scholarly journals Due window assignment and scheduling on parallel machines: a FPTAS for a bottleneck criterion

2014 ◽  
Vol 62 (4) ◽  
pp. 805-808
Author(s):  
A. Janiak ◽  
W. Janiak ◽  
M.Y. Kovalyov
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Window Size ◽  
Identical Parallel Machines ◽  
Polynomial Time Approximation Scheme ◽  
Maximum Cost ◽  
Time Approximation ◽  
Due Window ◽  
Job Tardiness ◽  
Due Window Assignment

Abstract A fully polynomial time approximation scheme (FPTAS) with run time is developed for a problem which combines common due window assignment and scheduling n jobs on m identical parallel machines. The problem criterion is bottleneck (min-max) such that the maximum cost, which includes job earliness, job tardiness and due window size costs, is minimized.

scholarly journals Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Shuguang Li
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
List Scheduling ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Delivery Times ◽  
Specific Subset ◽  
Job Delivery

The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived.

TWO APPROXIMATION SCHEMES FOR SCHEDULING ON PARALLEL MACHINES UNDER A GRADE OF SERVICE PROVISION

2012 ◽  
Vol 29 (05) ◽  
pp. 1250029 ◽  
Author(s):  
WEIDONG LI ◽  
JIANPING LI ◽  
TONGQUAN ZHANG
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Approximation Scheme ◽  
Approximation Schemes ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Running Time ◽  
Grade Of Service ◽  
Special Case ◽  
Polynomial Time Approximation

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

Multiple Common Due-Window Assignment Based on Common Flow Allowance and Resource-Dependent Processing Times

2014 ◽  
Vol 644-650 ◽  
pp. 2026-2029
Author(s):  
Cheng Xin Luo ◽  
En Min Feng
Keyword(s):  
Optimal Algorithm ◽  
Window Size ◽  
Optimal Size ◽  
Processing Times ◽  
Due Windows ◽  
Resource Cost ◽  
Due Window ◽  
Resource Allocation Scheme ◽  
Due Window Assignment ◽  
Flow Allowance

This paper studies a multiple common due-window assignment problem on a single machine. The job-dependent due-windows are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal size and location of the multiple common due-windows, the set of jobs assigned to each due window, the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location, earliness and tardiness of jobs and resource cost. We propose an optimal algorithm to solve the problem.

Single-Machine Due-Window Assignment Scheduling with Resource Allocation and Generalized Earliness/Tardiness Penalties

2021 ◽  
pp. 2150041
Author(s):  
Yu Tian
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Window Size ◽  
Single Machine Scheduling ◽  
Start Time ◽  
Optimal Sequence ◽  
Optimal Resource ◽  
Due Window ◽  
Weighted Earliness ◽  
Due Window Assignment

In this study, the due-window assignment single-machine scheduling problem with resource allocation is considered, where the processing time of a job is controllable as a linear or convex function of amount of resource allocated to the job. Under common due-window and slack due-window assignments, our goal is to determine the optimal sequence of all jobs, the due-window start time, due-window size, and optimal resource allocation such that a sum of the scheduling cost (including weighted earliness/tardiness penalty, weighted number of early and tardy job, weighted due-window start time, and due-window size) and resource consumption cost is minimized. We analyze the optimality properties, and provide polynomial time solutions to solve the problem under four versions of due-window assignment and resource allocation function.

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