International journal of computer integrated manufacturing , tập 24, số 3, 2011

International Journal of Computer Integrated Manufacturing Vol 24, No 3, March 2011, 189–197 An improved voting analytic hierarchy process–data envelopment analysis methodology for suppliers selection A Hadi-Vencheh* and M Niazi-Motlagh Department of Mathematics, Islamic Azad University, Mobarakeh Branch, Mobarakeh, Isfahan, Iran (Received March 2010; final version received January 2011) Selecting an appropriate supplier is now one of the most important decisions of the purchasing department Liu and Hai (Liu, F.H.F and Hai, H.L., 2005 The voting analytic hierarchy process method for selecting supplier International Journal of Production Economics, 97, 308–317) proposed a voting analytic hierarchy process method for selecting suppliers Despite its many advantages, Liu and Hai’s model (LH-model) has some shortcomings In this article, the authors present an extended version of the LH-model for multi-criteria supplier selection problem An illustrative example is presented to compare the authors’ model and the LH-model Keywords: data envelopment analysis (DEA); analytic hierarchy process (AHP); voting analytic hierarchy process (VAHP); multi-criteria decision making (MCDM) Introduction Supplier selection and evaluation is increasingly seen as a strategic issue for companies (Ceyhun and Irem 2007) Companies need to work with different suppliers to continue their activities In manufacturing industries the raw materials and component parts can equal up to 70% product cost In such circumstances the purchasing department can play a key role in cost reduction, and supplier selection is one of the most important functions of purchasing management They enhance customer satisfaction in a value chain Hence, strategic partnership with better performing suppliers should be integrated within the supply chain for improving the performance in many directions including reducing costs by eliminating wastages, continuously improving quality to achieve zero defects, improving flexibility to meet the needs of the end-customers, reducing lead time at different stages of the supply chain, etc (Kumar et al 2004, Amin and Razmi 2009) Selecting the right supplier is always a difficult task for the purchasing manager This is confirmed by many researchers (Kazerooni et al 1997, Bevilacqua and Petroni 2002, Humphreys et al 2003a, Kumar et al 2004, 2006, Ding et al 2005, Liu and Hai 2005, Guneri and Kuzu 2009, Hadi-Vencheh 2011) Suppliers have varied strengths and weaknesses which require careful assessment by the purchasers before ranking can be given to them So, every decision needs to be integrated by trading off performances of different suppliers at each supply chain stage (Liu and Hai 2005) *Corresponding author Email: ahadi@khuisf.ac.ir ISSN 0951-192X print/ISSN 1362-3052 online Ó 2011 Taylor & Francis DOI: 10.1080/0951192X.2011.552528 http://www.informaworld.com The analytic hierarchy process (AHP) has found widespread application in decision-making problems, involving multiple criteria in systems of many levels The strongest features of the AHP are that it generates numerical priorities from the subjective knowledge expressed in the estimates of paired comparison matrices The method is surely useful in evaluating suppliers’ weights in marketing, or in ranking order, for instance It is, however, difficult to determine suitable weight and order of each alternative (Lee 2009) Supplier selection is essentially a multiple criteria decision making (MCDM) problem, which involves multiple assessment criteria such as cost, quality, quantity, delivery and so on Therefore, MCDM approaches can be used for suppliers assessment Of the MCDM approaches, the AHP method is particularly suitable for modelling qualitative criteria and has found extensive applications in a wide variety of areas such as selection, evaluation, planning and development, decision making, forecasting, and so on However, due to the fact that there are some cases in which a large number of suppliers have to be evaluated and prioritised, while the AHP method can only compare a very limited number of decision alternatives, the pair-wise comparison manner is obviously infeasible in this situation Another way for gathering the decision makers’ opinion and selecting a candidate among a set of candidates is preference voting In preferential voting systems, each voter selects m candidates from among 190 A Hadi-Vencheh and M Niazi-Motlagh n candidates (m n) and ranks them from the most to the least preferred Each candidate may receive some votes in different ranking places The total score of each candidate is the weighted sum of the votes he/she receives in different places The winner is the one with the biggest total score So, the key issue of the preference aggregation in a preferential voting system is how to determine the weights associated with different ranking places (Wang et al 2007) Liu and Hai (2005) presented a voting AHP method henceforth LH-model, for supplier selection The voting AHP determines the weights of criteria not by pair-wise comparisons but by voting The data envelopment analysis (DEA) method was used to aggregate votes each criterion received in different ranking places into an overall score of each criterion The overall scores were then normalised as the relative weights of criteria They used Noguchi’s model (Noguchi et al 2002) to determine weights of criteria Despite its many advantages LH-model has some shortcomings For instance, to determine the lower bound of weights if we not know the number of voters we can not solve Noguchi’s model (Noguchi et al 2002) And for finding weights of R criteria we have to solve Noguchi’s model, R times (one linear programming (LP) for each criterion weight) Besides, steps and of the LH-model have some obscurities and in step we need a very high number of questionnaires and score sheets to measure supplier performance and identify supplier priority Of course, inspection of questionnaires and score sheets for determining scores is time consuming In this article the authors present a new voting AHP–DEA (voting analytic hierarchy process (VAHP)–DEA) methodology to overcome shortcomings mentioned above The remainder of this article is organised as follows In section 2, the authors give a brief description of the LH-model to provide a ground for the later development of methodology Shortcomings of the LH-model are presented in Section The authors present our method in Section and illustrate it using a real example In Section 5, the authors make a comparison between our method, LH-model and the AHP methodology proposed by Yahya and Kingsman (1999) for supplier selection Section concludes overall objective of the study then specifically on supplier rating of Dickson’s 23 criteria The criteria obtained from group decision fall into two categories, objective and subjective criteria The objective criteria are those that can be evaluated using factual data, and include quality, delivery, responsiveness, technical capability, facility, financial, etc Subjective criteria are those that are difficult to quantify and thus have to be evaluated qualitatively, and include discipline, management, etc Liu and Hai use the chosen criteria that must be satisfied in order to fulfil the goals of the selecting suppliers 2.2 Step 2: Structure the hierarchy of the criteria The AHP was developed to provide a simple but theoretically multiple-criteria methodology for evaluating alternatives Liu and Hai use the AHP to identify subcriteria under each criterion, and to investigate each level of the hierarchy separately They structure the problem into a hierarchy On the top level is the overall goal of selection suppliers On the second level are criteria that contribute to the goal On the