Importance of Coordination and Cultural Diversity for an Efficient and Flexible Manufacturing System
IImportance of Coordination and Cultural Diversity for an Efficient and FlexibleManufacturing System
Kashif Zia
Faculty of Computing and ITSohar University, Oman
Email: [email protected]
Alois Ferscha
Institute of Pervasive ComputingJohannes Kepler University, Austria
Email: [email protected]
Dari Trendafilov
Institute of Pervasive ComputingJohannes Kepler University, Austria
Email: dari.trendafi[email protected]
Abstract —Manufacturing systems of the future need to haveflexible resources and flexible routing to produce extremelypersonalized products, even of lot size equal to one. In this paper,we have proposed a framework, which is designed to achieve thisgoal. Towards this, we have integrated an established culturalevolution model to achieve desired flexibility of resources andacceptable routing time. Promising results are evidenced througha simple proof-of-concept simulation.
Keywords – Industry 4.0; resource flexibility; routing flexibility;personalized production; cultural dissemination; group coherence.
I. I
NTRODUCTION
The industrial manufacturing paradigm has already evolvedfrom mass production to mass customization. Fueled by initia-tives like Industry 4.0 [1], we foresee a further improvementin the coming years, namely the paradigm of personalized pro-duction. Personalized production targets an extremely flexiblemanufacturing system which could respond to predicted andunpredicted changes in the production environment.According to [2], this flexibility should be a collection ofthree aspects, at least: • Resource Flexibility: flexibility of ma-chines/processing stations to make multiple parts. • Routing Flexibility: flexibility to execute the sameoperation/function using multiple processing stations. • Lot Size Flexibility: ability to produce a very smallcustomized/personalized lot size in a non-batch mode.Historically, many research efforts have focused on specificfeatures of these aspects. Many scheduling [3] [4], resourceoptimization [2] [5], and constraint satisfaction [6] solutionshave been presented. However, all these mechanisms eitherconsider a mathematical abstraction or imitate a real-worldsituation as their manufacturing environment. The problemis that this results in a static configuration, and the solutionproposed only works in these boundaries.For modeling of a dynamical system, it is imperative touse a computational approach. For example, a more recentwork uses an agent-based model while considering mobileprocessing stations as a mean to achieve flexibility in themanufacturing process [2]. The idea is to make resourcesavailable when and where these are required. Although theirapproach addresses the challenge of routing flexibility to anextent, the capabilities of resources still remain static.In our research, we are mostly focusing on resourceflexibility, which means that the processing units are able to dynamically change their capabilities and therefore a resourceis able to perform several tasks. The goal is to keep resourcesstationary (and avoid expensive process of mobility) andarrange resources in groups of complementing capabilities.Ideally, a resource would designate itself for a capabilitythat would optimize the manufacturing process in severaldimensions, such as production rate, lead-time per order andreactivity index [2].In this context, our mechanism exploits the cultural natureof the scenario; i.e. groups of complementing capabilities; andwe are convinced that cultural diversity (complementation) hasa lot of potentials to explore about. We argue that flexibilityin resources, routing and personalizing closely relate to theevolution of culture, particularly cultural groups and diversi-fication. This would provide an entirely new perspective forfuture research in this domain.A culture is a multi-featured system evolving in time.One characteristic of culture is its coherence when seen fromoutside. Definitely, this coherence results due to a majority ofpeople trying to acquire a similar behavior (often termed as atrait) in a certain context (often termed as a feature). Hence, aconceptual framework comprising of resources and products,driven by related features and traits can be formulated. Aresource is a processing unit in the production line, whereasa product is obviously a product under production. Althougha product can also be considered as a cultural entity, it is notthe case for now. Only a resource is a cultural entity. Theframework particularly focuses on limited coherence betweencultural groups.Resources are flexible, initially having some randomlychosen features and a randomly chosen trait against a feature.For example, a processing unit may have ability to performone, two or more tasks T , T , ... with certain levels ofprecision P , P , .... Here, a tuple consisting of n values is aset describing capabilities of a resource. For example, the set { P , P , P } can be interpreted as: this resource can performtask 1 with precision 2, task 2 with precision 1 and task 3 withprecision 3. Furthermore, it cannot perform any other task.Such a scheme is naturally compatible with the requirementof a flexible manufacturing system stated above, namely,flexibility in resources, routing and personalizing. Axelrodprovides evidence in his seminal work [7] for such a simpleconfiguration of cultural descriptions which can result in a lo-cally coherent, but globally polarized culture as a consequenceof localized interactions of participating entities.However, in this paper, we argue that such a limitless co-herence has no control over where the boundaries of the global a r X i v : . [ c s . C Y ] M a y olarization would occur, which turned out to be harmful to asystem which usually seeks for the economy of resources andoptimizations in several dimensions. That is the reason, we tryto find conditions which end up in approximately acceptablestructuring in terms of coherence (termed as limited coherence)vs. polarization. To achieve this, we have used and refinedAxelrod’s model of cultural dissemination [7].Axelrod’s model provides evidence of observation that themore time we provide for cultural dissemination, the culturalgroups become increasingly coherent due to homophily. Forscenarios, which require diversification of resources, we needto find a balance between coherence and diversification. Thispaper provides first insights into these aspects for a productionshop floor. The paper presents an agent-based model, abstract-ing and simplifying the production process at a hypotheticalshop floor.The rest of the paper is structured as follows. In section II, adetailed description of the methods of modeling and simulationis given, followed by a discussion on initial findings in sectionIII. We end the paper with an elaborate outlook of future workgiven in section IV. II. M ETHODS
In the following, a detailed description of the models isgiven. Starting from desperation of Axelrod’s model of culturaldissemination, next the motivation of the proposed model isgiven, followed by the details of the proposed method itself.
