A Rule-Based Fuzzy-Logic Approach for the Measurement of Manufacturing Flexibility

A Rule-Based Fuzzy-Logic Approach for the Measurement of Manufacturing Flexibility
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  ORIGINAL ARTICLE A rule-based fuzzy-logic approach for the measurementof manufacturing flexibility Ankur Das  &  Rahul Caprihan Received: 6 December 2006 /Accepted: 23 July 2007 /Published online: 22 September 2007 # Springer-Verlag London Limited 2007 Abstract  Manufacturing flexibility is a difficult to quantifyconcept that defies universal definition. This paper presentsa novel fuzzy-logic approach for measuring manufacturingflexibility that exploits linguistic variables for quantifying pertinent factors affecting commonly utilized flexibilitytypes. Towards this end, we identify and measure thecontribution of specified state variables towards theassumed flexibility types in order to compute an overallflexibility index for a generic manufacturing system. Thesuggested framework provides a convenient end user approach amenable to software implementation that isexemplified through the development of a prototypicalsoftware tool called  “ Flexibility Evaluator  ” . Keywords  Manufacturingflexibilitymeasurement .Systemicstatechangevariables.Fuzzylogic 1 Introduction Flexibility has been widely proclaimed as being indispens-able to manufacturing organizations by several researchers,and yet its applicability has largely remained restricted to afew technologically advanced nations that have successful-ly harnessed its potential benefits to their advantage. One principal reason why other nations have remained deprivedof its latent benefits is the inadequate knowledge about itsconcepts coupled with an unclear understanding on the part of managers of the options afforded by flexibility, together with their underlying implications [31]. Such problemsexist primarily because flexibility is a  polymorphous  [24]and  multidimensional   concept [26, 37]. Nevertheless, Upton [46] reiterates its relevance and importance in themanufacturing arena by noting that,  “ 10 or 15 years ago,quality was much like flexibility is today: vague anddifficult to improve yet critical to competitiveness ” .In the literature, a key factor that has been identified for theenhancement of its conceptualization is the ability to measureit. Measurement of manufacturing flexibility imparts a great deal of insight at both the strategic and operational levels of afirm that equips managers to deal with current problems suchas shrinking product life cycles, fierce market competition, andthe ever-increasing demand for product variety. Extant literaturehoweverrevealsthatthereisconsiderablemultiplicityinthevariedattemptsatquantifyingthedifferentdimensionsof manufacturing flexibility. Consequently, quantifying such anelusive concept is not an easy task, given that flexibility is acomposite aggregate of several independent variable types,each in turn affected by various factors. Nevertheless, severalframeworks have been suggested for its measurement, includ-ing those that exploit measures such as entropy [19, 34, 39], graph theory [32], Petri nets [1], fuzzy logic [45, 48], together  with other mathematical programming approaches that areoften difficult for operations managers to interpret [29, 35]. Beach et al. [2] aptly view flexibility as  “ a product of enablers such as corporate culture, management structure, process technology, facility layout and information sys-tems ” . Clearly then, even if one focuses on the flexibilityconstruct from the perspective on a single firm, severaldifferent types of   “ flexibilities ”  are found to co-exist concurrently. This is a typical facet of the multidimensionalnature of flexibility, as a result of which its measurement necessitates the use of pre-established measurable parame-ters. More often than not, research results based on these Int J Adv Manuf Technol (2008) 38:1098  –  1113DOI 10.1007/s00170-007-1182-xA. Das :  R. Caprihan ( * )Department of Mechanical Engineering,Dayalbagh Educational Institute,Dayalbagh, Agra 282 005, Indiae-mail:   parameters do not span a diverse group of industries, but are based on feedback from some target group whoseoperational environment may be very different from that of others [9]. As a result, extant measurement frameworks areessentially situation specific since generalizations asregards their applicability are contingent upon severalfactors, including the primary target industry, its geograph-ical location as well as the prevailing socio-economicenvironment [9]. Moreover, since manufacturing systemsare operated and managed by people, it becomes necessaryto record and utilize human knowledge and perceptionsabout flexibility in its measurement [30, 45]. In light of the above observations, the need for analternative flexibility measurement framework that (a)mimics (and exploits) human expertise and judgment; and(b) is inherently adaptable to suit the specific systemicrequirements of a given manufacturing firm, is clearlymandated. Fuzzy rule-based systems