scholarly journals Solving a Real Problem in Plastic Industry: A Case in Trim-loss Problem

2020 ◽  
Author(s):  
Ivan Renata ◽  
Siana Halim ◽  
Bernardo Nugroho Yahya
Keyword(s):  
Machine Scheduling ◽  
Cutting Plane ◽  
Daily Basis ◽  
Cutting Stock ◽  
Real Problem ◽  
Hard Problem ◽  
Due Date ◽  
Np Hard Problem ◽  
Trim Loss ◽  
Visual Basic For Application

In this paper, a cutting plane model is presented for solving a problem in a cast polypropylene (CPP) plastic film manufacturer. The company produces plastic rolls from plastic pellets with widths ranging from 3 050 mm to 3 250 mm. The plastic rolls are trimmed according to customer’s orders. In prior to the trimming process, the production planning and inventory control (PPIC) department scheduled the machines and arranged the plastic trim compositions manually. In this work, the plastic trimming problem is solved by applying the trim loss model. Since trimmed loss problem is an NP-hard problem. In this case, the permutations are selected in advance so that the total length is feasible to the machine length. The computation is carried out using visual basic for application (VBA). The model outcomes are then used for optimizing the machine scheduling process. Modified earliest due date is proposed to schedule in which machines customer’s orders should be done. The machines scheduling represents the company conditions and the cutting production can be scheduled for daily basis. Keywords: cutting plane; cutting stock; earliest due date; machine scheduling; non-polinomial-hard problem.

An Improved Tabu Search Algorithm for a Type of Single Machine Sequencing Problem

2013 ◽  
Vol 756-759 ◽  
pp. 3997-4001
Author(s):  
Meng Lan Wang ◽  
Wen Bin Liu
Keyword(s):  
Tabu Search ◽  
Single Machine ◽  
Search Algorithm ◽  
Machine Scheduling ◽  
Tabu Search Algorithm ◽  
Scheduling Problem ◽  
Hard Problem ◽  
Sequencing Problem ◽  
Np Hard Problem ◽  
One Machine

Machine scheduling is a central task in production planning. In general it means the problem of scheduling job operations on a given number of available machines. In this paper we consider a machine scheduling problem with one machine, or the Single Machine Total Tardiness Problem. To solve this NP-hard problem, we develop an improved Tabu Search Algorithm, which is tested to have the ability to find good results by an example.

scholarly journals Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1383
Author(s):  
Ali H. Alkhaldi ◽  
Muhammad Kamran Aslam ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Metric Dimension ◽  
Hard Problem ◽  
Np Hard ◽  
Weighted Version ◽  
Sharp Bounds ◽  
Np Hard Problem ◽  
Metric Dimensions

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.

scholarly journals Offline Algorithms in Low-Frequency Trading

Queue ◽  
2020 ◽  
Vol 18 (6) ◽  
pp. 37-51
Author(s):  
Terence Kelly
Keyword(s):  
Real Time ◽  
Real World ◽  
High Frequency ◽  
Low Frequency ◽  
Combinatorial Auctions ◽  
Hard Problem ◽  
Np Hard ◽  
High Stakes ◽  
Drill Bits ◽  
Np Hard Problem

Expectations run high for software that makes real-world decisions, particularly when money hangs in the balance. This third episode of the Drill Bits column shows how well-designed software can effectively create wealth by optimizing gains from trade in combinatorial auctions. We'll unveil a deep connection between auctions and a classic textbook problem, we'll see that clearing an auction resembles a high-stakes mutant Tetris, we'll learn to stop worrying and love an NP-hard problem that's far from intractable in practice, and we'll contrast the deliberative business of combinatorial auctions with the near-real-time hustle of high-frequency trading. The example software that accompanies this installment of Drill Bits implements two algorithms that clear combinatorial auctions.

