A multi-objective optimization model for minimizing investment expenses, cycle times and co2 footprint of an automated storage and retrieval systems

A new optimization model of Automated Storage and Retrieval Systems (AS/RS) containing three objective and four constraint functions is presented in this paper. Majority of the researchers and publications in material handling field had performed optimization of different decision variables, but with single objective function only. Most common functions are: minimum travel time, maximum throughput capacity, minimum cost, maximum energy efficiency, etc. To perform the simultaneous optimization of objective functions (minimum: "investment expenses", "cycle times", "CO2 footprint") the Non-dominated Sorting Genetic Algorithm II (NSGA II) was used. The NSGA II is a tool for finding the Pareto optimal solutions on the Pareto line. Determining the performance of the system is the main goal of our model. Since AS/RS are not flexible in terms of layout and organizational changes once the system is up and running, the proposed model could be a very helpful tool for the warehouse planners in the early stages of warehouse design

A multi-objective optimization model for minimizing cost, travel time and Co2 emission in an AS/RS

U predstavljenom radu, diskutovano je i vršena je evaluacija višeciljne optimizacije automatskih skladišnih sistema. S obzirom da je većina istraživača u oblasti manipulacije materijalom i logistici, vršila optimizaciju promenljivih samo sa jednom funkcijom cilja (najčešće je to funkcija minimalno vreme ciklusa, maksimalni intenzitet opsluživanja, minimalna cena, tj. troškovi, maksimalna energetska efikasnost, itd.), predložen je model višeciljne optimizacije (sa trima funkcijama cilja: minimalni troškovi - minimalno vreme ciklusa - minimalna emisija CO2, odnosno maksimalna energetska efikasnost). Za optimizaciju promenljivih u funkcijama cilja, korišćeni su genetski algoritmi. Da bismo pronašli optimalna Pareto rešenja, upotrebili smo NSGA II genetske algoritme. Glavni zadatak našeg doprinosa jeste da se utvrde performanse automatskog skladišnog sistema, u skladu sa procedurom višeciljne optimizacije. Rezultati predloženog modela, mogu biti od koristi projektantima u ranim fazama projektovanja automatskog skladišnog sistema.A multi-objective optimization of automated warehouses is discussed and evaluated in the present paper. Since most of the researchers in material handling community had performed optimization of decision variables with single objective function only (usually named with minimum travel time, maximum throughput capacity, minimum cost, maximum energy efficiency, etc.), the multi-objective optimization (cost - travel time - CO2 emission/ energy efficiency) will be presented. For the optimization of decision variables in objective functions, the method with genetic algorithms was used. To find the Pareto optimal solutions, the NSGA II genetic algorithm was used. The main objective of our contribution is to determine the performance of the system according to the multi-objective optimization technique. The results of the proposed model could be useful tool for the warehouse designer in the early stage of warehouse design

Multi-objective optimization model for double-deep automated storage and retrieval systems

In the following paper, a new multi-objective optimization model for optimizing performances, costs and energy consumption of an automated storage and retrieval system with double-deep storage rack, will be presented. While majority of literature considers single objective function at a time, this model simultaneously optimizes three objective functions (minimum: investment costs, cycle time, CO2 emission) for a double-deep AS/RS. Analyses are performed in regard to different fillgrade factor of SR. For optimization, NSGA II algorithm is used as a tool to find Pareto optimal solutions. Since AS/RS require high initial investments, and are not flexible in terms of layout or other organizational changes once to system is built, this model could potentially be a very useful tool for warehouse designers in initial stages of planning

Multi-objective optimisation model of shuttle-based storage and retrieval system

This paper presents a multi-objective optimisation solution procedure for the design of the Shuttle-Based Storage and Retrieval System (SBS/RS). An efficient SBS/RS design should take into account multi-objectives for optimization. In this study, we considered three objective functions in the design concept which are the minimization of average cycle time of transactions (average throughput time), amount of energy (electricity) consumption and total investment cost. By also considering the amount of energy consumption as an objective function for minimization, we aimed to contribute to an environmentally friendly design concept. During the optimization procedure, we considered seven design variables as number of aisles, number of tiers, number of columns, velocities of shuttle carriers, acceleration/deceleration of shuttle carriers, velocity of the elevators lifting tables and acceleration/deceleration of the elevators lifting tables. Due to the non-linear property of the objective function, we utilized the Non-Dominated Sorting Genetic Algorithm II (NSGA II) genetic algorithm for facilitating the solution. Lastly, we searched Pareto optimal solutions to find out the optimum results. We believe that this study provides a useful and a flexible tool for warehouse planners and designers, while choosing a particular type of SBS/RS at the early stage of the warehouse design. First published online: 12 May 201

