## Rack Structure

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### Mohammadreza Vasili - One of the best experts on this subject based on the ideXlab platform.

2009 International Conference on Computers & Industrial Engineering, 2009
Co-Authors: Shamsuddin Sulaiman, Napsiah Ismail, Tang Sai Hong, Wong Shaw Voon, Mohammadreza Vasili
Abstract:

Automated storage and retrieval systems (AS/RSs) are a combination of equipment and control systems which handle, store and retrieve materials with great speed and accuracy, under a defined degree of automation. AS/RSs are warehousing systems that are widely used in distribution and production environments to manage products with cost-effective utilization of time, space and equipment. This paper presents an open-Rack Structure with unidirectional-upward mobile loads within the Rack, for miniload AS/RS. Bead-Sort Algorithm and a cellular automaton (CA) are used for defining and simulating of load shuffling in this AS/RS, respectively. Heuristic models are developed for load shuffling and travel time of the storage platform. A cellular automaton is a suitable choice for simulating natural physical systems because it is massively parallel, self-organizing and is driven by a set of simple, local rules. The Travel time and performance of proposed AS/RS are analyzed using Monte Carlo simulation and are compared with a conventional one. The results show that the open-Rack AS/RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

• ##### Open-Rack Structure for miniload automated storage and retrieval system:an innovative design approach
2008
Co-Authors: Mohammadreza Vasili, Sai Hong Tang, Napsiah Ismail, Shamsuddin Sulaiman
Abstract:

Miniload automated storage and retrieval system (AS/RSs) is a type of automatic storage and retrieval system that handles loads that are typically contained in small containers or totes, with load weights typically falling in the 100 to 500 lb. In this paper,the open-Rack Structure with unidirectional-upward mobile loads within the Rack is applied in miniload As/RS, in which the stacker crane is only used for the retrieval operations and the storage operations are carried out by separate devices namely, storage platform for each Rack to unload several loads at the same time into the Rack. Heuristics algorithms and models are developed for load shuffling and travel time of the storage platform, respectively. The travel time and the Performance of proposed AS/RS is analyzed using Monte Carlo simulation and is compared with a conventional one. The results show that the open-Rack AS?RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

• ##### Class-based storage assignments for miniload AS/RS with open-Rack Structure
2008
Co-Authors: Mohammadreza Vasili, Sai Hong Tang, Napsiah Ismail, Shamsuddin Sulaiman
Abstract:

Automated Storage and Retrieval Systems (AS/RSs) are warehousing systems that are used for the storage and retrieval of products in both distribution and production environments. This paper presents an open-Rack Structure with unidirectional-upward mobile loads within the Rack, for miniload AS/RS, in which the stacker crane is only used for the retrieval operations, and the storage operations are carried out by separate devices namely, storage platforms. Heuristics algorithms and models are developed for load shuffling and travel time of the storage platform, respectively. The well-known ABC approach is used to classify inventory items for determination of class-based storage assignments. Then the expected travel time of the proposed AS/RS is derived. The travel time model and the performance of proposed AS/RS are validated using Monte Carlo simulation and are compared with a conventional one. The results show that the open-Rack AS/RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

• ##### IC-AI - A Statistical Travel Time Model for Miniload Automated Storage and Retrieval Systems with Open-Rack Structure.
2008
Co-Authors: Napsiah Ismail, Sai Hong Tang, Suditama Sulaiman, Mohammadreza Vasili
Abstract:

In customary automated storage and retrieval systems (AS/RSs), stacker cranes (S/R machines) are used to store and retrieve loads into/from the storage cells. In this paper, the open-Rack Structure with unidirectionalupward mobile loads within the Rack is applied in AS/RS, in which the stacker crane is only used for the retrieval operations, and the storage operations are carried out by separate devices namely, storage platforms. Heuristics algorithms and models are developed for load shuffling and travel time of the storage platform, respectively. Then the expected travel time of the proposed AS/RS is derived. The travel time model and the performance of proposed AS/RS are validated using Monte Carlo simulation and are compared with a conventional one. The results show that the open-Rack AS/RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

### Mohamed Boucetta - One of the best experts on this subject based on the ideXlab platform.

• ##### Analytic linear Lie Rack Structures on Leibniz algebras
Communications in Algebra, 2020
Co-Authors: Hamid Abchir, Fatima-ezzahrae Abid, Mohamed Boucetta
Abstract:

AbstractA linear Lie Rack Structure on a finite dimensional vector space V is a Lie Rack operation (x,y)↦x⊳y pointed at the origin and such that for any x, the left translation Lx:y↦Lx(y)=x⊳y is li...