third level are criteria that are decomposed into subcriteria, and on the bottom (or fourth) level are candidate suppliers that are to be evaluated in terms of the subcriteria of the third level 2.3 Step 3: Prioritise the order of criteria or subcriteria 2.3.1 The first stage In this section, the authors give a brief description of LH-model for selecting suppliers In this step, Liu and Hai (2005) suppose that there are n managers (or voters) in the study, and they will select different orders of criteria or subcriteria for the candidates Every manager votes to S S R, R is the number of criteria For this purpose, assume there are R criteria The criteria will be regarded as candidates Hence, they get R orders from to R and sum every vote in a table It commonly happens that, when one has to select among many objects, a particular object is rated as the best in one evaluation, while others are selected by other evaluation methods The managers get the order of criteria but not the weights The weight of each ranking is determined automatically by the total votes each candidate obtains 2.1 Step 1: Select suppliers’ criteria All managers and supervisors of a company are used in this step They were first briefed about the 2.3.2 The second stage Liu and Hai use the same methodology to find the orders of subcriteria The LH-model (Liu and Hai 2005) 191 International Journal of Computer Integrated Manufacturing 2.4 Step 4: Calculate the weights of criteria or subcriteria 2.4.1 The first stage At the first stage of this step Liu and Hai (2005) use Noguchi’s voting and ranking model (model 1) to develop criteria varied level from hierarchy analysis process This model is as follows: yrr ¼ max X urs xrs ðs¼1$SÞ s:t: yrp ¼ X urp xrp 1; p ¼ 1; 2; ; r ðs¼1$SÞ ur1 ! 2ur2 ! ! Surs urs ! e ¼ ð1 þ þ þ SÞ Â n ¼ n  SðS þ 1Þ ð1Þ 2.4.2 The second stage In this stage, Liu and Hai (2005) use the voting data of subcriteria and the same method to determine weights of the second level criteria The second level gives the normalised values for all factors The sum of weights for the factors of criteria must add up to So a criteria performance will be made up from weighting its subcriteria weights 2.4.3 The third stage The values in the bottom level are the global weight for each of factors; they are the factor weight multiplied by the criterion weight, so for a factor the value is criteria weight multiply by subcriteria weight As the actual performance data are collected for the factor value, these weights in the bottom level can be used directly to calculate the overall rating of the suppliers and to provide a performance score that can be derived for each factor 2.5 their judgement on the qualitative scale of adjectival descriptors The general performance score guidelines are given in Table Therefore each supplier can be awarded a score from to 10 on each subcriterion 2.6 Step 6: Identify supplier priority Simple score sheets were provided to assist the manager to record the scores for each supplier on each of the factors Once the scores for each factor have been determined, then it is relatively easy to calculate the resulting supplier rating scores Mathematically, the supplier rating is equivalent to the sum of the product of each factor weight and the supplier performance score on that factor Issues on LH-model In what follows the authors express ambiguities and shortcomings of VAHP methodology presented by Liu and Hai (2005) Firstly, it uses Noguchi’s strong ordering, despite it has useful properties, this model has a main deficiency, that is, it uses the term 2/ nS(Sþ1) to bound urs and make it greater than zero There is a question: if we not know the number of voters (n), what should we do? Secondly, in step to obtain the weight of each criteria and subcriteria selection suppliers, we have to solve the model RþP times, where R is the number of criteria and P is the number of subcriteria Clearly this is time consuming Thirdly, in step 5, the managers have to compare each supplier with respect to each factor and award a score from to 10 to each supplier on each factor This one by one assessment is time consuming, too Fourthly, in step 6, it has not been identified that the scores which are applied to calculate the resulting supplier rating scores are the average of managers scores or for each manager scores we calculate the total scores and then average all of managers total scores to obtain resulting supplier rating scores Step 5: Measure supplier performance This step requires the managers to assess the performance of all suppliers on the factors identified as important for supplier scores A major problem was thus to ensure consistency between the managers and avoid any bias creeping in A set of standard guidelines was set up after discussions with the managers (or voters) of the company It is agreed that all performance scores would be based on an 11-point grade scale Each grade would have an adjective descriptor and an associated point score or range of point scores The managers preferred, in the first instance, to make Proposed six step procedure In this section, using a real example, the authors propose a new six-step procedure for supplier selection The authors illustrate our method by a real case Table Supplier criteria score guideline Grade Very dissatisfied Poor Acceptable Good Very satisfied Scores 0/1 2/3 7/8 9/10 192 A Hadi-Vencheh and M Niazi-Motlagh study to better describe the model The case study is related to the supplier selection of the Tiam Win Company Tiam Win Company concentrates on producing door and window in Shahr-e-kord, Iran This company, to produce its products, is required to purchase several kind of profile such as aluminium, PVC, UPVC and so on with different sizes Hence, Tiam Win Company buys its profiles from different suppliers with respect to demand of customers and its type of home and industrial customers Overall, Tiam Win Company possesses several suppliers from different countries, namely Germany, Italy, Turkey and Iran The aforementioned company, to evaluate five suppliers, applied our procedure as follows: The problem is to select one of five candidate suppliers The first step is the structuring of the problem into a hierarchy (see Figure 1) On the top level is the overall goal of selection suppliers On the second level are seven criteria that contribute to the goal On the third level are seven criteria that are decomposed into 13 subcriteria, and on the bottom (or fourth) level are five candidate suppliers that are to be evaluated in terms of the subcriteria of the third level categories, objective and subjective criteria The objective criteria are those that can be evaluated using factual data, and include quality, financial, responsiveness, accessibility and technical capability The authors will use the above seven criteria that must be satisfied in order to fulfil the goals of the selecting suppliers 4.1 Let us suppose that managers (or voters) in the study will select different orders of criteria or subcriteria for the candidates Every manager votes to S R, R is the number of criteria For this purpose, let us assume seven criteria including (1) quality, (2) Background, (3) financial, (4) responsiveness, (5) accessibility, (6) technical capability and (7) management These criteria will be regarded as candidates We will get seven orders from to and a sum of every vote is shown in Table It commonly happens that, when one has to select among many objects, a particular object is rated as the Step 1: Select suppliers’ criteria The authors suppose the number of managers or voters is unknown They were first briefed about the overall objective of the study then specifically on supplier rating of Dickson’s 23 criteria (Dickson 1966) and the other supplier selection criteria researches such as (Lehmann and O’Shaughnessy 