A multi-objective optimization model for minimizing investment expenses, cycle times and CO2 footprint of an automated storage and retrieval systems

A new optimization model of Automated Storage and Retrieval Systems (AS/RS) containing three objective and four constraint functions is presented in this paper. Majority of the researchers and publications in material handling field had performed optimization of different decision variables, but with single objective function only. Most common functions are: minimum travel time, maximum throughput capacity, minimum cost, maximum energy efficiency, etc. To perform the simultaneous optimization of objective functions (minimum: “investment expenses”, “cycle times”, “CO2 footprint”) the Non-dominated Sorting Genetic Algorithm II (NSGA II) was used. The NSGA II is a tool for finding the Pareto optimal solutions on the Pareto line. Determining the performance of the system is the main goal of our model. Since AS/RS are not flexible in terms of layout and organizational changes once the system is up and running, the proposed model could be a very helpful tool for the warehouse planners in the early stages of warehouse design

An Experimental and Computational Study of the High-Velocity Impact of Low-Density Aluminum Foam

The study presents the results of an experimental and computational study of the high-velocity impact of low-density aluminum foam into a rigid wall. It is shown that the aluminum foam samples deformed before hitting the rigid wall because of the high inertial forces during the acceleration. During the impact, the samples deformed only in the region contacting the rigid wall due to the high impact velocity; the inertial effects dominated the deformation process. However, the engineering stress–strain relationship retains its typical plateau shape until the densification strain. The experimental tests were successfully reproduced with parametric computer simulations using the LS-DYNA explicit finite element code. A unique computational lattice-type model was used, which can reproduce the randomness of the irregular, open-cell structure of aluminum foams. Parametric computer simulations of twenty different aluminum foam sample models with randomly generated irregular lattice structures were carried out at different acceleration levels to obtain representative statistical results. The high strain-rate sensitivity of low-density aluminum foam was also observed. A comparison of experimental and computational results during aluminum foam sample impact shows very similar deformation behavior. The computational model correctly represents the real impact conditions of low-density aluminum foam and can be recommended for use in similar high-velocity impact investigations

