Multi-objective optimization formulti-line and U-shape layout of sewing assembly line in apparel industry
The design of assembly line layout is one of the most important influential factors forthe company's performance.Theinappropriate arrangement of the order of workstations in the assembly line could cause the excessive movement of the material. In order to increase productivityand reduce production cost, a multi-objective optimization model with minimum the transfer distance of semi-finished products and the total area of assemblylinewas established in this paper. The Non-dominated Sorting Genetic Algorithm-II was applied to obtain the results of this model. The coding method, genetic operation and fitness function for three different kinds of sewing assemblylinelayouts (multi-line, U-shape two-line and U-shape three-line) were studied, while the workstations were organized in three ways: the order of processes, the type of machines, and thecomponents of garment. The efficiency of the model was verified by the practice of sewing assembly lines for men's shirt. The layout schemes are compared with other algorithms. https://vssewingmachine.in/ The results illustrated that NSGA-II algorithm is an effective tool to solve the sewing assembly line layout problem.
The transfer distances of semi-finished products in the multi-line and U-shape (three-line) layouts arranged by garment componentsworkstation layout were short. The multi-line layout arranged bythe type of machinesworkstation layout occupied the smallest area. The modelis suitable for solving the layout problem of the garment sewing workshop in practice, shortening the production cycle, and reducing the production cost.A variety of assembly line layout schemes are provided for apparel manufacturers in this paper. Apparel manufacturers can selectthe appropriate assembly line layout based on the actual conditions ofthe workshop and product.
With the rapid development of society, the demand ofclothing products is more diversified. In order to quickly respond to the demands of multi-variety, small batch and short-cycle production, and effectively improve the production efficiency, the role of workshop logistics planning and layout in manufacturing system has become increasingly prominent[1]. The reasonable assembly line layout andlogistic route improvethe operation efficiency, production quality andreduce costs. The reasonable layout of assembly line can reduce the waste rate of production space,increase the utilization rate of the workshop area andexpand theproduction scale. Thereasonable planning of the logistics route can effectively shortenthe transferdistance of semi-finished products, reduce the logistics cost, and improve the production efficiency of the workshop[2]. However, in practice, the assembly line layout is usually arranged based on the subjective experience of technicians. This empirical layout scheme hassome disadvantages such aspoor adaptability and low fluency of semi-finished products operation.
It may result in low production efficiency and high production logisticscost, thus reducing the economic benefits of enterprises [3].In the garment production process, most semi-finished products are in a state of stagnation or transfer, only5% of the time is used for processing the semi-finished products. 20%-50% of operating expenses are used for handlingand storage of semi-finished products [4]. VS Enterprises In addition, such as oil stains, chromatic aberrations, etc., may be caused during the stagnation and transferof semi-finished products [5]. The transferof the semi-finished productsrequires time and operators. Reasonable arrangement of the semi-finished product transferroutescan shortenthe transfertime,improve the production efficiency and the output [6].The transfer of semi-finished products ingarment sewing assembly line is complicated. There are great differences between the assembly lines based on the different organizationalmodels. In order to improve the operationefficiency of semi-finished products in the sewing assembly line, it is very meaningful to study the layout of assembly line according to the actual situation of enterprises. Generally, the assembly line layout can be divided into the five forms according to the arrangement shape and the flow pattern of semi-finished products.(1) Straight layout is to arrange the workstations ina straight line, so that the semi-finished products transferalong the straight line from the first workstation during processing. But straight layout space is often narrow. It is suitable for assembly lines thatthe production process is short and simple,or thenumber of processes and machinesis small.(2)U-shape layout is to arrange the workstations according to the processing order, so that the logistics route is U-shape. This kind of layout is more compact and suitable for production workshops with small length and width.(3) S-shape layout refers to the arrangement of workstations along the S-shape of logistics. Itcan be used to arrange longer processassembly line layouts in a larger shop area, such as automotive assembly line.(4) The circularlayout is to arrange the workstations along the circularshape. This layout is suitable to produce finished products thatneed to be returned to the starting point.(5) Multi-line layout means that the workstations are arranged in multi lines. Semi-finished products can be transferredbetween different workstations perpendicular to the line oralong the line. This layout can save the workshop space and the semi-finished products transferpaths are flexible. It is mainly applied to the assembly line layout with various kinds of processing products and complex processes.There are many kinds of processes and machines involved in garment sewing assembly line. The multi-line layout, U-shape (two-line)layout and U-shape (three-line)layout of garment sewing assembly line are discussed in this researchaccording to the characteristics of assembly line layout.In general, production process of garment is relatively long, which also affects the transferdistance of semi-finished products. Fortunately,the workstations can be arranged reasonably by three different layouts based on production cycle. The order of processes workstation layout (PWL) is to arrange the workstations according to the processing order, as shown in Fig.1(a).The type of machines workstation layout (MWL) is that machines required for the same processing contents are arranged in sameworkstation, as shown in Fig.1(b).And the components of garment workstation layout (GWL) is to produce each garment component asa workstation, as shown in Fig.1(c).