1974, Abratt 1986, Weber et al 1991, Min and Galle 1999, Stavropolous 2000, Ghodsypour and O’Brien 2001, Humphreys et al 2003b, Chen et al 2006, Lin and Chang 2008) The criteria obtained from group decision fall into two Figure Hierarchy of suppliers’ selection 4.2 Step 2: Structure the hierarchy of the criteria The AHP was developed to provide a simple but theoretically multiple-criteria methodology for evaluating alternatives The authors use the AHP to identify subcriteria under each criterion, and to investigate each level of the hierarchy separately The 13 subcriteria are quality-related certificates, factory audit, performance history, reputation, after sale service, on time delivery, conveyance way, distance, product rang, design capability, attitude, communication system and E-Commerce 4.3 Step 3: Prioritise the order of criteria or subcriteria 4.3.1 The first stage 193 International Journal of Computer Integrated Manufacturing Table Priority votes of seven criteria from respondents in the first stage Criteria First Second Third Fourth Fifth Sixth Seventh 18 8 14 10 10 10 13 11 12 12 10 11 Quality Background Financial Responsiveness Accessibility Technical capability Management Table Priority votes of subcriteria from respondents in the second stage Criteria Quality-related certificates Factory audit Conveyance way Distance Performance history Reputation Product range Design capability After sales service On time delivery Attitude E-Commerce Communication system Table First Second 13 34 23 24 40 30 17 19 28 24 17 34 13 24 23 40 17 30 28 19 21 20 Third max a þ ws s:t: a yr ¼ S X xrs ws r ¼ 1; 2; ; R s¼1 w1 ! 2w2 ! ! Sws ! S X ð2Þ ws ¼ 1; s¼1 20 17 10 Weights of seven criteria in the first stage Propose model develop criteria varied level from hierarchy analysis process Noguchi’s model Criteria Weight Normal Weight Normal Quality Background Financial Responsiveness Accessibility Technical capability Management 10.4573 6.5271 8.0285 5.5767 3.9734 6.2837 6.1534 0.2225 0.1389 0.1708 0.1187 0.0845 0.1337 0.1309 1.0000 0.5884 0.7677 0.5410 0.3800 0.6242 0.6009 0.2221 0.1307 0.1705 0.1202 0.0844 0.1386 0.1335 best in one evaluation, while others are selected by other evaluation methods The managers get the order of criteria but not the weights The weight of each ranking is determined automatically by the total votes each candidate obtains where xrs is the total votes of the rth criteria for the s th place The above model maximises the minimum of the total scores of the R criteria and determines a common set of weights for all the criteria In fact, this model maximises a (the minimum of the total scores) and the minimum weight ws at the same time and determines the most favourable weight for all criteria Indeed, ws is added as a component of the objective function to force ws not to equal to 4.4.1 The first stage The authors use the data of Table and find the weights of seven criteria by Equation (2) Table shows that weight for quality, background, financial, responsiveness, accessibility, technical capability and management are 10.4573, 6.5271, 8.0285, 5.5767, 3.9734, 6.2837, and 6.1534, respectively After normalising these data, the results are 0.2225, 0.1389, 0.1708, 0.1187, 0.0845, 0.1337 and 0.1309 The authors use the same methodology to find the orders of these subcriteria, presented in Table 4.4.2 The second stage The authors use the data of Table and the same method Table shows the weights of the second level criteria The sum of weights for the factors of criteria must add up to 4.4 Calculate the weights of criteria or subcriteria In this article, instead of Noguchi’s model, the authors propose the following model This model is used to 4.4.3 The third stage The authors obtain the global weight for each of the factors by multiplying factor weight by the criterion 4.3.2 The second stage 194 A Hadi-Vencheh and M Niazi-Motlagh weight, so for factory audit factor the value is 0.5745 times 0.2225 As the actual performance data are collected for the factor value, these weights in the Table can be used directly to calculate the overall rating of the suppliers and to provide a performance score that can be derived for each factor 4.5 Step5: Calculate supplier performance with respect to factors 4.5.1 The first stage This step again requires the managers to assess the performance of all suppliers on the 14 factors identified as important for supplier scores A major problem was Table Weights of 13 subcriteria in the second stage Propose model Noguchi’s model Criteria Weight Normal Weight Normal Quality-related certificates Factory audit Performance history Reputation After sales service On time delivery Conveyance way Distance Product range Design capability Attitude E-Commerce Communication system 20.0000 0.4255 0.7407 0.4255 27.0000 29.0000 18.0000 22.0000 25.0000 23.3333 23.6667 25.6667 21.3333 12.6364 17.8182 16.5455 0.5745 0.6170 0.3890 0.4681 0.5320 0.4965 0.5035 0.5461 0.4539 0.2689 0.3791 0.3520 1.0000 1.0000 0.6207 0.8800 1.0000 0.9859 1.0000 1.0000 0.8312 0.7092 1.0000 0.9752 0.5745 0.6170 0.3830 0.4681 0.5319 0.4965 0.5035 0.5461 0.4539 0.2642 0.3725 0.3633 Table thus to ensure consistency between the managers and avoid any bias creeping in For this purpose, the authors apply voting method like the authors used in step 3, that is, for each factor, every manager orders the suppliers and votes to T (T P, P is the number of suppliers) with respect to that factor Therefore to assist the manager to record the votes the authors provide a questionnaire with 14 columns and each column has P rows and at the top of each column the authors write the title of each factor While managers or experts vote and record their idea, we gather the sheets For each factor the authors prepare a table and enter the votes associated with that factor in it For instance, Table shows the priority votes of five suppliers with respect to performance history 4.5.2 The second stage By using the data of the last stage and the Equation (2) the authors obtain the score of each supplier with respect to each factor The authors show this method in Table and found the weight of suppliers with respect to performance history as shown in Table Table shows the scores of each supplier with respect to each factor that was obtained by the same methodology 4.6 Step 6: Identify supplier priority Whenever the scores for each factor are determined, then it is relatively easy to calculate the resulting supplier rating scores An example of this is shown in Table 10 Mathematically, the supplier rating is equivalent to the sum of the product of each factor global weight and the supplier performance score on Global weight of 14 factors Global weights Criteria Sub-criteria Quality Quality-related certificates Factory audit Performance history Reputation Financial After sales service On time delivery Conveyance way Distance Product range Design capability Attitude E-Commerce Communication system Background Financial Responsiveness Accessibility Technical capability Management Proposed model LH-model 0.0947 0.0945 0.1278 0.0857 0.1276 0.0806 0.0532 0.1708 0.0555 0.0631 0.0420 0.0426 0.0730 0.0607 0.0352 0.0496 0.0461 0.0501 0.1705 0.0562 0.0639 0.0419 0.0425 0.0757 0.0629 0.0353 0.0497 0.0485 Table Priority votes of five suppliers with respect to performance history from managers Suppliers First Second Third Fourth Fifth Supplier Supplier Supplier Supplier Supplier 11 18 13 12 11 9 15 12 14 10 13 13 3 24 Table The weights of suppliers with respect to performance history Suppliers Weight Supplier Supplier Supplier Supplier Supplier 9.9708 9.6788 12.088 8.1241 7.1387 195 International Journal of Computer Integrated Manufacturing Table The scores of suppliers with respect to 14 factors Factors Quality-related certificates Factory audit Performance history Reputation Financial