Two-agent scheduling with learning consideration

In traditional scheduling, job processing times are assumed to be known and fixed over the entire process. However, repeated processing of similar tasks improves workers’ skills. In fact, scheduling with learning effects has received considerable attention recently. On the other hand, it is assumed that there is a common objective for all the jobs. In many management situations, multiple agents pursuing different objectives compete on the usage of a common processing resource. In this paper, we studied a single-machine two-agent scheduling problem with learning effects where the objective is to minimize the total tardiness of jobs from the first agent given that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated several properties and a lower bound is developed to search for the optimal solution. In addition, two heuristic algorithms are also proposed to search for the near-optimal solutions. A computational experiment is conducted to evaluate the performance of the proposed algorithms.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

Scheduling deteriorating jobs on a single machine with release times

This paper investigates a single-machine deteriorating job scheduling problem with job release times where its objective is to minimize the makespan. The problem is known to be NP-hard. Therefore, a branch-and-bound algorithm incorporating with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, easy-implemented heuristic algorithms are also provided to obtain the near-optimal solution. The computational experiments indicate that the branch-and-bound algorithm can solve most of the medium-job-sized problems within a reasonable time, and the heuristic is quite accurate with an average error percentage of less than 0.3%.     

Two-machine flow shop problem with effects of deterioration and learning

In this paper we consider a two-machine flow shop scheduling problem with effects of deterioration and learning. By the effects of deterioration and learning, we mean that the processing time of a job is a function of its execution starting time and its position in a sequence. The objective is to find a sequence that minimizes the total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions.     

Two-machine flow shop scheduling with linear decreasing job deterioration

In this paper, we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time is a decreasing function of its execution start time. A proportional linear decreasing deterioration function is assumed. The objective is to find a sequence that minimizes total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational results for randomly generated problem instances are presented, which show that the heuristic algorithm effectively and efficiently in obtaining near-optimal solutions.     

Two-machine flowshop scheduling with truncated learning to minimize the total completion time

Scheduling with learning effects has received a lot of research attention lately. However, the flowshop setting is relatively unexplored. On the other hand, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of jobs increases. This is rather absurd in reality. Motivated by these observations, we consider a two-machine flowshop scheduling problem in which the actual processing time of a job in a schedule is a function of the job’s position in the schedule and a control parameter of the learning function. The objective is to minimize the total completion time. 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 to minimize total convex resource consumption with a constraint on total weighted flow time

In this paper, we consider single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function. The objective is to minimize the total amount of resource consumed subject to a constraint on total weighted flow time. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. For the general problem, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions. The results show that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%.     

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of ?1?a?a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.     

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.     

Ant colony algorithms for a two-agent scheduling with sum-of processing times-based learning and deteriorating considerations

This paper addresses a two-agent single-machine scheduling problem with the co-existing sum-of-processing-times-based learning and deteriorating effects. In the proposed model, it is assumed that the actual processing time of a job of the first (second) agent is a decreasing function of the sum-of-processing-times-based learning (or increasing function of the sum-of-processing-times-based deteriorating effect) in a schedule. The aim of this paper is to find an optimal schedule 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. For the proposed model, we develop a branch-and-bound and some ant colony algorithms for an optimal and near-optimal solution, respectively. Besides, the extensive computational experiments are also proposed to test the performance of the algorithms.     

A two-machine flowshop makespan scheduling problem with deteriorating jobs

In traditional scheduling problems, the job processing times are assumed to be known and fixed from the first job to be processed to the last job to be completed. However, in many realistic situations, a job will consume more time than it would have consumed if it had begun earlier. This phenomenon is known as deteriorating jobs. In the science literature, the deteriorating job scheduling problems are relatively unexplored in the flowshop settings. In this paper, we study a two-machine flowshop makespan scheduling problem in which job processing times vary as time passes, i.e. they are assumed as increasing functions of their starting times. First, an exact algorithm is established to solve most of the problems of up to 32 jobs in a reasonable amount of time. Then, three heuristic algorithms are provided to derive the near-optimal solutions. A simulation study is conducted to evaluate the performances of the proposed algorithms. In addition, the impact of the deterioration rate is also investigated.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The 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 the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.     