In this paper, the layout model of the apparel assembly line was analyzed bythe practice of men’s shirtmanufacturing. The NSGA-II algorithm (Non-dominated Sorting Genetic Algorithm-II) algorithm was applied to obtain the layout schemes of different sewing assemblylines. The optimum way of the sewing assembly line in different workstation layouts could be found according to the results obtained from the model calculation. This paper wasorganized as follows: The assumptions, constraints and objective functions of the assembly line layout model were described in Section 2. The NSGA-II algorithm design was specifically described in Section 3. The men's shirtassembly line was usedas an example, the different assembly line layouts fordifferent workstations layouts and wereoptimized. Each optimization scheme was compared to each other to select an effective solution. A detailed experimental design and results were presented in Section 4. Discussion wasillustrated in Section 5. In Section 6, several conclusions were summarized.
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A Compressive-Sensing-Based Approachf or the Detection and Characterization of Buried Objects
The problem of determining and understanding thenature of buried objects by means of nondestructive and non-invasive techniques represents an interesting issue for a greatvariety of applications. In this framework, the theory of electro-magnetic inverse scattering problems can help in such an issueby starting from the measures of the scattered field collectedon a surface. What will be presented in this communication isa two-dimensional (2-D) technique based on the so-called Bornapproximation (BA) combined with a compressive sensing (CS)approach, in order to improve reconstruction capabilities for aproper class of targets. The use of a multiview-multistatic configu-ration will be employed together with a multifrequency approachto overcome the limited amount of data due to the single-frequencytechnique. Therefore, after a first numerical analysis of the per-formance of the considered algorithm, some numerical examplesfor 2-D aspect-limited configurations will be presented. The sce-nario is composed of a simplified scene, which consists of twohalf-spaces, and with the probes located close to the interfacebetween the two media. As proposed in the following, it is easyto observe that the use of CS for this kind of problems mayimprove reconstruction capabilities, confirming the validity of thepresented approach.
The capability of electromagnetic fields to pene-trate different materials makes them very attractive toreconstruct, both in a qualitative and quantitative way, the mor-phological and electrical features of the unknown objects bymeans of a ondestructive technique, which starts from the mea-sures of the scattered field. Such a technique may be appliedin several field, including geophysics [1], characterization ofmaterials [2], monitoring in biomedical engineering [3], anddemining applications [4].In the framework of the so-called aspect-limited problems,an interesting application is related to ground penetrating radar (GPR), which employs signals whose frequencies vary froma few hundreds of megahertz till to some gigahertz accordingto the considered scenario. As most of the techniques basedon radar approaches, target information is retrieved from thetwo-travel time of a pulse radiated by a source and gatheredby a fixed-offset system between transmitter and receiver [5]. https://vssewingmachine.in/ The image obtained by joining the radar echoes collected whilemoving the antennas is referred to as a raw data “radargram.”Unfortunately, what radar techniques usually allow is onlythe extraction of qualitative information on the investigatedregion that is based on a subjective interpretation of the rawdata and on user experience. Therefore, since in many cases, itis not possible to provide detailed information on the targets,several data processing techniques have been proposed, amongwhich one can find focalization procedures [6] and tomographictechniques [7].Among all these techniques, tomographic imaging seems tobe a promising approach to overcome the limitations related tostandard procedures, since it makes possible to achieve not onlyinformation about the shape and localization of buried objects,but it also allows a quantitative electromagnetic characteriza-tion of these targets in the imaging domain under test [8].Nevertheless, the detection performance of GPR largelydepends on a lot of factors, which can partially or totally hideor distort the response of the buried targets. Among all thesefactors, it is remarkable to cite the coupling between antennasand soil, the electromagnetic features of the background, thespeed and scattering of wave propagation, and the electromag-netic contrast of the buried objects on which the intensity of thescattered fields depends [9].Therefore, there is a need to develop appropriate techniquesfor clutter reduction and subsurface imaging. In this category,detection techniques are employed on a subsurface image builtfrom a full GPR scan after clutter reduction. They includeadvanced algorithms for hyperbola detection [10]–[13], andmigration approaches [14], [15]; their performance mainlydepends on the data set quality and on the preprocessing methodused to subtract the contribution of the background.In this framework, a great variety of tomographic techniquesmay be found in the literature to find a solution to the electro-magnetic inverse scattering problem previously described [16]–[20]. More in detail, it is possible to divide these approachesin two main classes: the first one faces the inverse scatteringproblem without any approximation and, in principle, this classcan provide an accurate reconstruction of the region under test,but it drives into a nonlinear ill-posed inverse problem, and a second class of approximated approaches which simplifiesthe model. Even though the first class of algorithms mayrealize