Two-Machine Flowshop Problem with Release Dates, Rejection and Non-Availability Interval on the First Machine

2014 ◽  
Vol 620 ◽  
pp. 80-83 ◽  
Author(s):  
Xie Xie ◽  
Xiang Yu Kong ◽  
Yong Yue Zheng ◽  
Kun Wei
Keyword(s):  
Heuristic Method ◽  
Strong Sense ◽  
Release Dates ◽  
Np Hard ◽  
Worst Case ◽  
Maximal Profit ◽  
Rejection Penalty ◽  
Flowshop Problem

This paper studies a two-machine flowshop problem with release dates, rejection and non-availability interval on the first machine. The non-availability interval often origins from equipments maintain or man-power. Usually, in order to pursue maximal profit, some jobs which can be rejected, and in this situation the rejection penalty should be paid. Our objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. For this demonstrated NP-hard in strong sense, we propose a heuristic method and further demonstrate that its worst case performance is 3.

scholarly journals Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohammad Bayat ◽  
Mehdi Heydari ◽  
Mohammad Mahdavi Mazdeh
Keyword(s):  
Standard Deviation ◽  
Processing Time ◽  
Heuristic Method ◽  
Heuristic Procedure ◽  
Release Date ◽  
Numerical Examples ◽  
Processing Times ◽  
Flowshop Problem ◽  
Expected Makespan ◽  
Actual Processing Time

The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

Finding an Unknown Acyclic Orientation of a Given Graph

2009 ◽  
Vol 19 (1) ◽  
pp. 121-131 ◽  
Author(s):  
OLEG PIKHURKO
Keyword(s):  
Complete Graph ◽  
Discrete Mathematics ◽  
Np Hard ◽  
Worst Case ◽  
Acyclic Orientation ◽  
Multiplicative Factor ◽  
The Given

Let c(G) be the smallest number of edges we have to test in order to determine an unknown acyclic orientation of the given graph G in the worst case. For example, if G is the complete graph on n vertices, then c(G) is the smallest number of comparisons needed to sort n numbers.We prove that c(G) ≤ (1/4 + o(1))n2 for any graph G on n vertices, answering in the affirmative a question of Aigner, Triesch and Tuza [Discrete Mathematics144 (1995) 3–10]. Also, we show that, for every ϵ > 0, it is NP-hard to approximate the parameter c(G) within a multiplicative factor 74/73 − ϵ.

scholarly journals Channel Density Minimization by Pin Permutation

VLSI Design ◽  
1994 ◽  
Vol 2 (2) ◽  
pp. 171-183
Author(s):  
Yang Cai ◽  
D. F. Wong ◽  
Jason Cong
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Layout Design ◽  
Strong Sense ◽  
Np Hard ◽  
Wire Length ◽  
Channel Density ◽  
Time Optimal ◽  
Two Sides ◽  
Intergrated Circuits

We present in this paper a linear time optimal algorithm for minimizing the density of a channel (with exits) by permuting the terminals on the two sides of the channel. This compares favorably with the previously known near-optimal algorithm presented in [6] that runs in superlinear time. Our algorithm has important applications in hierarchical layout design of intergrated circuits. We also show that the problem of minimizing wire length by permuting terminals is NP-hard in the strong sense.

Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems

2014 ◽  
Vol 962-965 ◽  
pp. 2868-2871 ◽  
Author(s):  
Alexander V. Chekanin ◽  
Vladislav A. Chekanin
Keyword(s):  
Data Structure ◽  
Linked Data ◽  
Bin Packing ◽  
High Efficiency ◽  
Optimization Problems ◽  
Packing Problem ◽  
Strong Sense ◽  
Np Hard ◽  
Packing Problems ◽  
Orthogonal Packing Problem

The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.

SCHEDULING ON TWO PARALLEL MACHINES WITH TWO DEDICATED SERVERS

2017 ◽  
Vol 58 (3-4) ◽  
pp. 314-323
Author(s):  
YIWEI JIANG ◽  
PING ZHOU ◽  
HUIJUAN WANG ◽  
JUELIANG HU
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
List Scheduling ◽  
Np Hard ◽  
Worst Case ◽  
Identical Machines ◽  
Loading And Unloading ◽  
Parallel Identical Machines ◽  
Dedicated Servers ◽  
Nonpreemptive Scheduling

We study a nonpreemptive scheduling on two parallel identical machines with a dedicated loading server and a dedicated unloading server. Each job has to be loaded by the loading server before being processed on one of the machines and unloaded immediately by the unloading server after its processing. The loading and unloading times are both equal to one unit of time. The goal is to minimize the makespan. Since the problem is NP-hard, we apply the classical list scheduling and largest processing time heuristics, and show that they have worst-case ratios, $8/5$ and $6/5$, respectively.

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