A Note on Single-Machine Scheduling with Deteriorating Jobs

2011 ◽  
Vol 219-220 ◽  
pp. 483-486
Author(s):  
Yun Qiang Yin ◽  
Feng Lian Yuan
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Optimal Schedule ◽  
Real Life ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Proposed Model ◽  
Time Minimization ◽  
Polynomially Solvable ◽  
Job Deterioration

In many real life applications, jobs deteriorate at a certain rate while waiting to be processed. This paper introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. We show that the single-machine makespan minimization problem remains polynomially solvable under the proposed model. We also show that an optimal schedule of the total completion time minimization problem is polynomially solvable under some cases and-shaped with respect to job deterioration rates for other cases.

scholarly journals Single-Machine Scheduling Problems with a Sum-of-Processing-Time-Based Learning Function

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Xingong Zhang ◽  
Guangle Yan
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Proposed Model ◽  
Time Minimization ◽  
Polynomially Solvable

Recently, learning scheduling problems have received increasing attention. However, the majority of the research assume that the actual job processing time is a function of its position. This paper deals with the single-machine scheduling problem with a sum-of-processing-time-based learning effect. By the effect of sum-of-processing-time-based learning, we mean that the processing time of a job is defined by total normal processing time of jobs in front of it in the sequence. We show that the single-machine makespan problem remains polynomially solvable under the proposed model. We show that the total completion time minimization problem for a≥1 remains polynomially solvable under the proposed model. For the case of 0<a<1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.

Single Machine Two-Agent Scheduling with Deteriorating Jobs

2016 ◽  
Vol 33 (05) ◽  
pp. 1650034 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yu-Bin Wu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Weighted Completion Time

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

scholarly journals A Two-Agent Single-Machine Scheduling Problem with Learning and Deteriorating Considerations

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Wen-Hsiang Wu
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Proposed Model ◽  
Agent Scheduling ◽  
Increasing Function ◽  
Annealing Algorithms

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered the multiagent setting. Motivated by these observations, we consider two-agent scheduling on a single machine involving the learning effects and deteriorating jobs simultaneously. In the proposed model, we assume that the actual processing time of a job of the first (second) agent is a decreasing (increasing) function of the total processing time of the jobs already processed in a schedule. 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 a simulated annealing algorithms for the problem. We perform extensive computational experiments to test the performance of the algorithms.

SINGLE MACHINE SCHEDULING WITH LINEAR DETERIORATING JOBS UNDER PREDICTIVE DISRUPTION

2011 ◽  
Vol 28 (03) ◽  
pp. 419-429 ◽  
Author(s):  
CHUAN-LI ZHAO ◽  
HENG-YONG TANG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Completion Time ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Original Objective

This paper considers single machine scheduling problems with linear deteriorating jobs under predictive disruption. In this model, the actual processing time of a job is a increasing linear function of its starting time; and machine is subject to an availability constraint. We assume that an optimal schedule can be obtained by using some algorithms if machine is available at all time. Because of the machine disruption, the original schedule may become infeasible or too far from optimal. We want to create the new schedule that takes into account both the original objective function and a measure of deviation from the original schedule. We consider two versions of the problem. In the first one, the objective is weighted sum of total completion time and total tardiness while in the second one, the objective is weighted sum of total completion time and total earliness. We first prove some properties of the optimal schedule then dynamic programming algorithms are proposed, respectively.

Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

2015 ◽  
Vol 32 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Yuan-Yuan Lu ◽  
Fei Teng ◽  
Zhi-Xin Feng
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Exponential Sum ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Processing Times ◽  
Time Minimization ◽  
Weighted Completion Time

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity

2017 ◽  
Vol 34 (04) ◽  
pp. 1750011 ◽  
Author(s):  
Zhusong Liu ◽  
Zhenyou Wang ◽  
Yuan-Yuan Lu
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Maintenance Activity ◽  
Optimal Resource ◽  
Deteriorating Maintenance ◽  
Polynomially Solvable ◽  
Completion Times

This paper considers the single machine scheduling with learning effect, resource allocation and deteriorating maintenance activity simultaneously. For the convex resource allocation consumption function, we provide a bicriteria analysis where the first (schedule) criterion is to minimize the total weighted sum of makespan, total completion time and total absolute differences in completion times, and the second (resource) criterion is to minimize the total weighted resource consumption. Our aim is to find the optimal resource allocations and job sequence that minimize the three different models of considering the two criterion. We show that these three models are polynomially solvable respectively.

Sign in / Sign up

Export Citation Format

Share Document