provide an idealmodelling platform to address the above issues [33].Tsourveloudis and Phillis [45] were one of the firsts tosuggest a fuzzy rule-based approach to manufacturingflexibility measurement. Noting that flexibility is aninherently vague notion that warrants the involvement of human perception and belief, Tsourveloudis and Phillis [45]suggested a knowledge-based approach to model thefunctional dependencies between flexibility parameters(such as  setup time ,  cost  ,  versatility ,  part variety  etc.)affecting specific flexibility types. However, severalresearchers have stressed the need for addressing themanufacturing flexibility issue from a systemic perspective[4, 5, 10, 19, 21, 41, 47, 48]. Further, Tsourveloudis and Phillis [45] did not incorporate this important notion in thedevelopment of their fuzzy rule-based approach. The fuzzy-logic approach to flexibility measurement suggested in this paper aims to bridge this gap through the development of anovel fuzzy rule-based approach that explicitly incorporatesthe above systemic viewpoint.With this in view, the specific objectives of this paper areas follows:a) To suggest a (fuzzy logic-based) methodologicalframework to measure manufacturing flexibility basedon a systemic view of the parameters affectingindividual flexibility types. b) To measure the contribution of each state definingvariable towards its corresponding flexibility parameter.c) To compute an overall manufacturing flexibility index for a firm as a fuzzy aggregation of the individual factor contributions affecting individual flexibility types.In Sect. 2, we review the relevant literature with a viewto position the existing research on manufacturing flexibil-ity measurement. Seven commonly identified flexibilitytypes are considered and measures for each are aggregatedon the basis of past efforts. In Sect. 3, a novel measurement approach is proposed based on a systemic viewpoint of manufacturing flexibility. Section 4 presents the implemen-tation details for the developed framework, and is followed by a worked through example in Sect. 5. Section 6 provides a summary conclusion of the key contributions of the paper. 2 Manufacturing flexibility  –   types and measures Arguably, the most widely accepted classification of manufacturing flexibility is that by Browne et al. [11],wherein eight distinct types of flexibilities were identified.Several other authors have given alternate definitions of flexibility types as well. While Gerwin ’ s [25] viewpoint  focused on the influence of environmental uncertainty onmanufacturing flexibility, Suarez et al. [43] discussed thecontingency relationship between market uncertainty andmanufacturing flexibility.Simply put, manufacturing flexibility is the ability of asystem to adapt to changes. Typically, it is difficult tocompute an exact estimate of the flexibility of a given systemdue to varying contribution levels of its underlying elements.Furthermore, the extant states of the manufacturing systemmay include multiple sets of flexibility elements. Each suchelement affects the system to a  certain degree  correspondingto its level of importance. Chang et al. [19] point out that the elements of manufacturing flexibility are many andcomplicated. Also, while there have been several alternateattempts at identifying flexibility elements [2, 3, 26, 36  –  38,50], the flexibility construct however, continues to remaintoo abstract for operationalisation.Van Hop and Ruengsak [48] note that in order tounderstand the underlying nature of manufacturing flexi- bility, it is necessary to address three primary questions:(a) What factors contribute to the flexibility degree of manufacturing systems?(b) How do you model/measure these factors correctly?(c) How should these factors be aggregated to evaluate themanufacturing flexibility of the system?The development of flexibility-measurement models inthe past has partially answered these questions fromdifferent viewpoints. For example, while Koste andMalhotra [31] classify flexibility elements into four groups,viz.,  range-number  ,  range-heterogeneity ,  mobility  and uniformity , Chang et al. [19] consider   versatility  and/or  efficiency  as the manufacturing flexibility elements. Thisfact could lead to confusion regarding flexibility concepts[48]. In addition, Gupta [28] suggests that any flexibility measure must inevitably depend on factors such as thedegree of uncertainty in the environment, management objectives, machine capability and configuration. Int J Adv Manuf Technol (2008) 38:1098  –  1113 1099  Although there have been several notable attempts at exploiting fuzzy-logic approaches in the context of manufacturing planning, scheduling, and control [8, 12, 16, 18, 44, 49, 52], there have been relatively few attempts at using fuzzy theoretic approaches in the context of manufacturing flexibility modelling. One of the first is that of Bernardo and Mohamed [6] who formulated manufactur-ing flexibility elements based on fuzzy present-worthanalysis. In another significant work, Tsourveloudis andPhillis [45] suggested a novel computational approach tomeasure manufacturing flexibility using fuzzy  “ If   –   Then ” decision rules. Wang and Chuu [51] suggested a groupdecision-making structure model for manufacturing mea-surement. In particular they proposed two algorithms for determining the degree of manufacturing flexibility using afuzzy linguistic approach. They attributed the novelty of theapproach to the absence of bias in the measurement  procedure on account of results being generated via agroup-evaluation approach. Further, Beskese et al. [7]fuzzified Bernardo and Mohamed ’ s [6] loading and routing model to quantify manufacturing flexibility using a fuzzymathematical programming approach. In a recent effort, VanHop and Ruengsak [48] extended Chang et al. ’ s [19] earlier  work by identifying new elements for manufacturingflexibility and developed a novel way to model theseelements as fuzzy and/or crisp sets.The above pioneering attempts have revealed severaladvantages of using fuzzy models for measuring flexibilityelements in terms of expressing imprecise data pervadingreal-world problems. However, the above models for fuzzy flexibility measurement simply focus on fuzzifyingexisting flexibility elements instead of incorporating other  possible underlying elements. In practice, given theinherent intervention of the human element in thedecision-making process, flexibility constructs implicitlyinvolve both crisp as well as fuzzy elements. Apart fromVan Hop and Ruengsak  ’ s [48] work, none of the other  researchers have attempted to aggregate both crisp andfuzzy elements simultaneously to assess manufacturingflexibility. The novel ideas of Chang et al. [19] and VanHop and Ruengsak [48], together with those of Tsourve-loudis and Phillis [45] have been exploited in this paper for suggesting an alternate framework for manufacturingflexibility measurement that uses a semantic reasoning procedure based on a fuzzy-logic approach in the measure-ment framework.2.1 Flexibility typesIn this sub-section, measures for seven commonlydefined flexibilities types viz.,  machine, routing, opera-tion, product, volume, expansion and process flexibility  areenlisted on the basis of past research efforts by Browneet al. [11], Brill and Mandelbaum [10], Sethi and Sethi [37], Das [21], and Koste and Malhotra [31]. The definitions, together with the respective parametersaffecting each of these flexibility types, are mentioned below. Importantly, it is noted here that the identified parameters for the different flexibility types mentioned below are only representative of a (possibly) much larger set of flexibility specific parameters. However, keeping infocus the primary objective of this paper, this represen-tative selection suffices. 2.1.1 Machine flexibility Machine flexibility has almost universally been a part of extensive reviews concerning the conceptual as well asempirical flexibility literature and has also been studiedas the primary variable in the job shop schedulingliterature [15, 16]. The primary focus in development of  measures of machine flexibility proposed in the past research has been to capture characteristics of machineflexibility not portrayed by other equipment descriptorssuch as price, size, speeds, tolerances, weight and part limits as noted by Brill and Mandelbaum [10], Sethi andSethi [37], Das [21], and Koste and Malhotra [31]. The  parameters for machine flexibility typically describe theability to change between operations with minimal setupsand delays; they should be stated in terms of performancerather than monetary aspects. Based on the past literature,generalizable parameters for machine flexibility can thus beidentified as follows:  –   Number of different operations performed  –   Time taken for each operation  –   Time consumed during change of states  –   Output quality and reliability  –   Throughput from the machine 2.1.2 Routing flexibility The major areas in which routing flexibility has receivedattention are shop floor control and FMS scheduling [12  –  14, 17] It relates to the ability to use alternate processing centers, which proves useful in the event of machine breakdowns (potential routing flexibility, Browne et al.[11]) or overloads (actual routing flexibility, Browne et al.[11]). Based on the extant literature, generalizable param-eters for routing flexibility can thus be identified asfollows:  –   Average number of machines to process different part type operations (actual routing flexibility).  –   Ability to reroute and reschedule parts in the event of machine breakdowns (potential routing flexibility). 1100 Int J Adv Manuf Technol (2008) 38:1098  –  1113  2.1.3 Operation flexibility Operation flexibility has been alternatively referred to as  sequencing flexibility  in the job-shop scheduling literature.It is basically considered to be an attribute of a part (not a production process) as noted by Sethi and Sethi [37] and isenabled by the usage of multiple processing plans for individual part types. The main difference between routingand operation flexibility is that while the former changesthe machines that do the processing for a given sequence of operations, the latter involves changing the actual sequenceof operations performed.Based on Brill and Mandelbaum ’ s [10] observations, indicative parameters for operation flexibility can beidentified as follows:  –   Number of production sequences with minimal switchingtimes.  –   Number of production sequences with minimal switchingcosts. 2.1.4 Product flexibility While product flexibility has been described as theflexibility of introduction of new products, Ettlie andPenner-Hahn [23] related it with both the introduction of new products and the modification of existing ones.In compliance with Brill and Mandelbaum ’ s [10] observations, indicative parameters for product flexibilitycan be identified as follows:  –   Number of different products produced by manufacturingfacility  –   Number of new products produced per year   –   Time required to produce new products  –   Cost of introducing new products  –   Rate at which a machine becomes obsolete when a new product is introduced 2.1.5 Volume flexibility The concept of volume flexibility evolved from theeconomics literature and appears frequently in both con-ceptual and empirical flexibility research. If a manufactur-ing facility possesses the required amount of volumeflexibility, then it achieves the capacity to respond quicklyand efficiently to both increases and decreases in aggregatedemand levels. The measures of volume flexibility shouldgauge the range of profitable volumes and the limits of thisrange. According to Browne et al. [11] volume flexibilitymay be measured  “  by how small the volumes can be for all part types with the system still being run profitably ” .Following Brill and Mandelbaum ’ s [10] observations, three representative parameters for volume flexibility are asfollows:  –   Range of volumes that can be produced  –   Time required in increasing or decreasing the output   –   Cost of increasing or decreasing the volume of output  2.1.6 Expansion flexibility Sethi and Sethi [37] relate expansion flexibility to increas-ing the capacity, e.g., output or capability or quality or technological state of the system. According to Stecke andRaman [42], a measure of expansion flexibility would be afunction of   “ the magnitude of the incremental capital outlayrequired for providing additional capacity: the smaller themarginal investment, the greater the expansion flexibility ” .In accordance with Brill and Mandelbaum ’ s [10] observations, two possible parameters for expansion flex-ibility can be identified as follows:  –   Modularity index for the manufacturing facility  –   Expansion ability of the manufacturing facility 2.1.7 Process flexibility Process flexibility finds its application in several areas of amanufacturing facility including those concerning machine breakdowns, re-routing or re-sequencing of jobs, andchanges in the master schedule. Along the lines of Brilland Mandelbaum ’ s [10] work, the following three param- eters can be identified for process flexibility:  –   Set of different part types being processed  –   Time required to switch from one product mix to another   –   Cost required to switch from one product mix to another  3 Systemic view of manufacturing flexibility When viewed from a systemic viewpoint, a flexible systemcan be observed to transit through various states, where the ‘ state ’  of the system is essentially a set of parametric valuesof the systems ’  sub-components that define it completely at a specified point in time. Typically, the observed values of various performance measures such as  throughput  ,  number of permissible production sequences , and  range of produc-tion volumes  are often used as indicators to define thesystem state at a given point in time. The object is toimprove the system ’ s state by improving the performanceof each of these performance measures.A few researchers in the past have attempted to addressflexibility in terms of   ‘ state ’ . Evans [24] defined flexibility Int J Adv Manuf Technol (2008) 38:1098  –  1113 1101  in terms of   capability  and  capacity  where the term ‘ capability ’  has been inferred by others [19] to imply thescope, range, or envelope of the states embodied in the tasksthat a system can perform; and  ‘ capacity ’  as the efficiency of  performing an arbitrary changeover between the states.Upton [47] defined the  mobility  element of flexibility asthe ease with which an organization moves from one state toanother. Chang et al. [19] summarize past research onflexible systems by implying that such systems contain theability to produce a wide range of   states  for a particular   task  at   high efficiency . Here Chang et al. [19] refer to the term  state  as the outcome of the performance comprising anumber of parameters, in terms of quantity, time, cost,reliability, quality availability etc., depending on the charac-teristics of the system or the requirements of management.Brill and Mandelbaum [10] proposed a model based onthe product of the  weight of importance of a task   