better quantitative reconstructions, the nonlinearity ofthe model makes the solution of such problems be usually verysensitive to the availability of adequate information about thereference scenario, so that any sensible information about thescene has to be dealt with: such a feature may limit their appli-cability since an accurate knowledge of the electromagneticfeatures of the scenario is required to model correctly the prob-lem. Despite the increasing interest in this class of approaches,the inaccuracy in the knowledge of the reference scenario (soilpermittivity and conductivity) and the not-perfect knowledgeof the antennas radiation characteristics in the presence of thesoil affect the quality of the reconstruction problems. Moreover,the nonlinearity of the relationship between data and unknownsmay drive into false solutions that still exist, thus affectingthe reliability of the overall solution strategy [21], [22], andincreasing the computational time. VS Sewing Machines The second class of solutionapproaches exploits simplified models of the electromagneticscattering to develop linear inversion approaches [23]–[25].What has been proposed in this paper is an inversion strategywhich belongs to the second class of the approaches presentedbefore, since it is based on the so-called Born approxima-tion (BA). Due to the linearity of the problem, the solution issearched as the global minimum of a quadratic cost function,for which no false-solutions exist. Moreover, for linear inverseproblems, the adoption of well-assessed regularization schemes[26] is possible and reconstruction capabilities can be foreseen.Despite of the advantages said above by the adoption of suchmodels, the class of targets that may be recovered is limitedto those objects for which the BA is still valid, as for smallobjects whose electromagnetic features are very close to thoseof the background. In addition, since the aspect-limited natureof data implies that single-frequency data are not sufficient torealize effective inversions, a multifrequency approach will beconsidered throughout this communication. In order to assessthe actual performance of the approach in a relatively simplesituation, the canonical and significant two-dimensional (2-D)geometry is considered, together with the use of a regularizationtechnique based on compressive sensing (CS), which makes itpossible to reduce the number of data considerably.
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Exact Classical Simulation of the Quantum-Mechanical GHZ Distribution
John Bell has shown that the correlations entailedby quantum mechanics cannot be reproduced by a classicalprocess involving non-communicating parties. But can they besimulated with the help of bounded communication? This prob-lem has been studied for more than two decades, and it is nowwell understood in the case of bipartite entanglement. However,the issue was still widely open for multipartite entanglement,even for the simplest case, which is the tripartite Greenberger–Horne–Zeilinger (GHZ) state. We give an exact simulation ofarbitrary independent von Neumann measurements on generaln-partite GHZ states. Our protocol requiresO(n2)bits ofexpected communication between the parties, andO(nlogn)expected time is sufficient to carry it out in parallel. Furthermore,we need only an expectation ofO(n)independent unbiasedrandom bits, with no need for the generation of continuous realrandom variables nor prior shared random variables. In the caseof equatorial measurements, we improve on the prior art with aprotocol that needs onlyO(nlogn)bits of communication andO(log2n)parallel time. At the cost of a slight increase in thenumber of bits communicated, these tasks can be accomplishedwith a constant expected number of rounds.
The issue of non-locality in quantum physics was raisedin 1935 by Einstein, Podolsky and Rosen when they intro-duced the notion of entanglement [1]. Thirty years later, Bellproved that the correlations entailed by entanglement cannotbe reproduced by classical local hidden variable theoriesbetweennoncommunicating(e.g.space-likeseparated) parties [2].
This momentous discovery led to the question ofquantifyingquantum non-locality.A natural quantitative approach to the non-locality inherentin a given entangled quantum state is to study the amount ofresources that would be required in a purely classical theory toreproduce exactly the probabilities corresponding to measur-ing it. More formally, we consider the problem ofsamplingthejoint discrete probability distribution of the outcomes obtainedby people sharing this quantumstate, on which each partyapplies locally some measurement on his share. Each partyis given a description of his own measurement but is notinformed of the measurements assigned to the other parties. https://vssewingmachine.in/ This task would be easy (for a theoretician!) if the partieswere indeed given their share of the quantum state, but theyare not. Instead, they mustsimulatethe outcome of thesemeasurements without any quantum resources, using as littleclassical communicationas possible. Notice that we insist onexactsampling since approximate sampling can obviously berealized by having the parties communicate in order to shareapproximations of their measurement parameters.
This conundrum was introduced by Maudlin [3] in 1992in the simplest case of linearpolarization measurementsat arbitrary angles on the two photons that form a Bellstate such as| +〉=1√2|00〉+1√2|11〉. Maudlin claimed thatthis required “the capacity to send messages of unboundedlength”, but he showed nevertheless that the task could beachieved with a bounded amount ofexpectedcommunication.Similar concepts were reinvented independently years laterby other researchers [4], [5]. This led to a series of results,culminating with the protocol of Toner and Bacon to simulatearbitrary von Neumann measurements on a Bell state with asingle bit of communicationin the worst case[6], thus con-tradicting Maudlin’s claim.