A. Axelrod’s Model of Cultural Dissemination
Axelrod’s model [7] thrived for cultural homogeneity [8],where adjacent cultures gets influence from each other. Themodel is based on cultural components defined by threefactors; features, traits, and persons. Culture has many features,such as habits of eating, recreation, and leisure. These featuresmay not be identical across different cultures. Each of thesefeatures has several traits, which may differ across cultures.A person is a placeholder of a culture described by one of f features and t traits. Axelrod proposed a model seekingfor cultural homogeneity proclaiming that different culturesare destined to cohere together so that they appear as acultural unity, but at the same time, there exists a clear-cutdifferentiation between cultures.Axelrod model was able to demonstrate that the abovetwo (rather contradictory) goals can be achieved by a simpleinteraction model (realized through N coordination games)between neighboring persons. Axelrod showed that N coor-dination games are necessary for a broader scale evolutionof culture. Furthermore, groups’ consistency across differentaspects of societal norms makes a group culturally coherentand different from others. In the following, a hypothetical casestudy representing Axelrod’s model of cultural diversificationis presented.In Figure 1, a grid of × cells is shown. Each cellis represented by a person or a culture depicted by color (oneunique combination out of f × t possible combinations). Eachcell’s color has a meaning; for example, all green cells havethe capability to perform task 1 with precision value 0, whichis followed by precision values of task 2 (0, 1 or 2); last valueis not path dependent and represented by z. A product has a Figure 1. Initial distribution of a × grid constituted by blocks of culture;each block a tuple of 3, representing three features (green, blue, yellow) havingthree traits (3 shades of a color) each. Average diversity index of randomsetting is around 0.660.Figure 2. Axelrod’s Model: Evolution of cultures shown in Figure 1. (a)at simulation iteration 6055 showing clusters of cultures starting to form.(b) at simulation iteration 12207 showing further consolidation of clusters ofcultures. The evolution is destined to end up in very few cultures (1 or 2). unique sequence of the task to perform represented with anarrow shape (at the center of the space).Axelrod model calculated similarity s between neighboringcultures. If s is not 1 ( ), with a probability p , thevalue of a dif f erent column of a person is replaced by thecorresponding value of the neighboring person. This simplemechanism is able to generate clusters of coherent culturesas shown in Figure 2. If we define diversity index as themean diversification of cultures of all persons when comparedto their neighbors, the Axelrod model would converge into asingle culture most of the time with diversity index equalto 0. This is not desirable in the context in which we want touse this model. Therefore, the model was extended as detailedin the following. B. The Motivation: Constrained, N-Coordination Games forCultural Diversity
Before the description of the model, we formalize thescenario given in Figure 1 as a manufacturing process. Givethat a processing unit is able to perform three possible tasks igure 3. Extended Axelrod’s Model: Cultural Diversity at iteration 50000.Three random outcomes shown in (a), (b) and (c) having a diversity index of around 0.320. with three possible precision values, we can see a clear capa-bility matching through colors. Further, a product is introducedwhich need to complete a sequence of three tasks offered bydifferent resources. We hypothesize that using the constraint,N coordination games, we can achieve cultural diversity, whichis closer to what is desirable. This would directly impactproducts’ traversing efforts in a positive way. A comparisonof Figure 2 with Figure 3 shows less diversification from priorto the later. We hypothesize that this would help in reducingthe traversing efforts of the products.An Example Walkthrough: Referring to Figure 1 again, eachresource (black agent at the center of a cell) is randomlypopulated with vector [x y z], where x, y, and z may havethree possible values 0, 1 and 2. The product has to performthree tasks in a sequence. Task 1 with precision 0, task 2 withprecision 1 and task 3 with precision 2. It starts at the shownposition. First, it will perform task 1 with precision 0. That isright away available at the cell the product is situated. Next, ithas to perform task 2 with precision 1. The nearest resource,which has first column equal to 0 (assuming a connectionbetween task 1 and 2) and second column equal to 1 is theresource on immediate top-left; hence the product would movethere. Next task is task 3 with precision 2. Assuming that it isan independent task, the product would try to find the nearestresource that has the third column equal to 2 (any color). Thiscan be any resource (two valid possibilities are shown withdotted lines).It seems that random configurations would be the best, butthis cannot be the case in a structured environment, particularlyin case of an assembly line type of manufacturing. The Axelrodmodel is too skewed towards coherence and would end upin too few cultures. Hence we propose to refine the Axelrodmodel in the following way.