Frequent Closed Partial Orders Mining in Sequences

2013 ◽  
Vol 846-847 ◽  
pp. 1304-1307
Author(s):  
Ye Wang ◽  
Yan Jia ◽  
Lu Min Zhang
Keyword(s):  
Sequence Data ◽  
Real Data ◽  
Partial Orders ◽  
Hard Problem ◽  
Important Data ◽  
Data Set ◽  
Pruning Algorithm ◽  
Equal Chance ◽  
Np Hard Problem ◽  
General Sequences

Mining partial orders from sequence data is an important data mining task with broad applications. As partial orders mining is a NP-hard problem, many efficient pruning algorithm have been proposed. In this paper, we improve a classical algorithm of discovering frequent closed partial orders from string. For general sequences, we consider items appearing together having equal chance to calculate the detecting matrix used for pruning. Experimental evaluations from a real data set show that our algorithm can effectively mine FCPO from sequences.

Single machine scheduling with a variable common due date and resource-dependent processing times

2003 ◽  
Vol 30 (8) ◽  
pp. 1173-1185 ◽  
Author(s):  
C.T.Daniel Ng ◽  
T.C.Edwin Cheng ◽  
Mikhail Y. Kovalyov ◽  
S.S. Lam
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Due Date ◽  
Common Due Date ◽  
Processing Times

scholarly journals A Recursive Formula for the Reliability of a r-Uniform Complete Hypergraph and Its Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ke Zhang ◽  
Haixing Zhao ◽  
Zhonglin Ye ◽  
Lixin Dong
Keyword(s):  
Recurrence Relations ◽  
Recursive Formula ◽  
Finite Graph ◽  
Hard Problem ◽  
Np Hard ◽  
Spanning Subgraph ◽  
Reliability Polynomial ◽  
Np Hard Problem

The reliability polynomial R(S,p) of a finite graph or hypergraph S=(V,E) gives the probability that the operational edges or hyperedges of S induce a connected spanning subgraph or subhypergraph, respectively, assuming that all (hyper)edges of S fail independently with an identical probability q=1-p. In this paper, we investigate the probability that the hyperedges of a hypergraph with randomly failing hyperedges induce a connected spanning subhypergraph. The computation of the reliability for (hyper)graphs is an NP-hard problem. We provide recurrence relations for the reliability of r-uniform complete hypergraphs with hyperedge failure. Consequently, we determine and calculate the number of connected spanning subhypergraphs with given size in the r-uniform complete hypergraphs.

scholarly journals Metric dimension of metric transform and wreath product

2019 ◽  
Vol 11 (2) ◽  
pp. 418-421
Author(s):  
B.S. Ponomarchuk
Keyword(s):  
Wreath Product ◽  
Metric Space ◽  
Metric Spaces ◽  
Metric Dimension ◽  
Hard Problem ◽  
Np Hard ◽  
Resolving Set ◽  
Np Hard Problem ◽  
Metric Transform ◽  
Empty Subset

Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called the metric dimension $md(X)$ of the metric space $(X,d)$. In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbitrary metric space is equal to the metric dimension of its metric transform.

scholarly journals Solving the Traveling Salesman Problem on the D-Wave Quantum Computer

2021 ◽  
Vol 9 ◽  
Author(s):  
Siddharth Jain
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Quantum Computer ◽  
Traveling Salesman ◽  
Hard Problem ◽  
Problem Size ◽  
Quadratic Unconstrained Binary Optimization ◽  
Np Hard Problem ◽  
The Traveling Salesman Problem ◽  
D Wave

The traveling salesman problem is a well-known NP-hard problem in combinatorial optimization. This paper shows how to solve it on an Ising Hamiltonian based quantum annealer by casting it as a quadratic unconstrained binary optimization (QUBO) problem. Results of practical experiments are also presented using D-Wave’s 5,000 qubit Advantage 1.1 quantum annealer and the performance is compared to a classical solver. It is found the quantum annealer can only handle a problem size of 8 or less nodes and its performance is subpar compared to the classical solver both in terms of time and accuracy.

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

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