and the efficiency of the machine utilized for executing the task  .Chen and Chung [20] proposed two types of machineflexibilities  –   unweighted   and  weighted  . While  ‘ unweight-ed ’  machine flexibility addressed the  versatility  (or capa- bility) component of flexibility,  ‘ weighted ’  machineflexibility essentially followed Brill and Mandelbaum ’ s[10] approach in computing the product of weight andefficiency of a task.Slack [40] measured the ease of movement betweenstates in terms of cost, time and organizational disruption.Later, Slack [41] defined the range element of flexibility as ‘ the total envelope of capacity or range of states which theoperations system is capable of achieving ’ , thereby imply-ing the term  versatility . Upton [46] supported Slack  ’ s views by stating that: (i) increasing the range in terms of the breadth of product characteristics a system could produce;(ii) increasing mobility in terms of changeover time; and (iii)achieving uniform performance in terms of cost, quality or other measures, across a specified range of products,increases a system ’ s flexibility. The  ease  factor was stressedupon by Brill and Mandelbaum [10] and Benjaafar andTalavage [4, 5] who embodied it in the form of   efficiency .Das [21] stated that the basic purpose of a flexiblemanufacturing project is to recognize the changes occurringin a manufacturing facility ’ s environment, and to counter those changes by expending efforts in attaining different states. In these approaches, the penalty of a system to effect state changes, or the effort expended in achieving differ-ent states is in fact the efficiency of performing an operation.It is seen that past research has highlighted the importanceof the following three factors for measurement of flexibility: the state change required with respect to the existing system state, the relative weightage or importance between tasks,and the efficiency with which the tasks are executed  .However, the literature review reveals that most researchershave addressed state transition issues and the task executionissues and/or their relative importance for flexibility measure-mentinisolation.Stillothershave usedthe  state of the system as a reference for comparing task efficiency. However, in our view, the primary reason why the process of flexibilitymeasurement still remains incomplete is that these threefactors have not yet been addressed in conjunction, an aspect which we deem crucial for the comprehensive development of a composite measure for manufacturing flexibility.We view the contribution of any factor towards aflexibility type to be dependent upon the following threevariables: First, its  relative importance  (or weightage) vis-à-vis other extant factors, i.e., the extent of change that it can bring about in the system. Therefore, if the relativeimportance of a factor is high it has the potential of causinga significant change in the system ’ s performance, eventhough it might presently not be manifest. Second, afactor  ’ s present   manifestation level   in the system, i.e., anassessment of the state in which it presently exists.Accordingly, if the current level of manifestation is low, it will require a commensurately large change in its present state in order for it to be deemed effective. Third, the  statechange efficiency  for a factor, i.e., a measure of theefficiency with which its manifestation level in the systemcan improve. A factor possessing a high state changeefficiency can transit from a low to a high manifestationlevel with a commensurately low effort level expended inthe process. The above three variables are now expandedfor exposition purposes.3.1 Relative importance (or weightage) of a factor The  relative importance (or weightage) of a factor  ,W i  = FLX  i ð Þ , determines its relative significance level vis-à-vis other factors affecting a specific flexibility type.Clearly, these weightages would be situation specific andwould therefore differ from firm to firm.Take,forexample,thecaseoftwofirmsAandB,bothwithflexible manufacturing capabilities. Firm A is primarily arandom order facility [27] capable of producing a substantialvariety of parts in relatively low volumes. In contrast, firm Bcomprises of a dedicated FMS facility [27] geared for themanufacture of larger volumes of a few specialized highquantity parts, i.e., with much less part variety than firm A.For the case of machine flexibility then, firm A wouldconsider the factor   “ number of different operations per-formed by the machine ”  more important than the factor  “ throughput of the machine ”  when measuring this flexibilitytype. Conversely, firm B would give greater weightage to thefactor   “ throughput of the machine ”  than the factor   “ number of different operations performed by the machine ” .Similarly in the context of routing flexibility, firm Awould assign a higher weightage to the factor   “ averagenumber of machines to process different part type oper- 1102 Int J Adv Manuf Technol (2008) 38:1098  –  1113
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