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.     

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.     

Single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times

In this paper, we consider single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times. We study three objectives which are to minimize makespan, total completion time and total weighted completion time. Furthermore, we show that these three problems are polynomially solvable under position-dependent fuzzy learning effects with fuzzy processing times. In order to model the uncertainty of fuzzy model parameters such as processing time and learning effect, we use an approach called likelihood profile that depends on the possibility and necessity measures of fuzzy parameters. For three objective functions, we build Fuzzy Mixed Integer Nonlinear Programming (FMINP) models using dependent chance constrained programming techniques for the same predetermined confidence levels. Furthermore, we present polynomially solvable algorithms for different confidence levels for these problems.     

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 group scheduling problems under the effects of deterioration and learning

This paper investigates single-machine group scheduling problems with simultaneous considerations of deteriorating and learning effects to minimize the makespan and the total completion time of all jobs. The group setup time is assumed to follow a simple linear time-dependent deteriorating model. Two models of learning for the job processing time are examined in this study. We provided polynomial time solutions for the makespan minimization problems. We also showed that the total completion time minimization problems remain polynomially solvable under agreeable conditions.     

Flowshop scheduling of deteriorating jobs on dominating machines

In this paper we consider the general, no-wait and no-idle permutation flowshop scheduling problem with deteriorating jobs, i.e., jobs whose processing times are increasing functions of their starting times. We assume a linear deterioration function with identical increasing rates for all the jobs and there are some dominating relationships between the machines. We show that the problems to minimize the makespan and the total completion time remain polynomially solvable when deterioration is considered, although these problems are more complicated than their classical counterparts without deterioration.     

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.     

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.     

Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation

We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating.     

Single-machine group scheduling with resource allocation and learning effect

This paper addresses single-machine scheduling problems under the consideration of learning effect and resource allocation in a group technology environment. In the proposed model of this paper the actual processing times of jobs depend on the job position, the group position, and the amount of resource allocated to them concurrently. Learning effect and two resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost, and the weighted sum of total completion time and total resource cost. We show that the problems for minimizing the weighted sum of makespan and total resource cost remain polynomially solvable. We also prove that the problems for minimizing the weighted sum of total completion time and total resource cost have polynomial solutions under certain conditions.     

Bounded parallel-batching scheduling with two competing agents

We consider a scheduling problem in which two agents, each with a set of non-preemptive jobs, compete to perform their jobs on a common bounded parallel-batching machine. Each of the agents wants to minimize an objective function that depends on the completion times of its own jobs. The goal is to schedule the jobs such that the overall schedule performs well with respect to the objective functions of both agents. We focus on minimizing the makespan or the total completion time of one agent, subject to an upper bound on the makespan of the other agent. We distinguish two categories of batch processing according to the compatibility of the agents. In the case where the agents are incompatible, their jobs cannot be processed in the same batch, whereas all the jobs can be processed in the same batch when the agents are compatible. We show that the makespan problem can be solved in polynomial time for the incompatible case and is NP-hard in the ordinary sense for the compatible case. Furthermore, we show that the latter admits a fully polynomial-time approximation scheme. We prove that the total completion time problem is NP-hard and is polynomially solvable for the incompatible case with a fixed number of job types.     

Single machine scheduling problems with resource dependent release times

We consider two single machine scheduling problems with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. In the first problem, the objective is to minimize the total resource consumption with a constraint on the sum of job completion times. We show that a recognition version of the problem is NP-complete. In the second problem, the objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. We provide some optimality conditions and show that the problem is polynomially solvable.     

A note on optimal policies for two group scheduling problems with deteriorating setup and processing times

Conventionally, job processing times are known and fixed. However, there are many situations where the job processing time deteriorates as time passes. In this note, we consider the makespan problems under the group technology with deteriorating setup and processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. For both linear functions, we show that the makespan problems remain polynomially solvable. In addition, the constructive algorithms are also provided.     

Single-machine scheduling jobs with exponential learning functions

In a manufacturing system workers are involved in doing the same job or activity repeatedly. Hence, the workers start learning more about the job or activity. Because of the learning, the time to complete the job or activity starts decreasing, which is known as “learning effect”. In this paper, an exponential sum-of-actual-processing-time based learning effect is introduced into single-machine scheduling. By the exponential sum-of-actual-processing-time based learning effect, we mean that the processing time of a job is defined by an exponential function of the sum-of-the-actual-processing-time of the already processed jobs. Under the proposed learning model, we show that under a sufficient condition, the makespan minimization problem, the sum of the θth (θ > 0) power of completion times minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem remain polynomially solvable.     

On scheduling a single machine with resource dependent release times

We consider a single machine scheduling problem with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. The objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. It is known that the problem is polynomially solvable in O(n⁴) with n the number of jobs.     

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.     

A single-machine scheduling problem with learning effects in intermittent batch production

This paper studies a single-machine scheduling problem with three models of learning and forgetting effects in intermittent batch production. They are the models of no transmission, partial transmission and total transmission of learning from batch to batch. The phenomena exist in many realistic production systems. The objective is to minimize the makespan. We show that the problems with the models of no transmission and partial transmission of learning from batch to batch are polynomially solvable. We also provide two polynomial time algorithms for two special cases in the problem with the total transmission model.     

Scheduling a variable maintenance and linear deteriorating jobs on a single machine

We investigate a single machine scheduling problem in which the processing time of a job is a linear function of its starting time and a variable maintenance on the machine must be performed prior to a given deadline. The goals are to minimize the makespan and the total completion time. We prove that both problems are NP-hard. Furthermore, we show that there exists a fully polynomial time approximation scheme for the makespan minimization problem. For the total completion time minimization problem we point out that there exists a fully polynomial time approximation scheme for a special case.