After sales service On time delivery Conveyance way Distance Product range Design capability Attitude E-Commerce Communication system Table 10 Supplier Supplier Supplier Supplier Supplier 9.7591 9.6423 9.9708 10.5468 12.8925 7.4562 8.0211 9.6531 6.7452 8.7795 11.8529 10.8854 9.8021 9.6076 11.5766 10.8102 9.6788 9.0253 12.0251 10.2567 9.7301 8.9564 8.6491 13.2178 9.9812 14.5806 10.0988 8.2904 14.6350 8.5401 12.0876 14.0685 6.4521 6.0325 4.8597 6.6028 3.0912 16.3945 11.8567 4.3828 18.0079 9.6522 5.5328 8.6277 8.1241 6.1532 8.0256 11.2051 11.1350 10.2958 15.4219 3.4197 7.3703 7.0921 5.0017 8.4985 5.4964 9.3796 7.1387 7.2062 7.6047 12.0495 13.2541 11.4919 13.0926 5.1885 5.9389 10.0591 4.0895 10.9513 Rating of supplier-1 Criteria Sub-criteria Weights Scores Sub-totals Quality Quality-related certificates Factory audit Performance history Reputation Financial After sales service On time delivery Conveyance way Distance Product range Design capability Attitude E-Commerce Communication system 0.0947 0.1278 0.0857 0.0532 0.1708 0.0555 0.0631 0.0420 0.0426 0.0730 0.0607 0.0352 0.0496 0.0461 9.7591 9.6423 9.9708 10.5468 12.8925 7.4562 8.0211 9.6531 6.7452 8.7795 11.8529 10.8854 9.8021 9.6076 0.9240 1.2325 0.8544 0.5609 2.2023 0.4141 0.5062 0.4051 0.2871 0.6410 0.7193 0.3832 0.4865 0.4428 10.0595 Background Financial Responsiveness Accessibility Technical capability Management Total score that factor The supplier rating value for supplier-1 is obtained by summing up the products of the respective elements in columns and for each row and given in the final column The rating method used in supplier-1 can also be used to find the total scores of the other five suppliers The supplier with the highest supplier rating value should be regarded as the best performing supplier and the rest can be ranked accordingly Table 11 shows the rating value of each supplier and its rank in the proposed method as well 4.7 Comparison In this section the authors make a comparison between our method, LH-model and the AHP method proposed by Yahya and Kingsman (1999) In what follows the authors compare the three methods, step by step: As we see in Table 12, steps and are the same in the three methods Step is the same in the proposed method and LH-model but differs from AHP In fact this is the main difference between voting approaches Table 11 Ranking using proposed model and a comparison of our and LH-model Score Ranking Suppliers Proposed model LH-model Proposed model LH-model Supplier Supplier Supplier Supplier Supplier 10.0595 10.7365 9.8233 8.0212 8.3597 5.9466 5.8895 6.4066 4.7043 4.9643 5 4 and the AHP This is why the authors call these approaches VAHP In this step, the voting methods use voting to prioritise the order of alternatives but AHP method uses comparison matrices that take time, so if the number of criteria increase, pairwise comparisons are certainly impossible to be made The traditional AHP method can only compare a very limited number of decision alternatives, which is usually not more than 15 When there are hundreds 196 A Hadi-Vencheh and M Niazi-Motlagh Table 12 model Step Differences between LH-model and proposed Old VAHP Proposed VAHP Select suppliers, criteria Structure the hierarchy of the criteria Prioritise the order of criteria or subcriteria Calculate the weights (Noguchi’s ordering) Select suppliers, criteria Structure the hierarchy of the criteria Prioritise the order of criteria or subcriteria Calculate the global weights using model (2) Calculate suppliers weights with respect to factors Identify supplier priority Measure supplier performance Identify supplier priority or thousands of alternatives to be compared, the pairwise comparison manner provided by the traditional AHP is obviously infeasible To overcome this difficulty, the authors combine the AHP with a new voting DEA model and propose an integrated VAHP– DEA methodology in this article The purpose of step is the same as all of methods but the ways is different The LH-model uses Noguchi’s model which has some shortcomings mentioned before The authors proposed a new DEA model which overcomes those shortcomings In step 5, AHP and LH-model use comparing scores but the authors used again ‘voting’ and proposed a model (2) to measure supplier performance, it gives rise to avoid any bias creeping in and is easy Finally, step is the same as in the three methods So the difference of LH-model and proposed VAHP is steps 3, and 5 Conclusion Outsourcing decisions are an integral aspect of the logistics function Traditionally, they have dealt primarily with the supply of raw materials and component parts and some services such as transportation In recent years, with the increase in contract logistics, many firms are outsourcing activities that were once performed in-house To remain competitive with these third-party providers, logistics managers must use more sophisticated techniques when performing their duties In this article, the authors proposed a new weighting procedure instead of AHPs’ paired comparison for selecting suppliers The proposed model uses an integrated VAHP–DEA methodology to evaluate alternatives It provides a simpler calculation of the weights to be used and for scoring the performance of suppliers It is shown that the new integrated VAHP– DEA methodology is simple enough, easy to use, applicable to any number of decision alternatives, and particularly useful and effective for complex MCDM problems with a large number of decision alternatives, where pair-wise comparisons are certainly impossible to be made It is expected that in the near future this method will be applied effectively to various issues such as policy making, business strategies and performance assessment References Abratt, R., 1986 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such as semiconductor manufacturing systems, automobile manufacturing systems, and chemical processes because these are better modelled by discrete event models than by differential or difference equation models at higher levels of abstraction Moreover, decentralised supervisory control is an efficient method for large complex systems according to the divide-and-conquer principle This article presents a solution and a design procedure of supervisory control problem for the case of decentralised control We apply the proposed design procedure to an experimental miniature computer-integrated manufacturing (CIM) system This article presents the design of fourteen modular supervisors and one high-level supervisor to control the experimental miniature CIM system These supervisors are controllable, non-blocking, and non-conflicting After the verification of the supervisors by simulation, the collision avoidance supervisors for automated guided vehicle system have been implemented to demonstrate their efficacy Keywords: decentralised control; discrete event systems; manufacturing automation; supervisory control theory Introduction As any manufacturing system becomes larger and more complex, more systematic and rigorous methods are needed for the modelling and control of such large complex systems Supervisory control theory (Ramadge and Wonham 1987, Wonham and Ramagde 1987), which was proposed by Ramadge and Wonham and based on discrete event system (DES) methods, is recognised as one of the promising techniques for the design and control of large complex systems, such as semiconductor manufacturing systems, chemical processes, HVAC (heating, ventilation and air conditioning), and power plants Recently, the supervisory control theory has received much focus in many applications, such as robotics (Ricker et al 1996, Chung and Lee 2005), traffic control (Giua and Seatzu 2001), logistics (Jafari et al 2002), failure diagnosis (Son and Lee 2007) and manufacturing systems (Golmakani et al 2006), because it can satisfy control