Later, Regev and Toner extendedthis result by giving a simulation of the correlation (butnot the marginals) entailed by arbitrary binary von Neumannmeasurements (meaning that the outcome for each party cantake only two values) on arbitrary bipartite states of anydimension using only two bits of communication, also in theworst case [7].
Inspired by Steiner’s work [5], Cerf, Gisin andMassar showed that the effect of an arbitrary pair of positive-operator-valued measurements (POVMs) on a Bell state canalso be simulated with a bounded amount of expected commu-nication [8]. A more detailed early history of the simulationof quantum entanglement can be found in Ref. [9, Sec. 6]. VS Sewing Machines All this prior work is concerned strictly with the simulationofbipartiteentanglement. Much less is known when itcomes to simulating multipartite entanglement with clas-sical communication, a topic that was still teeming with major open problems. Consider the simplest case, whichis the simulation of independent arbitrary von Neumannmeasurements on the tripartite GHZ state, named afterGreenberger, Horne and Zeilinger [10], which we shall denote| 3〉=1√2|000〉+1√2|111〉, or more generally on itsn-partitegeneralization| n〉=1√2|0n〉+1√2|1n〉.The easiest situation arises in the special case ofequatorialmeasurements (defined in Section II) on the GHZ state becauseall the marginal probability distributions obtained by tracingout one or more of the parties are uniform. Hence, it sufficesin this case to simulate then-partite correlation. Once thishas been achieved, all the marginals can easily be madeuniform [11]. Making the best of this observation, Bancal,Branciard and Gisin have given a protocol to simulate equato-rial measurements on the tripartite and fourpartite GHZ statesat an expected cost of 10 and 20 bits of communication,respectively [12]. Later on, Branciard and Gisin improved thisin the tripartite case with a protocol using 3 bits of commu-nication in the worst case [13]. The simulation of equatorialmeasurements on| n〉forn≥5 was handled subsequentlyby Brassard and Kaplan, with an expected cost ofO(n2)bitsof communication [14]. This was the best result obtained untilnow on this line of work.Despite substantial effort, the case ofarbitraryvonNeumann measurements, even on the original tripartiteGHZ state| 3〉, was still wide open. Here, we solve thisproblem in the general case of the simulation of then-partiteGHZ state| n〉,foranyn, under therandom bit modelintroduced in 1976 by Knuth and Yao [15], in which theonly source of randomness comes from the availability ofindependently distributed unbiased random bits. Furthermore,we have no needs for prior shared random variables betweenthe parties.1Our simulation proceeds withO(n)expectedperfect random bits and its expected communication cost isO(n2)bits, but onlyO(nlogn)timeif we count one stepfor sending bits in parallel according to a realistic scenarioin which no party has to send or receive more than onebit in any given step. Furthermore, in the case of equatorialmeasurements, we improve the earlier best result [14] withan expected communication cost of onlyO(nlogn)bits andO(log2n)parallel time. At the cost of a slight increase inthe number of bits communicated and the number of requiredrandom bits, these tasks can be accomplished with a constantexpected number of rounds.More formally, the quantum task that we want to simulateis as follows. Each partyjholds one qubit (quantum bit) fromstate| n〉=1√2|0n〉+1√2|1n〉and is given the descriptionof a von Neumann measurementMj. By local operations,they collectively perform⊗nj=1Mjon| n〉, thus obtainingone outcome each, saybj∈{−1,+1}, which is their output.The joint probability distributionp(b)of thebj’s is definedby the joint set of measurements. Our purpose is to sampleexactlythis joint probability distribution by a purely classicalprocess that involves no prior shared random variables and as little communication as possible. As mentioned above,previous solutions [12]–[14] required each individual measure-ment to be equatorial. In order to overcome this limitation,our complete solution builds on three ingredients: (1) Gravel’sdecomposition ofp(b)as a convex combination of two sub-distributions [17], [18]; (2) Knuth and Yao’s algorithm [15] tosample exactly discrete probability distributions assuming onlya source of unbiased identically independently distributedbits,rather than a source ofcontinuousuniform random variableson the interval[0,1]; and (3) our own distributed version ofthe classicvon Neumann’s rejection algorithm[19].
We conclude in Section VIwith a discussion, open problems, and the announcement ofa forthcoming generalization of our results. For complete-ness, the appendices derive from first principles our convexdecomposition of the GHZ distribution, as well as elementaryapproximation and truncation formulas useful in the analysisof the parallel model.
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