C. The Proposed Diversity Dissemination Mechanism
Axelrod model sought for similarity s between neighboringcultures. If s is not 1 ( ), with a probability p , thevalue of a dif f erent column of culture is replaced by thecorresponding value of the neighboring culture. We extend thismodel by applying an extra constraint. That is, the replacementis only possible if s is also less than a threshold th , which isfor now given a static value of 0.5. This is expected to increaseoverall diversity index of the system. Before analyzing theimpact of this refinement the mechanism of product traversingis explained. Figure 4. Comparison of time series of diversity index . D. Traversing Mechanism
All products have a sequence of tasks to perform in theform [x, y, z]. A product first gets the value x, and maps itonto resources with an identical capability and residing close toits position. Let’s denote the resource at r . After visiting r , theproduct seeks for the next nearest resource corresponding to y.It is assumed that y has a relationship with x. This means that,in terms of colors, this cell (and the resource residing on top ofit) should have the same color. The last task z is independentand just show the range of flexibility that the system may have.III. A NALYSIS OF I NITIAL F INDINGS
Definitely, the introduction of threshold th retains diversity index in case of extension of Axelrod’s model, asshown in Figure 4. This helps in task completion capability ofthe system due to the provisioning of a more diverse arrayof complementing capabilities. The graph shown in Figure4 evidences this fact. The diversity index of the proposedmodel is much higher than the Axelrod’s model throughoutthe simulation and it never dies out no matter how long thesystem evolves, unlike Axelrod’s model.This can be verifiedby analyzing the mobility of products in case of randomconfigurations. In Figure 5, we can see five products whichstart from the center of the space. Products 100 and 101needed to perform task 1, so they did it as the first step usingthe resource where product 102 is stationed now. Next, theymove to the right and performed task 2. That means that bothcompleted the first two task of their schedule successfully. Thesimilar is true for the other three products. The system couldacquire a mobility index equal to 2 on average for the first twotasks, which it did without any problem. As we mentionedalready, a random configuration is most flexible and wouldalways be best in its task completion capability. However, thisconfiguration is unrealistic. In reality, we need to plan theplacement of resources and put them in order.In case of Axelrod’s model, we have analyzed the resultsfor diversity index diversity index , the average mobility index drops.After running the simulation several times, it was observedthat mobility index is 1.8 ( diversity index = 0.5), 1.4( diversity index = 0.25) and 0.03 ( diversity index = 0.10).As shown in Figure 6, this decrease is due to nonavailabilityof resources indicated by products turning into black color. igure 5. Traversing behavior in random configuration of resource capability.Figure 6. Traversing behavior in Axelord’s Model. Lastly, the extended models solve the above issue. We cansee a smooth performance of tasks for all the products, whichis evident from Figure 7. For even minimum possible diversity(0.33), in the majority of the cases, the mobility index achievedis 2 (the possible maximum).IV. C
ONCLUSION AND F UTURE W ORK
Manufacturing systems of the future need to have flexibleresources and routing to produce an extremely personalizedproduct, even of lot size equal to one. What we have seenis that flexible manufacturing system can be realized withoutmoving the resources (processing units) by enabling reconfig-
Figure 7. Traversing behavior in Extended Axelrod’s Model. uration of capabilities of resources based on dissemination ofculture concept proposed by Axelrod. However, the Axelrodmodel has a focus on the coherence of cultural groups, whichmost of the times end up in one or very few cultures. If weequate such an instance of a culture with a single capability ofa resource, we are left with extremely limited resources andproducts cannot complete their production life cycle.Hence, we proposed to have a constrained cultural coher-ence mechanism by introducing a threshold. This tiny develop-ment has a significant impact on the increase in diversity of theculture along with related resources being in close vicinity toeach other on average. This did not only ensure an increase inresource availability as a whole, but also managed to decreasethe mobility of products in search of suitable resources.However, the real contribution of the paper is the integra-tion of manufacturing processes with cultural considerations,which naturally fits into the problem. In our view, this isa novel approach of real significance. However, the workreported in this paper is just a proof-of-concept. We need tohave more thorough experiments to measure the efficiency ofthe model in challenging environments such as environmentshaving inflow and outflow points, more in-depth capabilitiesand richer relationships between tasks.In the next phase of the project, we will induct modelsof dynamics, which will include timing of tasks, conflictand deadlock resolution between products seeking identicalresources, and more realistic analytics such as production rate,lead-time per order and reactivity index. Lastly, we would alsoinclude an autonomous learning system, which would helpresources learn and change their configurations on the fly basedon product types, requirements, and trajectories.A
CKNOWLEDGMENT