specifications of a plant to be controlled systemically by permitting eligible events in the plant maximally Also, it has been proved that the supervisory control theory is very efficient for the control of highly complex systems (Cassandra and Lafortune 1989, Ramadge and Wonham 1989), which are modelled as Petri nets (Basile et al 2004, Dai et al 2009) or *Email: hyoungil.son@tuebingen.mpg.de ISSN 0951-192X print/ISSN 1362-3052 online Ó 2011 Taylor & Francis DOI: 10.1080/0951192X.2011.552530 http://www.informaworld.com automata (Lee and Lee 2002, Ramirez-Serrano and Benhabib 2003) A general problem in the design and control of target systems based on the supervisory control theory (Wonham 1998) is named as supervisory control problem (SCP) The SCP is, generally, used to find a supervisory controller, i.e centralised supervisor, which satisfies the legal language (behaviour specification) of a system (Wonham 1998) However, as the system becomes larger and more complex, the computational complexity of the SCP increases exponentially due to the increase of eligible events The divide-andconquer principle is very useful to solve this problem because the computational complexity can be decreased exponentially if the SCP is solved by dividing the system into several sub-systems (Rudie and Wonham 1992) Based on this approach, supervisory controllers designed are called as modular supervisory controllers horizontally (Wonham and Ramadge 1988) and high-level supervisory controllers hierarchically (Leduc et al 2006) Finally, a decentralised supervisory control system is defined as a supervisory control system, which consists of the modular supervisors and the high-level supervisors (Yoo and Lafortune 2002) A hierarchical supervisory control is presented by Tittus and Lennartson (2002) as a Petri net-based International Journal of Computer Integrated Manufacturing approach, and by Leduc et al (2005, 2009) as an automata-based approach Theoretically, they proved that a proposed hierarchical supervisor is by far less complex than a non-hierarchical one Yoo and Lafortune (2002) presented a generalised form of the conventional decentralised control architecture for DESs They proposed a concept of fusion operation using both the union and the intersection of enabled events Their method is extended to allow the making of conditional decisions also, ‘enable if nobody disables’ and ‘disable if nobody enables’, in addition to unconditional decisions, ‘enable’ and ‘disable’ (Yoo and Lafortune 2004) They, however, did not present a design procedure with a practical example for the easy use of the presented theory even though their method was rigorous Feng et al (2009) proposed a similar method for a decentralised non-blocking supervisory control They briefly outlined the proposed theory with a practical example The other approach, the so-called supervisor localisation, is proposed by Cai and Wonham (2010) for the distributed control architecture of large scale DESs They analysed trade-offs between the decentralised and the distributed control architecture A practical implementation method is not presented by Feng et al (2009) and Cai and Wonham (2010) Queiroz and Cury (2002) presented an implementation method of modular supervisory controller using a programmable logic controller (PLC) They explained their method with a simple manufacturing cell example They, however, showed only simulation results using the proposed method Supervisor implementation using the PLC is also presented by Ramirez-Serrano et al (2002) and by Petin et al (2007) Petri net is, usually, more efficient as a modelling and analysis method for the deadlock avoidance (Lerrarini et al 1999) and performance evaluation (Tsinarakis et al 2005) of a manufacturing system We, therefore, use automata to model the manufacturing system for the supervisory control in this article In this article, a concept of sub-plant is proposed to reduce the computational complexity for controllability in the SCP, and then, a generalised solution of the SCP for the modular supervisors is also proposed A solution of the SCP for a high-level plant with respect to a high-level behaviour specification is also developed using the proposed concept of the sub-plant and Wonham et al.’s method The developed solutions are proved theoretically Modular and high-level supervisors are designed, implemented and verified using an experimental miniature computer-integrated manufacturing (CIM) system using the proposed decentralised supervisory control scheme The experimental miniature CIM 243 system consists of three industrial robots, two automated guided vehicles (AGVs), two numerical controlled (NC) machines, several conveyor belts and sensors A plant of the miniature CIM system is modelled as the deterministic automaton The operation rules of the miniature CIM system are defined as the behaviour specifications (legal languages), and the supervisors are then designed with respect to these specifications The designed supervisors are later transformed into the clocked Moore synchronous state machine (CMSSM; Wakerley 1990) for the implementation We, finally, verify a supervisor for a collision avoidance of AGVs via an experiment, which is a critical problem for the material transfer in production lines (Singh et al 2010) This article is organised into six sections In the section following this introduction, a background of the supervisory control theory is presented In the third section, the design methodologies of the decentralised supervisory control and its theoretical proofs are presented An application to the experimental miniature CIM system of the proposed control and an implementation of the designed controller are presented in the fourth and fifth sections, respectively Finally, the main contributions of this article are summarised in the last section Background 2.1 System modelling DES is modelled as the automaton G ¼ {Q, S, d, q0, Qm}, where Q is the state set, S is the event set, d: Q S*!Q is the state transition function, q0 is the initial state and Qm is the marked state set, which is a subset of Q In d, S* is the set of null event, and string (sequence) is expressed as e and s1 s2 s3 .sk, k ! 1, respectively In particular, the event set S is divided into two disjoint sets, i.e the controllable event set Sc and the uncontrollable event set Suc And S is also partitioned into the observable event set So and the unobservable event set Suo The language that is generated by G is defined as shown in Equation (1) LðGÞ ¼ fsjs Sà ; dðq0 ; sÞ!g ð1Þ where d(q0, s)! means that a next state is defined after the occurrence of the string s in the state q0 The prefix closure of L(G) is defined as LðGÞ ¼ ft Sà jt s for somes LðGÞg ð2Þ And the marked language of G is defined as follows Lm ðGÞ ¼ fsjdðq0 ; sÞ! Qm ; Lm ðGÞ  KðGÞg ð3Þ 244 H.I Son If G satisfies Lm ðGÞ ¼ LðGÞ, then L(G) is nonblocking The non-blockingness is then the necessary condition to design a proper supervisor in the supervisory control theory And if the prefix closures of two languages are disjoint, then these languages are nonconflicting as defined in Equation (4) LðGÞ ¼ LðG1 Þ [ LðG2 Þ; null ¼ LðG1 Þ \ LðG2 Þ ð4Þ ) LðG1 Þ ^ ðG2 Þ Finally, the projection map P is defined as P(s) ¼ e and P(ss) ¼ P(s) for s Suo, s L(G) 2.2 Supervisory control Supervisor is also defined as the automaton S ¼ {X, S, x, x0, Xm}, where X, S, x: X S* !X, x0 and Xm are the state set, the event set, the state transition function, the initial state and the marked state, respectively Let the plant to be controlled be defined as G, then the behaviour of plant G under the supervision of S is represented as Equation (5) S=G ¼ fX  Q; S; x  d; ðx0 ; q0 Þ; Xm  Qm g ð5Þ The controllability and the observability of L(S) with respect to L(G) are defined in Definitions and 2, respectively