A two-machine flowshop problem with two agents

The multiple-agent scheduling problems have received increasing attention recently. However, most of the research focuses on deriving feasible/optimal solutions or examining the computational complexity of the intractable cases in a single machine. Often a number of operations have to be done on every job in many manufacturing and assembly facilities (Pinedo, 2002 [1]). In this paper, we consider a two-machine flowshop problem where the objective is to minimize the total completion time of the first agent with no tardy jobs for the second agent. We develop a branch-and-bound algorithm and simulated annealing heuristic algorithms to search for the optimal solution and near-optimal solutions for the problem, respectively.     

Solving a two-agent single-machine scheduling problem considering learning effect

Scheduling with multiple agents and learning effect has drawn much attention. In this paper, we investigate the job scheduling problem of two agents competing for the usage of a common single machine with learning effect. The objective is to minimize the total weighted completion time of both agents with the restriction that the makespan of either agent cannot exceed an upper bound. In order to solve this problem we develop several dominance properties and a lower bound based on a branch-and-bound to find the optimal algorithm, and derive genetic algorithm based procedures for finding near-optimal solutions. The performances of the proposed algorithms are evaluated and compared via computational experiments.     

A new heuristic for scheduling the two-stage flowshop with additional resources

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines at the first stage and a single machine at the second stage. At the first stage, jobs use some additional resources which are available in limited quantities at any time. The resource requirements are of 0–1 type. The objective is the minimization of makespan. The problem is NP-hard. Heuristic algorithms are proposed which solve to optimality the resource constrained scheduling problem at the first stage of the flowshop, and at the same time, minimize the makespan in the flowshop by selecting appropriate jobs for simultaneous processing. Several rules of job selection are considered. The performance of the proposed heuristic algorithms is analyzed by comparing solutions with the lower bound on the optimal makespan. The extensive computational experiment shows that the proposed heuristic algorithms are able to produce near-optimal solutions in short computational time.     

Flowshop scheduling with a general exponential learning effect

This paper investigates flowshop scheduling problems with a general exponential learning effect, i.e., the actual processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The objective is to minimize the makespan, the total (weighted) completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times, respectively. Several simple heuristic algorithms are proposed in this paper by using the optimal schedules for the corresponding single machine problems. The tight worst-case bound of these heuristic algorithms is also given. Two well-known heuristics are also proposed for the flowshop scheduling with a general exponential learning effect.     

Two-machine flowshop scheduling with job class setups to minimize total flowtime

This paper studies the two-machine flowshop scheduling problem with job class setups to minimize the total flowtime. The jobs are classified into classes, and a setup is required on a machine if it switches processing of jobs from one class to another class, but no setup is required if the jobs are from the same class. For some special cases, we derive a number of properties of the optimal solution, based on which we design heuristics and branch-and-bound algorithms to solve these problems. Computational results show that these algorithms are effective in yielding near-optimal or optimal solutions to the tested problems.     

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

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.Received: 21 April 2003, Accepted: 9 October 2003, Published online: 16 January 2004     

A single-machine bi-criterion learning scheduling problem with release times

The learning effect in scheduling has received considerable attention recently. However, most researchers consider a single criterion with the assumption that jobs are all ready to be processed. The research of bi-criterion problems with learning effect is relatively limited. This paper studies a single-machine learning effect scheduling problem with release times where the objective is to minimize the sum of makespan and total completion time. First, we develop a branch-and-bound algorithm incorporating with several dominance properties and a lower bound to derive the optimal solution. Secondly, we propose a genetic algorithm to obtain near-optimal solutions. Finally, a computational experiment is conducted to evaluate the performance of the branch-and-bound and the genetic algorithms.     

Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times

In scheduling of batch processing machines in the diffusion and oxidation areas of a wafer fabrication facility, it can be found that the processing times of these batching operations can be extremely long (10 h) when compared to other operations (1-2 h) in a wafer fab. Moreover, the jobs to be processed may have different priorities/weights, due dates and ready times. In the presence of unequal ready times, it would be better to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, repeated processing of similar tasks improves workers’ skills. Motivated by these observations, we consider a single-machine problem with the sum of processing times based learning effect and release times. The objective is to find a schedule to minimize the total completion times. We first develop a branch-and-bound algorithm for the optimal solution. Then we propose a simulated-annealing heuristic algorithm for a near-optimal solution. Finally, we conduct a computational experiment to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 24 jobs, and the average error percentage of the simulated-annealing algorithm is less than 0.1482%.