Single machine scheduling problems with exponentially time-dependent learning effects

In this paper, we introduce a single-machine scheduling problem with an exponentially time-dependent learning effect. The processing time of a job is assumed to be an exponential function of the total normal processing time of jobs already processed before it. For such a scheduling problem, we first provide the upper bound for the maximum lateness and for the total weighted completion time. Next, we show that problems with the following criteria: makespan, the total completion time, the total weighted completion time, the total earliness/tardiness penalties and the maximum lateness under some agreeable conditions, are polynomially solvable.     

Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns

The focus of this study is to analyze position-based learning effects in single-machine stochastic scheduling problems. The optimal permutation policies for the stochastic scheduling problems with and without machine breakdowns are examined, where the performance measures are the expectation and variance of the makespan, the expected total completion time, the expected total weighted completion time, the expected weighted sum of the discounted completion times, the maximum lateness and the maximum tardiness.     

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 job’s 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.     

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.     

Single-machine scheduling problems with deteriorating jobs and learning effects

In this paper, we introduce a new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously. By deterioration and the learning effect, we mean that the actual processing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position. For the single-machine case, we show that the problems of makespan, total completion time and the sum of the quadratic job completion times remain polynomially solvable, respectively. In addition,we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.     

Single-machine scheduling with truncated sum-of-processing-times-based learning effect including proportional delivery times

The single-machine scheduling problem with truncated sum-of-processing-times-based learning effect and past-sequence-dependent job delivery times is considered. Each job’s delivery time depends on its waiting time of processing. For some regular objective functions, it is proved that the problems can be solved by the smallest processing time first rule. For some special cases of the total weighted completion time and the maximum lateness objective functions, the thesis shows that the problems can be solved in polynomial time.     

A note on machine scheduling with sum-of-logarithm-processing-time-based and position-based learning effects

Recently, Biskup [2] classifies the learning effect models in scheduling environments into two types: position-based and sum-of-processing-time-based. In this paper, we study scheduling problem with sum-of-logarithm-processing-time-based and position-based learning effects. We show that the single machine scheduling problems to minimize the makespan and the total completion time can both be solved by the smallest (normal) processing time first (SPT) rule. We also show that the problems to minimize the maximum lateness, the total weighted completion times and the total tardiness have polynomial-time solutions under agreeable WSPT rule and agreeable EDD rule. In addition, we show that m-machine permutation flowshop problems are still polynomially solvable under the proposed learning model.     

Two-agent singe-machine scheduling with release times to minimize the total weighted completion time

In many management situations multiple agents pursuing different objectives compete on the usage of common processing resources. In this paper we study a two-agent single-machine scheduling problem with release times where the objective is to minimize the total weighted completion time of the jobs of one agent with the constraint that the maximum lateness of the jobs of the other agent does not exceed a given limit. We propose a branch-and-bound algorithm to solve the problem, and a primary and a secondary simulated annealing algorithm to find near-optimal solutions. We conduct computational experiments to test the effectiveness of the algorithms. The computational results show that the branch-and-bound algorithm can solve most of the problem instances with up to 24 jobs in a reasonable amount of time and the primary simulated annealing algorithm performs well with an average percentage error of less than 0.5% for all the tested cases.     

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

In this paper, we study a scheduling model with the consideration of both the learning effect and the setup time. Under the proposed model, the learning effect is a general function of the processing time of jobs already processed and its scheduled position, and the setup time is past-sequence-dependent. We then derive the optimal sequences for two single-machine problems, which are the makespan and the total completion time. Moreover, we showed that the weighted completion time, the maximum lateness, the maximum tardiness, and the total tardiness problems remain polynomially solvable under agreeable conditions.     

Dual constrained single machine sequencing to minimize total weighted completion time

