scholarly journals Preemptive Scheduling with Controllable Processing Times on Parallel Machines

2015 ◽  
Vol 3 (1) ◽  
pp. 68-76
Author(s):  
Guiqing Liu ◽  
Kai Li ◽  
Bayi Cheng
Keyword(s):  
Polynomial Time ◽  
Resource Use ◽  
Parallel Machines ◽  
Optimal Algorithm ◽  
Parallel Machine Scheduling ◽  
Controllable Processing Times ◽  
Scheduling Problems ◽  
Processing Times ◽  
Online Problems ◽  
Machine Scheduling Problems

AbstractThis paper considers several parallel machine scheduling problems with controllable processing times, in which the goal is to minimize the makespan. Preemption is allowed. The processing times of the jobs can be compressed by some extra resources. Three resource use models are considered. If the jobs are released at the same time, the problems under all the three models can be solved in a polynomial time. The authors give the polynomial algorithm. When the jobs are not released at the same time, if all the resources are given at time zero, or the remaining resources in the front stages can be used to the next stages, the offline problems can be solved in a polynomial time, but the online problems have no optimal algorithm. If the jobs have different release dates, and the remaining resources in the front stages can not be used in the next stages, both the offline and online problems can be solved in a polynomial time.

scholarly journals Scheduling on a Single Machine and Parallel Machines with Batch Deliveries and Potential Disruption

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hua Gong ◽  
Yuyan Zhang ◽  
Puyu Yuan
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Manufacturing Industry ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Approximation Schemes ◽  
Scheduling Problems ◽  
Delivery Scheduling ◽  
Production Part

In this paper, we study several coordinated production-delivery scheduling problems with potential disruption motivated by a supply chain in the manufacturing industry. Both single-machine environment and identical parallel-machine environment are considered in the production part. The jobs finished on the machines are delivered to the same customer in batches. Each delivery batch has a capacity and incurs a delivery cost. There is a situation that a possible disruption in the production part may occur at some particular time and will last for a period of time with a probability. We consider both resumable case and nonresumable case where a job does not need (needs) to restart if it is disrupted for a resumable (nonresumable) case. The objective is to find a coordinated schedule of production and delivery that minimizes the expected total flow times plus the delivery costs. We first present some properties and analyze the NP-hard complexity for four various problems. For the corresponding single-machine and parallel-machine scheduling problems, pseudo-polynomial-time algorithms and fully polynomial-time approximation schemes (FPTASs) are presented in this paper, respectively.

scholarly journals A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

2021 ◽  
Vol 55 (2) ◽  
pp. 561-569
Author(s):  
Shan-Shan Lin
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Controllable Processing Times ◽  
Learning Effects ◽  
Scheduling Problems ◽  
Total Load ◽  
Processing Times ◽  
Dependent Learning

This note studies a unrelated parallel-machine scheduling problem with controllable processing times and job-dependent learning effects, where the objective function is to minimize the weighted sum of total completion time, total load, and total compression cost. We show that the problem can be solved in O(nm+2) time, where m and n are the numbers of machines and jobs. We also show how to apply the technique to several single-machine scheduling problems with total criteria.

scholarly journals Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

2021 ◽  
Author(s):  
Bartłomiej Przybylski
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Positive Function ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problems ◽  
Processing Times ◽  
Maximum Completion Time ◽  
Machine Scheduling Problems

AbstractWe consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

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