COMPUTATIONAL MODELING OF IRREGULAR CELLULAR STRUCTURES

Obstoječi konstitutivni modeli celičnih gradiv, ki so danes vključeni v različnih sistemih za inženirske računalniške simulacije, ne upoštevajo vpliva geometrijske neurejenosti na spremembo makroskopskih lastnosti celičnega gradiva ob istočasnem upoštevanju različnih deformacijskih hitrosti oziroma ob upoštevanju dinamičnih obremenitev. Zaradi tega je bil razvit nov rešetkasti model neurejenih odprto-celičnih gradiv, ki omogoča upoštevanje vpliva neurejenosti in različnih deformacijskih hitrosti na lastnosti odprto-celičnih gradiv pri velikih deformacijah. Zaradi velikega vpliva neurejenosti strukture odprto-celičnih gradiv na njihove lastnosti in pomanjkanja podatkov o geometrijski strukturi odprto-celičnih gradiv, je bila za namen modeliranja neurejenih odprto-celičnih gradiv razvita tehnika avtomatizirane 3D rekonstrukcije njihovih geometrijskih značilnosti na osnovi tomografskih posnetkov. Analize rekonstruiranih modelov so pokazale, da imajo realne trdne pene bogato in raznoliko porazdelitev osnovnih geometrijskih značilnosti in se njihove geometrijske lastnosti bistveno razlikujejo od urejenih struktur s tetrakaidekaedrično oziroma kubično osnovno celico, ki so služile kot osnova številnim raziskavam v preteklosti. Na podlagi statistično obdelanih podatkov o strukturi realnih aluminijastih pen je bila narejena primerjava s statistično obdelanimi podatki dveh računalniških modelov neurejenih odprto-celičnih gradiv, ki sta osnovana na ravnotežnih Kelvinovih in Weaire-Phelanovih celicah. Dokazano je, da modeli osnovani na Weaire-Phelanovi delitvi prostora bolje opisujejo strukturo realnih pen. Pokazalo se je tudi veliko odstopanje realnih pen od popolnoma naključnih računalniških modelov, kar potrjuje predpostavko, da trdne pene vendarle niso povsem naključne strukture, ampak na njihov nastanek močno vpliva fizikalno ozadje načina penjenja med proizvodnim postopkom. S primerjalno analizo je bila določena tudi ustrezna stopnja neurejenosti novo razvitega modela odprto-celičnih struktur, pri kateri lastnosti računalniško generiranih modelov najbolj sovpadajo z lastnostmi podobnih realnih aluminijastih pen. Za namen validacije uporabe razvitih Weaire-Phelanovih modelov v računalniških simulacijah so bili opravljeni eksperimentalni kvazi-statični in dinamični (udarni) tlačni enoosni eksperimentalni preizkusi vzorcev aluminijastih odprto-celičnih pen, kjer je bil ugotovljen pričakovano velik vpliv relativne gostote na togost celičnih gradiv. Primerjava rezultatov eksperimentalnih preizkusov in računalniških simulacij je pokazala dobro ujemanje makroskopskih mehanskih lastnosti, kar dokazuje primernost uporabe neurejenih rešetkastih modelov odprto-celičnih aluminijastih pen na osnovi Weaire-Phelanovih celic v računalniških simulacijah obnašanja teh gradiv pri različnih hitrostih tlačnega obremenjevanja.Constitutive models of cellular materials integrated into existing computer simulation software do not account for the effects of cell shape irregularity of such materials on their macroscopic mechanical properties in combination with different strain rates under impact loading conditions. Thus a new lattice computer model of irregular open-cell materials was developed which accounts for irregularity and strain rate effects on the mechanical properties of open-cell materials at large deformations. Due to large effect of the cell shape irregularity on mechanical properties of open-cell materials and lack of data on geometrical structure of open-cell materials, an automated 3D geometry reconstruction technique based on analysis of tomographic pictures was developed for the purpose of more realistic modelling of irregular open-cell materials. Analyses of the reconstructed models showed that real open-cell structures have rich and diverse distribution of basic geometrical properties and that their geometrical properties significantly differ from the regular structures with cubic or tetrakaidekahedral basic cells, which where used in many research studies in the past. Geometrical data of aluminium foam samples was statistically analysed and compared with similarly statistically analysed geometrical data of two irregular open-cell computer models, which were based on equilibrium Kelvin cells and Weaire-Phelan cells. It was proven that models based on Weaire-Phelan cells describe the structure of real foams better in comparison with models based on Kelvin cells. Also, a significant discrepancy between the real foam geometry and the geometry of completely random generated computer models was determined, which confirms the assumption that the structure of a solid real foam is not random and that its formation is strongly influenced by the physical background of the foaming type during the production process. Comparative analysis was used to determine the irregularity parameter of newly developed representative lattice model of open-cell materials, at which the properties of computer generated models concur best with properties of similar real aluminium foams. Quasi-static and dynamic (impact) experimental uni-axial compression tests of aluminium open-cell foam samples were carried out to validate the developed Weaire-Phelan computer models. The results showed expected significant influence of relative density on open-cell foam load carrying capacity. Comparison of experimental results and results of computer simulations showed a good agreement of macroscopic mechanical properties, which confirms that irregular lattice modelling of open-cell aluminium foams based on Weaire-Phelan cell model is appropriate for simulating the behaviour of such materials under different compressive loading rates

A computational model for analysing the dry rolling/sliding wear behaviour of polymer gears made of POM

This study presents a computational model to determine the wear behaviour of polymer gears. Using PrePoMax finite element numerical calculation software, a proposed computational model was built to predict dry rolling/sliding wear behaviour based on Archard’s wear model. This allows the calculation of the wear depth in each loading cycle with constant mesh updating using the finite element method. The developed computational model has been evaluated on a spur gear pair, where the pinion made of POM was meshed with a support gear made of steel. The computational results obtained were compared with the analytical results according to the VDI 2736 guidelines. Based on this comparison, it was concluded that the proposed computational model could be used to simulate the wear behaviour of contacting mechanical elements like gears, bearings, etc. The main advantage of the model, if compared to the standardised procedure according to the VDI 2736 guidelines, is the geometry updating after a chosen number of loading cycles, which enables a more accurate prediction of wear behaviour under rolling/sliding loading conditions

Behavior of metallic foam under shock wave loading

In this manuscript, the behavior of metallic foam under impact loading and shock wave propagation has been observed. The goal of this research was to investigate the material and structural properties of submerged open-cell aluminum foam under impact loading conditions with particular interest in shock wave propagation and its effects on cellular material deformation. For this purpose experimental tests and dynamic computational simulations of aluminum foam specimens inside a water tank subjected to explosive charge have been performed. Comparison of the results shows a good correlation between the experimental and simulation results