We study a single-machine sequencing problem with both release dates and deadlines to minimize the total weighted completion time. We propose a branch-and-bound algorithm for this problem. The algorithm exploits an effective lower bound and a dynamic programming dominance technique. As a byproduct of the lower bound, we have developed a new algorithm for the generalized isotonic regression problem; the algorithm can also be used as an O(nlogn)-time timetabling routine in earliness-tardiness scheduling. Extensive computational experiments indicate that the proposed branch-and-bound algorithm competes favorably with a dynamic programming procedure. Note to Practitioners-Real-life production systems usually involve multiple machines and resources. The configurations of such systems may be complex and subject to change over time. Therefore, model-based solution approaches, which aim to solve scheduling problems for specific configurations, will inevitably run into difficulties. By contrast, decomposition methods are much more expressive and extensible. The single-machine problem and its solution procedure studied in this paper will prove useful to a decomposition method that decomposes multiple-machine, multiple-resource scheduling problems into a number of single-machine problems. The total weighted completion time objective is relevant to production environments where inventory levels and manufacturing cycle times are key concerns. Future research can be pursued along two directions. First, it seems to be necessary to further generalize the problem to consider also negative job weights. Second, the solution procedure developed here is ready to be incorporated into a machine-oriented decomposition method such as the shifting bottleneck procedure.     

On the equivalence of single machine earliness/tardiness problems with job rejection

We present optimal algorithms for single-machine scheduling problems with earliness criteria and job rejection and compare them with the algorithms for the corresponding problems with tardiness objectives. We present an optimal O(n log n) algorithm for minimizing the maximum earliness on a single machine with job rejection. Our algorithm also solves the bi-criteria scheduling problem is which the objective is to simultaneously minimize the maximum earliness of the scheduled jobs and the total rejection cost of the rejected jobs. We also show that the optimal pseudo-polynomial time algorithm for the total tardiness problem with job rejection can be used to solve the corresponding total earliness problem with job rejection.     

A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors’ previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.     

具有线性恶化加工时间的调度问题

讨论了工件具有线性恶化加工时间的调度问题.在这类问题中,工件的恶化函数为线性 函数.对单机调度问题中目标函数为极小化最大完工时间加权完工时间和,最大延误以及最大费 用等问题分别给出了最优算法.对两台机器极小化最大完工时间的Flowshop问题,证明了利用 Johnson规则可以得到最优调度.对于一般情况,如果同一工件的工序的加工时间均相等,则 Flowshop问题可以转化为单机问题.     

Single-machine scheduling with a common due window

We study several single-machine non-preemptive scheduling problems to minimize the sum of weighted earliness–tardiness, weighted number of early and tardy jobs, common due window location, and flowtime penalties. We allow the due window location to be either a decision variable or a given parameter. We assume that the due window location has a tolerance and the window size is a given parameter. We further make the assumption that the ratios of the job processing times to the earliness–tardiness weights are agreeable for the first problem. We propose pseudo-polynomial dynamic programming algorithms to optimally solve the problems. We also provide polynomial time algorithms for several special cases.Scope and purpose The widespread use of Just-In-Time philosophy in manufacturing to eliminate inventories leads to a new class of scheduling problems in which the earliness and/or number of early jobs are penalized as well as the tardiness and/or tardy jobs. In this type of environments, the jobs are sometimes associated with a period of time within which they incur no penalty since the customers will generally allow a time interval for the delivery of the products. This time period is called a due window. There are a variety of applications with due windows in factory automation, production maintenance, and so on. In this paper, we consider the common due window problems to minimize the weighted earliness–tardiness, weighted number of early–tardy jobs and weighted flowtime on a single machine. The main contributions of this paper are identifying the computational complexity of the problems, developing dynamic programming algorithms to optimally solve them, and providing efficient and exact polynomial algorithms for the special cases.     

Single-machine scheduling with deteriorating jobs under a series–parallel graph constraint

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series–parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.     

An exact algorithm for single-machine scheduling without machine idle time

This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.     

Several flow shop scheduling problems with truncated position-based learning effect

The concept of truncated position-based learning process plays a key role in production environments. However, it is relatively unexplored in the flow shop setting. In this paper, we consider the flow shop scheduling with truncated position-based learning effect, i.e., the actual processing time of a job is a function of its position and a control parameter in a processing permutation. The objective is to minimize one of the six regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the discounted total weighted completion time, the sum of the quadratic job completion times, and the maximum lateness. We present heuristic algorithms and analyze the worst-case bound of these heuristic algorithms. We also provide the computational results to evaluate the performance of the heuristics.     

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.     

Single-machine scheduling with learning effect and deteriorating jobs

In this paper we consider the single-machine scheduling problems with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their starting times and positions in the sequence. It is shown that even with the introduction of learning effect and deteriorating jobs to job processing times, single machine makespan and sum of completion times (square) minimization problems remain polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion times and the maximum lateness, this paper proves that the WSPT rule and the EDD rule can construct the optimal sequence under some special cases, respectively.