• ##### Analytic Linear Lie Rack Structures on Leibniz Algebras
arXiv: Differential Geometry, 2019
Co-Authors: Hamid Abchir, Fatima-ezzahrae Abid, Mohamed Boucetta
Abstract:

A linear Lie Rack Structure on a finite dimensional vector space $V$ is a Lie Rack operation $(x,y)\mapsto x\rhd y$ pointed at the origin and such that for any $x$, the left translation $\mathrm{L}_x:y\mapsto \mathrm{L}_x(y)= x\rhd y$ is linear. A linear Lie Rack operation $\rhd$ is called analytic if for any $x,y\in V$, $x\rhd y=y+\sum_{n=1}^\infty A_{n,1}(x,\ldots,x,y),$where $A_{n,1}:V\times\ldots\times V\Leftarrow V$ is an $n+1$-multilinear map symmetric in the $n$ first arguments. In this case, $A_{1,1}$ is exactly the left Leibniz product associated to $\rhd$. Any left Leibniz algebra $(\mathfrak{h},[\;,\;])$ has a canonical analytic linear Lie Rack Structure given by $x\stackrel{c}{\rhd} y=\exp(\mathrm{ad}_x)(y)$, where $\mathrm{ad}_x(y)=[x,y]$. In this paper, we show that a sequence $(A_{n,1})_{n\geq1}$ of $n+1$-multilinear maps on a vector space $V$ defines an analytic linear Lie Rack Structure if and only if $[\;,\;]:=A_{1,1}$ is a left Leibniz bRacket, the $A_{n,1}$ are invariant for $(V,[\;,\;]:)$ and satisfy a sequence of multilinear equations. Some of these equations have a cohomological interpretation and can be solved when the zero and the 1-cohomology of the left Leibniz algebra $(V,[\;,\;])$ are trivial. On the other hand, given a left Leibniz algebra $(\mathfrak{h},[\;,\;])$, we show that there is a large class of (analytic) linear Lie Rack Structures on $(\mathfrak{h},[\;,\;])$ which can be built from the canonical one and invariant multilinear symmetric maps on $\mathfrak{h}$. A left Leibniz algebra on which all the analytic linear Lie Rack Structures are build in this way will be called rigid. We use our characterizations of analytic linear Lie Rack Structures to show that $\mathfrak{sl}_2(\mathbb{R})$ and $\mathfrak{so}(3)$ are rigid. We conjecture that any simple Lie algebra is rigid as a left Leibniz algebra.

### Shamsuddin Sulaiman - One of the best experts on this subject based on the ideXlab platform.

2009 International Conference on Computers & Industrial Engineering, 2009
Co-Authors: Shamsuddin Sulaiman, Napsiah Ismail, Tang Sai Hong, Wong Shaw Voon, Mohammadreza Vasili
Abstract:

Automated storage and retrieval systems (AS/RSs) are a combination of equipment and control systems which handle, store and retrieve materials with great speed and accuracy, under a defined degree of automation. AS/RSs are warehousing systems that are widely used in distribution and production environments to manage products with cost-effective utilization of time, space and equipment. This paper presents an open-Rack Structure with unidirectional-upward mobile loads within the Rack, for miniload AS/RS. Bead-Sort Algorithm and a cellular automaton (CA) are used for defining and simulating of load shuffling in this AS/RS, respectively. Heuristic models are developed for load shuffling and travel time of the storage platform. A cellular automaton is a suitable choice for simulating natural physical systems because it is massively parallel, self-organizing and is driven by a set of simple, local rules. The Travel time and performance of proposed AS/RS are analyzed using Monte Carlo simulation and are compared with a conventional one. The results show that the open-Rack AS/RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

• ##### Open-Rack Structure for miniload automated storage and retrieval system:an innovative design approach
2008
Co-Authors: Mohammadreza Vasili, Sai Hong Tang, Napsiah Ismail, Shamsuddin Sulaiman
Abstract:

Miniload automated storage and retrieval system (AS/RSs) is a type of automatic storage and retrieval system that handles loads that are typically contained in small containers or totes, with load weights typically falling in the 100 to 500 lb. In this paper,the open-Rack Structure with unidirectional-upward mobile loads within the Rack is applied in miniload As/RS, in which the stacker crane is only used for the retrieval operations and the storage operations are carried out by separate devices namely, storage platform for each Rack to unload several loads at the same time into the Rack. Heuristics algorithms and models are developed for load shuffling and travel time of the storage platform, respectively. The travel time and the Performance of proposed AS/RS is analyzed using Monte Carlo simulation and is compared with a conventional one. The results show that the open-Rack AS?RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

• ##### Class-based storage assignments for miniload AS/RS with open-Rack Structure
2008
Co-Authors: Mohammadreza Vasili, Sai Hong Tang, Napsiah Ismail, Shamsuddin Sulaiman
Abstract:

