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.     

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 single-machine scheduling problems with a truncation learning effect

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called “sum-of processing-times-based learning” in which the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, we propose a truncation learning model where the actual job processing time is a function which depends not only on the processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. Under the proposed learning model, we show that some single-machine scheduling problems can be solved in polynomial time. In addition, we further provide the worst-case error bounds for the problems to minimize the maximum lateness and total weighted 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 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.     

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.     

One-machine scheduling problems with deteriorating jobs and position-dependent learning effects under group technology considerations

In this paper, we introduce a group scheduling model with general deteriorating jobs and learning effects in which deteriorating jobs and learning effects are both considered simultaneously. This means 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. In our model, the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent learning effects and time-dependent deterioration. The objective of scheduling problems is to minimise the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.     

Note on a unified approach to the single-machine scheduling problem with a deterioration effect and convex resource allocation

In many resource allocation problems in physical or economic systems, a linear resource consumption function is commonly considered, and job processing times are assumed to be fixed parameters. However, the former assumption fails to reflect the law of diminishing returns, and the latter may be controlled by changing the allocation of resources to jobs. Motivated by these observations, we provide a unified model for solving single-machine scheduling problems in which each job's processing time is a function of its starting time and convex resource allocation. The objective is to find the optimal sequence of jobs subject to a limited resource consumption. We first show how this unified model can be useful in solving scheduling problems under due date assignment considerations. We analyze the problem with four different due date assignment methods, and our objective function includes costs for earliness, tardiness and due date assignments. We also consider scheduling problems without involving due date assignment decisions. The objective function is to minimize the makespan, total completion time, total absolute variation in completion times, and total absolute variation in waiting times. We show that several existing well-known problems can be reduced to a special case of our unified model and solved in O(nlogn) time.     

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.     

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.     

Decision support for unrelated parallel machine scheduling with discrete controllable processing times

In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.     

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Scheduling independent jobs on uniform parallel machines to minimize tardiness criteria

The problem of scheduling N jobs on M uniform parallel machines is studied. The objective is to minimize the mean tardiness or the weighted sum of tardiness with weights based on jobs, on periods or both. For the mean tardiness criteria in the preemptive case, this problem is NP-hard but good solutions can be calculated with a transportation problem algorithm. In the nonpreemptive case the problem is therefore NP-hard, except for the cases with equal job processing times or with job due dates equal to job processing times. No dominant heuristic is known in the general nonpreemptive case. The author has developed a heuristic to solve the nonpreemptive scheduling problem with unrelated job processing times. Initially, the algorithm calculates a basic solution. Next, it considers the interchanges of job subsets to equal processing time sum interchanging resources (i.e. a machine for a given period). This paper models the scheduling problem. It presents the heuristic and its result quality, solving 576 problems for 18 problem sizes. An application of school timetable scheduling illustrates the use of this heuristic.     

Single machine scheduling with past-sequence-dependent setup times and learning effects

This paper studies a single machine scheduling problem with setup times and learning considerations. The setup times are proportional to the length of the already scheduled jobs. That is, the setup times are past-sequence-dependent. It is assumed that the learning process reflects a decrease in the process time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. The following objectives are considered: the makespan, the total completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalty. Polynomial time algorithms are proposed to optimally solve the above objective functions.     

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.     

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 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 to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity

This note considers a single machine scheduling and due-window assignment problem, in which the processing time of a job is a linear function of its starting time and the job-independent deterioration rates are identical for all jobs. We allow an option for performing a rate-modifying activity for changing the normal processing times of the jobs following this activity. The objective is to schedule the jobs, the due-window and the rate-modifying activity so as to minimize the sum of earliness, tardiness and due-window starting time and due-window size costs. We introduce a polynomial solution for the problem.     

Exact and parallel metaheuristic algorithms for the single processor total weighted completion time scheduling problem with the sum-of-processing-time based models

In this paper, the single processor scheduling problem to minimize the total weighted completion times is analysed, where the processing times of jobs are described by functions dependent on the sum of the normal processing times of previously processed jobs, which can model learning or aging (deteriorating) effects. We construct the exact pseudopolynomial time algorithm based on the dynamic programming, which solves the problem, where the processing time of each job is described by an arbitrary stepwise function. Moreover, the parallel metaheuristic algorithms are provided for the general version of the problem with arbitrary sum-of-processing time based models. The efficiency of the proposed algorithms is evaluated during numerical analysis.