Definition 1: For S  G, S is controllable with respect to (G, Suc) if the following is satisfied ð8s; sÞs LðSÞ; s Suc ; ss LðGÞ ) ss LðSÞ ð6Þ The physical meaning of controllability is that an arbitrary string s, which is permissible by the supervisor S and an uncontrollable event s, is eligible in the plant G, if the string ss is eligible in G and if S also permits ss, then, S is controllable with respect to G Definition 2: For S  G, S is observable with respect to (G, P, Suo) if the following is satisfied 8s; s0 ; s LðSÞ; PðsÞ ¼ Pðs0 Þ; s Suo ; ss LðSÞ; s0 s LðGÞ ) s0 s LðSÞ ð7Þ Observability means that if ss is permissible by S and s0 s is eligible in G, then S also have to permit s0 s, where two strings s and s0 are recognised as the same string by the projection map P and are also permissible by the supervisor S and where s is an unobservable event SCP is defined in Definition based on Definition Definition 3: For a given K and G, where K  G, find a supremal language S that satisfies L(S/G) ¼ K and LðS=GÞ ¼ Lm ðS=GÞ and is controllable with respect to (G, Suc) If K is, therefore, defined as the legal language for the plant G to be controlled, then the SCP is to find a supervisor, which satisfies L(S/G) ¼ K and is nonblocking and controllable with respect to G In addition, the supervisor, which satisfies the constraints and is controllable, need not be unique Among these supervisors, a supremal controllable sub-language of G with respect to K is the unique solution of the SCP Therefore, the supervisor S, which satisfies Definition 3, can permit the language to occur in the plant G maximally A supervisory control system is illustrated in Figure Decentralised supervisory control 3.1 Design of modular supervisor Let us consider two fundamental issues in this section, the computational complexity and the implementation simplicity First, a method to reduce the computational complexity is presented Solving the SCP with respect to all the plants takes a tremendous computational complexity Therefore, the computational complexity can be decreased exponentially if the SCP is solved with respect to several sub-plants This approach is presented in Theorem Theorem 1: For a given plant G, which can be expressed as G ¼ G1 G2 Gn, let us define a sub-plant Gsub,i G for the legal language Ki, i ¼ 1, , m If Si is a solution of the SCP with respect to (Ki, Gsub,i) and is non-conflicting with the Gsub,j, i 6¼ j, then Si is the solution of the SCP with respect to (Ki, G) Proof: Based on the SCP, we have to prove that Si is controllable with respect to (Ki, G), is non-blocking and is the maximally permissible language First, let us consider the controllability of Si If the event sets of G and Gsub,i are defined S and Ssub,i, respectively, then Pas c the new event set sub;i ¼ S À Ssub;i can be defined Here, every uncontrollable event, which is an element of ðScsub;i Þuc  Scsub;i , is permitted by Si because Scsub;i is Figure Concept of supervisory control system International Journal of Computer Integrated Manufacturing the event set consisting of self-loops in Si Therefore, Si is controllable with respect to G And Si is non-blocking because it is non-conflicting with respect to Gsub,j, i 6¼ j Finally, Ki is the maximally permissible language because every event in Scsub;i is permitted by Si Next, let us consider finding an equivalent supervisor, which is less complex to implement because it has less states and less state transitions even if it generates same language with the original solution of the SCP Generally, the supervisor S satisfies the following: LðS=GÞ ¼ LðSÞ ð8Þ However, the supervisor S becomes much complex because it has much more states than those in the legal language K with respect to the events generated in the plant G Practically, this complexity creates a problem in the implementation of the supervisor Therefore, it will be relatively easier to implement the simpler supervisor S0 , which satisfies Equation (9) LðS0 =GÞ ¼ LðSÞ ð9Þ This means that the supervisor S0 , which is simpler than S, can be designed by satisfying Equation (9) while the language of plant behaviour under the supervision of S0 is same with the one under the supervision of S If the legal language K is defined, then the maximum number of state in S0 is the same with that of K while the maximum number of states in S is the same with that of K ^ G We have summarised this issue in Theorem Theorem 2: If the supervisor S0 satisfies the following conditions, then S0 is an optimal (or minimally restrictive) proper supervisor with respect to the plant G (1) The supervisor S0 is controllable with respect to the plant G (2) Lm ðS0 Þ ¼ LðS0 Þ (3) Lm ðGÞ ^ Lm ðS0 Þ ¼ LðGÞ ^ LðS0 Þ (4) If S is the supremal controllable sub-language with respect to K, then L(S0 /G) ¼ L(S) has to be satisfied Proof: The first condition means that the designed supervisor has to satisfy the controllability with respect to the plant, and the second condition represents that the supervisor has to be non-blocking The nonconflictness of the supervisor with the plant is represented in Condition (3) In other words, the third condition means that the supervisor has to be non- 245 blocking with respect to the plant Therefore, if S0 satisfies Conditions (1), (2) and (3), then S0 is a proper supervisor Condition (4) represents the behaviour of the plant under the supervision of S0 , which has to generate the maximally controllable sub-language Finally, S0 becomes the optimal supervisor The modular supervisor is defined in Definition based on Theorems and Definition 4: For the legal languages Kj, j ¼ 1, 2, ., n, let us design the supervisors Si, i ¼ 1, 2, , m which satisfy Theorems and And if Si satisfies the nonconflictness condition S ¼ S1 ^ S2 ^ ^ Sm , then Si is defined as the modular supervisor Finally, the solution of the modular SCP is presented in Theorem using Theorems and The computational complexity of the algorithm for the controllability, the non-blocking, the non-conflictness tests, which is presented in Theorem 3, is same when compared with the one proposed by Ramadge and Wonham (1987, 1989) Theorem 3: For a given plant G and legal languages Ki, i ¼ 1, 2, , m, modular supervisors Si or Si0 are the solutions of the SCP using the following procedure Modular SCP solution procedure: Step 0: Define the automaton G of the plant to be controlled and the automation Ki of the legal languages Step 1: Design the sub-plants Gsub,i Step 2: Check the controllability of Ki with respect to Gsub,i using the controllable events in Ki If Ki is controllable, go to Step 5, otherwise go to next step Step 3: Reconstruct Ki by considering the events that not satisfy the controllability in the controllable events in Ki Step 4: Go to Step If Ki cannot be reconstructed while satisfying the controllability, then go to Step Step 5: Check the non-blockingness of Ki Delete the state that makes Ki as blocking, and then go to Step Step 6: Check the non-conflictness of Ki with respect to Gsub,i If Ki is non-conflicting, then S0 i ¼ Ki Otherwise, reconstruct Ki by checking the string, which makes Ki as conflicting, and then go to Step Step 7: Find the supremal controllable sub-language Si of Ki with respect to Gsub,i Si is the solution of the modular SCP with respect to (Ki, Gsub,i) Step 8: If L(Si) ¼ L(S0 i/Gsub,i), then S0 i is the solution of the modular SCP with respect to (Ki, Gsub,i) Proof: The proof is omitted because it is straightforward from the proofs of Theorems and 246 3.2 H.I Son Design of high-level supervisor Let us represent the plant G as the low-level plant Glo ¼ {Qlo, Slo, dlo, qlo, 0, Q10, m} and define the high-level plant Ghi which satisfies L(Ghi) ¼ Y{L(Glo)} with the information map Y The information map is defined as Y: L(Glo)!T*, where T ¼ {t0, t1, t3, } is the set of events which have the