A polynomial algorithm for the homogeneously non-idling scheduling problem of unit-time independent jobs on identical parallel machines

2018 ◽  
Vol 243 ◽  
pp. 132-139 ◽  
Author(s):  
Philippe Chrétienne ◽  
Alain Quilliot
Keyword(s):  
Parallel Machines ◽  
Polynomial Algorithm ◽  
Scheduling Problem ◽  
Identical Parallel Machines

An Optimal Preemptive Algorithm for the Single-Server Parallel-Machine Scheduling with Loading and Unloading Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450039 ◽  
Author(s):  
Yiwei Jiang ◽  
Huijuan Wang ◽  
Ping Zhou
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Solution Algorithm ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Loading And Unloading

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

scholarly journals Scheduling Two Identical Parallel Machines Subjected to Release Times, Delivery Times and Unavailability Constraints

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1025
Author(s):  
Adel M. Al-Shayea ◽  
Mustafa Saleh ◽  
Moath Alatefi ◽  
Mageed Ghaleb
Keyword(s):  
Parallel Machines ◽  
Release Time ◽  
Processing Unit ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Central Processing ◽  
Cpu Time ◽  
Release Times ◽  
Delivery Times ◽  
Input Variables

This paper proposes a genetic algorithm (GA) for scheduling two identical parallel machines subjected to release times and delivery times, where the machines are periodically unavailable. To make the problem more practical, we assumed that the machines are undergoing periodic maintenance rather than making them always available. The objective is to minimize the makespan (Cmax). A lower bound (LB) of the makespan for the considered problem was proposed. The GA performance was evaluated in terms of the relative percentage deviation (RPD) (the relative distance to the LB) and central processing unit (CPU) time. Response surface methodology (RSM) was used to optimize the GA parameters, namely, population size, crossover probability, mutation probability, mutation ratio, and pressure selection, which simultaneously minimize the RPD and CPU time. The optimized settings of the GA parameters were used to further analyze the scheduling problem. Factorial design of the scheduling problem input variables, namely, processing times, release times, delivery times, availability and unavailability periods, and number of jobs, was used to evaluate their effects on the RPD and CPU time. The results showed that increasing the release time intervals, decreasing the availability periods, and increasing the number of jobs increase the RPD and CPU time and make the problem very difficult to reach the LB.

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