Proportionate Flow Shop Scheduling with Rejection

2017 ◽  
Vol 34 (04) ◽  
pp. 1750015 ◽  
Author(s):  
Shi-Sheng Li ◽  
De-Liang Qian ◽  
Ren-Xia Chen
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Shop Scheduling ◽  
Total Weighted Completion Time ◽  
Processing Times ◽  
Proportionate Flow Shop ◽  
Total Penalty ◽  
Scheduling With Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

A STOCHASTIC BATCHING AND SCHEDULING PROBLEM

2001 ◽  
Vol 15 (4) ◽  
pp. 465-479 ◽  
Author(s):  
Ger Koole ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Semiconductor Manufacturing ◽  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Time ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Deterministic Problem

We consider a batch scheduling problem in which the processing time of a batch of jobs equals the maximum of the processing times of all jobs in the batch. This is the case, for example, for burn-in operations in semiconductor manufacturing and other testing operations. Processing times are assumed to be random, and we consider minimizing the makespan and the flow time. The problem is much more difficult than the corresponding deterministic problem, and the optimal policy may have many counterintuitive properties. We prove various structural properties of the optimal policy and use these to develop a polynomial-time algorithm to compute the optimal policy.

scholarly journals Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 668 ◽  
Author(s):  
Lili Zuo ◽  
Zhenxia Sun ◽  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Rejection Cost ◽  
Scheduling With Rejection

In this paper, we study two scheduling problems on a single machine with rejection and an operator non-availability interval. In the operator non-availability interval, no job can be started or be completed. However, a crossover job is allowed such that it can be started before this interval and completed after this interval. Furthermore, we also assume that job rejection is allowed. That is, each job is either accepted and processed in-house, or is rejected by paying a rejection cost. Our task is to minimize the sum of the makespan (or the total weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. For two scheduling problems with different objective functions, by borrowing the previous algorithms in the literature, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme (FPTAS), respectively.

TWO-MACHINE FLOW SHOP SCHEDULING WITH INDIVIDUAL OPERATION'S REJECTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450002 ◽  
Author(s):  
QIANG GAO ◽  
XIWEN LU
Keyword(s):  
Approximation Scheme ◽  
Flow Shop ◽  
Dynamic Programming Algorithm ◽  
Flow Shop Scheduling ◽  
Programming Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Shop Scheduling ◽  
Processing Times ◽  
Total Penalty

A two-machine flow shop scheduling problem with rejection is considered in this paper. The objective is to minimize the sum of makespan of accepted operations and total penalty of rejected operations. Each job has two operations that could be rejected, respectively. Operations on the first machine have penalties α1 times of their processing times and operations on the second machine have penalties α2 times of their processing times. A [Formula: see text]-approximation algorithm is presented for the case where min{α1, α2} < 1 and max{α1, α2} ≥ 1. A dynamic programming algorithm is provided for general α1 and α2. A fully polynomial-time approximation scheme (FPTAS) is designed for all NP-hard cases.

Single-Machine Due-Window Assignment and Scheduling with Learning Effect and Resource-Dependent Processing Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450036 ◽  
Author(s):  
Ji-Bo Wang ◽  
Ming-Zheng Wang
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Processing Time ◽  
Window Size ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Earliness And Tardiness ◽  
Processing Times ◽  
Due Window ◽  
Due Window Assignment

We consider a single-machine common due-window assignment scheduling problem, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, window size, earliness, and tardiness. For two different processing time functions, we provide a polynomial time algorithm to find the optimal job sequence and resource allocation, respectively.

OPTIMAL SEMI-ONLINE ALGORITHMS FOR m-BATCH-MACHINE FLOW SHOP SCHEDULING

2012 ◽  
Vol 04 (04) ◽  
pp. 1250051 ◽  
Author(s):  
MING LIU ◽  
CHENGBIN CHU
Keyword(s):  
Online Algorithms ◽  
Processing Time ◽  
Flow Shop ◽  
Optimal Algorithm ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Batch Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Over Time

This paper deals with semi-online scheduling on m-batch-machine flow shop. The objective is to minimize the makespan. A parallel batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. The problem is online in the sense that jobs arrive over time. Let pi, j(i = 1,…,m) denote the processing time of job Jj on machines Mi, respectively. Let Jj+1 be the following job of Jj in a job instance. We study semi-online problem with jobs' nondecreasing processing times. We focus on the case where p1, j = ⋯ = pm, j for i = 1, …, m and pi, j+1 ≥ βpi, j (β ≥ 1). For this problem, we propose an optimal algorithm [Formula: see text] with a competitive ratio [Formula: see text].

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

Scheduling with Discretely Compressible Processing Times to Minimize Makespan

2014 ◽  
Vol 575 ◽  
pp. 926-930
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Processing Time ◽  
Parallel Machines ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
Release Times ◽  
Scheduling Model

In this paper, we address the scheduling model with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost on identical parallel machines. Jobs may have simultaneous release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

scholarly journals Cyclic flow shop scheduling problem with two-machine cells

2017 ◽  
Vol 27 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Wojciech Bożejko ◽  
Andrzej Gnatowski ◽  
Radosław Idzikowski ◽  
Mieczysław Wodecki
Keyword(s):  
Problem Solving ◽  
Flow Shop ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Shop Scheduling ◽  
Cyclic Flow ◽  
Cyclic Production ◽  
Machine Cell

Abstract In the paper a variant of cyclic production with setups and two-machine cell is considered. One of the stages of the problem solving consists of assigning each operation to the machine on which it will be carried out. The total number of such assignments is exponential. We propose a polynomial time algorithm finding the optimal operations to machines assignment.

scholarly journals Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xianyu Yu ◽  
Yulin Zhang ◽  
Kai Huang
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Single Machine Scheduling ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Processing Times ◽  
Polynomially Solvable ◽  
Machine Scheduling Problems ◽  
Normal Processing

This paper investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions.

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