physical meaning in the high-level plant among the low-level events The information map is an arbitrary projection map The high-level plant Ghi is also represented as the automation Ghi ¼ {Qhi, Shi, dhi, qhi,0, Qhi,m} similar to Glo Therefore, the high-level supervisor can be designed if we solve the SCP with respect to the high-level plant Ghi and the high-level legal language Khi The information map Y is defined by mapping the high-level event t as the state output of the states of Glo The state in Glo, which has the state output about Y, is defined as the vocal state And then Ghi can be constructed from Y and Glo Before constructing Ghi, Glo has to be reconstructed using the following two conditions to make Ghi maintain the control structure of Glo Condition for the high-level plant: Output Control Consistency (OCC) High-level SCP solution procedure Step 0: Define the automaton Glo of the low-level plant to be controlled and the automation Khi,i of the high-level legal languages And also define the information map Y Step 1: Design the sub-plants (Glo)sub,i Step 2: Construct ðGlo Þvocal sub;i of (Glo)sub,i using Y vocal Step 3: Construct fðGlo Þvocal sub;i gOCC of ðGlo Þsub;i using Equation (10) vocal Step 4: Construct fðGlo Þvocal sub;i gSOCC of fðGlo Þsub;i gOCC using Equation (11) h i Step 5: Construct Ghi ¼ Y fðGlo Þvocal g sub;i SOCC , and define Ghi as the high-level plant Step 6: Run from Steps 2–8 of Theorem with respect to (Kh,i, Ghi) Proof: The proof is omitted because it is straightforward from the OCC and SOCC conditions and the proofs of Theorems and Finally, the architecture of decentralised supervisory control is illustrated in Figure 4.1 YÀ1 fLðGhi Þg" ¼ LðGlo Þ ð10Þ Condition for the high-level plant: Strictly OCC (SOCC) YYÀ1 fLðGhi Þg" Š ¼ LðGhi Þ ð11Þ Condition means that in a certain low-level state, when there is a state transition by the low-level event which has the state output, and also, there is a state transition by the low-level event which, however, has no state output, this low-level state has to be divided with respect to two different state transitions And Condition represents that the state outputs have to be redefined according to whether the low-level event, which makes the state transition with respect to the reconstructed low-level states by Condition 1, is controllable or not Both Conditions are defined as the hierarchical consistency The design procedure of the high-level supervisor is presented in Theorem using Theorem and OCC and SOCC conditions Theorem 4: For a given low-level plant Glo, an information map Y, high-level legal languages (Khi,i, i ¼ 1, 2, , m) and high-level supervisors (Shi,i or S0 hi,i) are solutions of the SCP using the following procedure Application: miniature CIM system Layout In this article, an experimental miniature CIM system is experimented to verify the proposed decentralised supervisory control The miniature CIM system consists of two NC machines, three industrial robots, two AGVs, several conveyor belts, detection sensors, etc This system is designed to have two types of production lines, the cumulative and the non-cumulative way, under the assumption of the manufacturing of two products The layout of the miniature CIM system is shown in Figure 4.2 Plant model The automaton of the plant G can be designed by the synchronous product (Wonham 1998) of all the Figure system Structure of decentralised supervisory control International Journal of Computer Integrated Manufacturing Figure 247 Experimental miniature computer-integrated manufacturing system automata of each component, after modelling the components of the plant such as the NC machine, the industrial robot, etc as automata In this article, the number of states and events is minimised in the component model This minimisation is done by the projection of the events, which are unnecessary to observe and unobservable by a supervisor and not affect the behaviour of a legal language towards the null event e For example, a velocity change of AGV is not modelled in the automaton of AGV because the velocity is controlled not by the supervisor but by a local controller of the AGV The designed automata are projected to generate same language regardless of the states because this article applies the supervisory control theory as the event-based approach The number of states can also be minimised by this state projection However, if the designed automata are changed to the non-deterministic ones after the state projection, the automata are transformed into the deterministic ones using the subset construction (Giua and Seatzu 2001) Every component in the miniature CIM system (two AGVs, three robots, two NC machines, five conveyor belts, seventeen detection sensors, restraint pin and solenoid) is modelled as an automaton with two states The designed plant models are shown in Figures 4–10 Every event defined in the miniature Figure Automation model of AGVs, AGVi CIM system is listed in Table The automaton of the plant G is constructed by Equation (12) using the designed automata of all components This article used the open software for the supervisory control theory, TCT (Wonham 1998), for the design and calculation of the automata The state number of G is 4, 294, 967, 296, which is constructed using SYNC function of TCT as shown in Equation (12) G ¼SYNCðAGVi ; ROBOTj ; NCMachinek ; ConvBeltm ; SENSORn ; ResPin; SolÞ ð12Þ 4.3 Modular supervisor In this section, the modular supervisors are presented for the decentralised supervisory control of the 248 H.I Son Figure Figure 10 Automation model of restraint pin, ResPin Automation model of solenoid, Sol experimental miniature CIM system using Theorem The specifications for the modular supervisors are as follows: Figure Automation model of robots, ROBOTi (a) Robot 1, (b) Robot and (c) Robot Figure Automation NCMachinei Figure model of NC machines, Automation model of conveyor belts, ConvBelti (1) Buffer size of the conveyor belts 2, and are two work-pieces (2) The robot picks up the work-piece from the conveyor belt and moves it into the NC machine After the completion of machining in the NC machine 1, the robot picks up the work-piece and moves it onto the conveyor belt (3) The robot picks up the work-piece from the conveyor belt and moves it into the NC machine After the completion of machining in the NC machine 2, the robot picks up the work-piece and moves it onto the conveyor belt (4) The robot picks up the work-pieces from the conveyor belts and and moves those into the AGV-1 and AGV-2 separately (5) The solenoid separates the work-pieces onto the conveyor belts and (6) Two AGVs unload two types of work-pieces to the specific places separately; AGV-1 and AGV-2 unload work-pieces and at S16 and S14, respectively (7) AGVs travel only in counterclockwise direction and have to avoid the collision The modular supervisors are designed which satisfy the non-blockingness and the non-conflictness with respect to the specifications The number of designed supervisors are eight for the specifications 1) * 5) and six for the specifications 6) and 7) Figure Automation model of sensors, SENSORi (a) sensor for conveyor belt and (b) sensor for AGV 4.3.1 Modular supervisors for production line Firstly, the legal languages are designed for the specifications 1) *5) The eight modular supervisors International Journal of Computer Integrated Manufacturing are designed with respect to the designed legal languages using Theorem These supervisors are shown in Figures 11–13 Table Event list Plant Event Controllability AGVs mv_AGVi umv_AGVi op1 op2 op3 op4 op5 op6 end_op5 end_op6 opi end_opi mv_Convi umv_Convi WP_ati noWP_ati AGVi_atk noAGVi_atk pin_down pin_up mv_Sol umv_Sol Controllable Uncontrollable Controllable Controllable Controllable Controllable Controllable Controllable Uncontrollable