of-processing-time-based learning model takes into account the experience the workers gain from producing the jobs. In this paper, we propose a learning model which considers both the machine and human learning effects simultaneously. We first show that the position-based learning and the sum-of-processing-time-based learning models in the literature are special cases of the proposed model. Moreover, we present the solution procedures for some single-machine and some flowshop problems.

Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations

Scheduling with learning effects has attracted growing attention of the scheduling research community. A recent survey classifies the learning models in scheduling into two types, namely position-based learning and sum-of-processing-times-based learning. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the first model and when the normal job processing times are large in the second model. Motivated by this observation, we propose a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. The use of the logarithm function is to model the phenomenon that learning as a human activity is subject to the law of diminishing return. Under the proposed learning model, we show that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time. We further show that the problems to minimize the maximum lateness, maximum tardiness, weighted sum of completion times and total tardiness have polynomial-time solutions under some agreeable conditions on the problem parameters.

Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine

The scheduling problem with deteriorating jobs to minimize the makespan on a single machine where the facility has an availability constraint is studied in this paper. By a deteriorating job we mean that the processing time for the job is a function of its starting time. Even with the introduction of the availability to a facility, the linear deteriorating model can be solved using the 0-1 integer programming technique if the actual job processing time is proportional to the starting time.

Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties

We consider a scheduling environment with two agents and a linear non-increasing deterioration. By the linear non-increasing deterioration we mean that the actual processing time of a job belonging to the two agents is defined as a non-increasing linear function of its starting time. Two agents compete to perform their respective jobs on a common single machine and each agent has his own criterion to be optimized. The goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents. Three different objective functions are considered for one agent, including the maximum earliness cost, total earliness cost and total weighted earliness cost, while keeping the maximum earliness cost of the other agent below or at a fixed level U. We propose the optimal (nondominated) properties and present the complexity results for the problems addressed here.