Automated Storage and Retrieval Systems (AS/RSs) are warehousing systems that are used for the storage and retrieval of products in both distribution and production environments. This paper presents an open-Rack Structure with unidirectional-upward mobile loads within the Rack, for miniload AS/RS, in which the stacker crane is only used for the retrieval operations, and the storage operations are carried out by separate devices namely, storage platforms. Heuristics algorithms and models are developed for load shuffling and travel time of the storage platform, respectively. The well-known ABC approach is used to classify inventory items for determination of class-based storage assignments. Then the expected travel time of the proposed AS/RS is derived. The travel time model and the performance of proposed AS/RS are validated using Monte Carlo simulation and are compared with a conventional one. The results show that the open-Rack AS/RS represents a higher performance and the proposed models are reliable for the design and analysis of this kind of AS/RS.

### Jong Bae Baek - One of the best experts on this subject based on the ideXlab platform.

• ##### CFD modeling and fire damage analysis of jet fire on hydrogen pipeline in a pipe Rack Structure
International Journal of Hydrogen Energy, 2015
Co-Authors: Chang Bong Jang, Sang Won Choi, Jong Bae Baek
Abstract:

The fire accident to most frequently occur at a process plant may be generated at any place transporting or handling combustible materials. Especially, in the case of a jet fire at a process plant pipe operated under high pressure, a critical outcome may arise. To review this, this study was designed to apply the CFD simulation on the outcome of a jet fire generated at a high pressure hydrogen pipeline within a pipe Rack Structure to compute the consequences. For the simulation, Kameleon FireEx(KFX) was used, and for results, the temperature of a jet fire and heat flux distribution under the complex geometry of a pipe Rack Structure, boundary conditions, and turbulent combustion were reviewed.

### Hamid Abchir - One of the best experts on this subject based on the ideXlab platform.

• ##### Analytic linear Lie Rack Structures on Leibniz algebras
Communications in Algebra, 2020
Co-Authors: Hamid Abchir, Fatima-ezzahrae Abid, Mohamed Boucetta
Abstract:

AbstractA linear Lie Rack Structure on a finite dimensional vector space V is a Lie Rack operation (x,y)↦x⊳y pointed at the origin and such that for any x, the left translation Lx:y↦Lx(y)=x⊳y is li...

• ##### Analytic Linear Lie Rack Structures on Leibniz Algebras
arXiv: Differential Geometry, 2019
Co-Authors: Hamid Abchir, Fatima-ezzahrae Abid, Mohamed Boucetta
Abstract:

A linear Lie Rack Structure on a finite dimensional vector space $V$ is a Lie Rack operation $(x,y)\mapsto x\rhd y$ pointed at the origin and such that for any $x$, the left translation $\mathrm{L}_x:y\mapsto \mathrm{L}_x(y)= x\rhd y$ is linear. A linear Lie Rack operation $\rhd$ is called analytic if for any $x,y\in V$, $x\rhd y=y+\sum_{n=1}^\infty A_{n,1}(x,\ldots,x,y),$where $A_{n,1}:V\times\ldots\times V\Leftarrow V$ is an $n+1$-multilinear map symmetric in the $n$ first arguments. In this case, $A_{1,1}$ is exactly the left Leibniz product associated to $\rhd$. Any left Leibniz algebra $(\mathfrak{h},[\;,\;])$ has a canonical analytic linear Lie Rack Structure given by $x\stackrel{c}{\rhd} y=\exp(\mathrm{ad}_x)(y)$, where $\mathrm{ad}_x(y)=[x,y]$. In this paper, we show that a sequence $(A_{n,1})_{n\geq1}$ of $n+1$-multilinear maps on a vector space $V$ defines an analytic linear Lie Rack Structure if and only if $[\;,\;]:=A_{1,1}$ is a left Leibniz bRacket, the $A_{n,1}$ are invariant for $(V,[\;,\;]:)$ and satisfy a sequence of multilinear equations. Some of these equations have a cohomological interpretation and can be solved when the zero and the 1-cohomology of the left Leibniz algebra $(V,[\;,\;])$ are trivial. On the other hand, given a left Leibniz algebra $(\mathfrak{h},[\;,\;])$, we show that there is a large class of (analytic) linear Lie Rack Structures on $(\mathfrak{h},[\;,\;])$ which can be built from the canonical one and invariant multilinear symmetric maps on $\mathfrak{h}$. A left Leibniz algebra on which all the analytic linear Lie Rack Structures are build in this way will be called rigid. We use our characterizations of analytic linear Lie Rack Structures to show that $\mathfrak{sl}_2(\mathbb{R})$ and $\mathfrak{so}(3)$ are rigid. We conjecture that any simple Lie algebra is rigid as a left Leibniz algebra.