Uncontrollable Controllable Uncontrollable Controllable Uncontrollable Uncontrollable Uncontrollable Uncontrollable Uncontrollable Controllable Controllable Controllable Uncontrollable Robots NC machines Conveyor belts Sensors Restraint pin Solenoid 249 Let us explain how the supervisor controls the plant using the example of the buffer size supervisor for the conveyor belt as shown in Figure 11(a) The control data of this supervisor are enabling all events at the initial state and the state and disabling the event mv_Conv1 at the state This means that the buffer size supervisor for the conveyor belt will not Figure 12 Routing supervisor (a) routing supervisor for robot and NC machine 1, (b) routing supervisor for robot and NC machine 2, (c) routing supervisor for robot and production lines and and (d) routing supervisor for robot and conveyor belt Figure 11 Buffer size supervisor (a) buffer size supervisor for conveyor belt 2, (b) buffer size supervisor for conveyor belt 4, and (c) buffer size supervisor for conveyor belt Figure 13 Workpiece selection supervisor 250 H.I Son permit the occurrence of the event mv_Conv1 after the occurrence of the string e Á mv_Conv1 Á e Á WP_at1 Á e Á mv_Conv1 Á e Á WP_at1 Á e 4.3.2 Modular supervisors for AGV The seven modular supervisors for the supervisory control of AGVs are designed with respect to the specifications 6) and 7) using Theorem The modular supervisor for the specification 6) is shown in Figure 14 The legal languages for the specification 7) are designed as six legal languages by dividing the AGV lane into six sections as shown in Figure and then six supervisors are designed with respect to each legal language The AGVs always travel under the supervision of these seven modular supervisors The AGV collision avoidance supervisor for the section is shown in Figure 15 For other sections, the collision avoidance supervisors can be easily designed by changing only transition events according to the sensor signals of each section The AGV collision avoidance supervisor for the section has the control data which disables the event mv_AGV2 and mv_AGV1 at the state and 4, respectively This means that the event mv_AGV2 and mv_AGV1 will be disabled after the occurrence of the string e Á (mv_AGV1 þ mv_AG V2) Á e Á AGV1_at12 Á e Á (mv_AGV1 þ mv_AGV2) Á e ÁAG V2_at17Á mv_AGV1Á e and the string e Á (mv_AGV1 þ m v _AGV2)Á e Á AGV2_at12Á e Á (mv_AGV1 þ mv_AGV2)Á e Á AGV1_at17Á e Á mv_AGV1Á e, respectively Figure 14 Figure 15 section AGV unloading supervisor AGV collision avoidance supervisor 4.4 High-level supervisor The high-level specification of the miniature CIM system is shown in the following High-level specification: (1) The total buffer size of the conveyor belts * is three work pieces The designed high-level supervisor for the highlevel specification is shown in Figure 16 All high-level events which are not illustrated in Figure 16, form the self-loop events at all states The design procedure of the high-level supervisor, as shown in Figure 16, is specifically represented using Theorem in the following All automaton constructed during the design procedure are represented as the number of the states and the transitions because the states are too many to illustrate Design procedure for the high-level supervisor: Step 0: The low-level plant Glo is constructed as SENSOR1 SENSOR2 SENSOR3 SENSOR4 SENSOR5 SENSOR6 SENSOR7 ConvBelt1 ConvBelt2 ConvBelt3 ConvBelt4 The number of states and transitions in Glo are 1,024 and 13,312 respectively The high-level legal language K0hi;1 is defined as the automation shown in Figure 16 except the self-loop at every states The designed K0hi;1 has states and transitions Finally, the information map Y is defined in Table The controllability of the highlevel events is same with the low-level event defined in Table Step 1: (Glo)sub,1 is designed as the synchronous product of the buffer size supervisor for the conveyor belt and the buffer size supervisor for the conveyor belt which are shown in Figure 11(a) and (b) respectively The designed (Glo)sub,1 has states and 102 transitions Step 2: ðGlo Þvocal sub;1 is constructed from (Glo)sub,1 The designed ðGlo Þvocal sub;1 has 27 states and 309 transitions The part of this construction is illustrated in Figure 17 The event WP_at1 makes the transition from the state to the state 11 and the state output becomes t1 in ðGlo Þvocal sub;1 as shown in Figure 17(b) And the state becomes the state and 10 after the occurrence of the events WP_at7 and mv_conv1, respectively and the for Figure 16 High-level supervisor International Journal of Computer Integrated Manufacturing Table Information map Y Low-level event t ¼ Y(s) High-level event WP_at1 noWP_at1 WP_at2 noWP_at2 WP_at3 noWP_at3 WP_at5 noWP_at5 WP_at6 noWP_at6 WP_at7 noWP_at7 mv_Conv1 umv_Conv1 mv_Conv2 umv_Conv2 mv_Conv3 umv_Conv3 mv_Conv4 umv_Conv4 t1 t0 t0 t0 t0 t0 t0 t0 t0 t0 t2 t0 t3 t0 t0 t0 t0 t0 t0 t0 WP_at1 null null null null null null null null null WP_at7 null mv_Conv1 null null null null null null null Figure 17 (a) Part of (Glo)sub,1 (b) ðGlo Þvocal sub;1 for (Glo)sub,1 shown in Figure 17(a) 251 state output becomes t2 and t3 at the state and 10, respectively The state output at other states is t0 vocal Step 3: fðGlo Þvocal sub;1 gOCC is constructed from ðGlo Þsub;1 vocal fðGlo Þsub;1 gOCC has 48 states and 548 transitions This procedure is explained using Figure 18 as follows The state output of the case, when the event WP_at7 has occurred without the occurrence of the event mv_Conv3 at the state 0, has to be defined differently with the case when the event WP_at7 has occurred after the occurrence of the event mv_Conv3 at the state Because mv_Conv3 is the controllable event, the former case cannot disable the occurrence of WP_at7 while the latter case can disable WP_at7 by disabling mv_Conv3 Therefore, in the latter case, the state output has to be defined as the controllable event The information map, which has to be added into the information map Y defined in Table 2, is defined in Table to solve this problem In fðGlo Þvocal sub;1 gOCC shown in Figure 18(b), which is redesigned using the additional information map, the state goes to the state and the state output becomes t2 after the occurrence of WP_at7 And the next state becomes the state 27 after the occurrence of mv_Conv3 and if WP_at7 has occurred again, the state output becomes t5 but not t2 Step 4: The designed fðGlo Þvocal sub;1 gSOCC has 39 states and 499 transitions Because the new events t4 and t5 which are defined in Table are not eligible in the plant, those events have to be redefined as t2 in this step, which are eligible high-level events This means vocal Figure 18 (a) Part of ðGlo Þvocal sub;1 (b) fðGlo Þsub;1 gOCC for vocal ðGlo Þsub;1 shown in Figure 18(a) 252 H.I Son that the information map makes the state output as t2 if WP_at7 has occurred regardless of the previous string and new state outputs, i.e new high-level events, have to be defined for the low-level event occurred after WP_at7 Let us make the partition for the lowlevel events as (13) before defining the new information map Y < S1 ¼ fWP at1;WP at7;mv Conv1g PfðS10Þsub;1 g ¼ S2 ¼ fmv Conv3g : S3 ¼ ðSlo Þsub;1 À S1 À S2 ð13Þ The physical meaning of the partition P{(Slo)sub,1} is as follows The high-level events, which are defined in Table 2, are partitioned into S1 The controllable events and the uncontrollable events in the other low-level events are partitioned into S2 and S3, respectively The final information map Y is defined in Table according to this partition New high-level events t6 * t17 only represent whether the controllable event, which occurred in the low-level plant, has transferred into the high-level plant And those events are partitioned according to the state of fðGlo Þvocal sub;1 gOCC after the occurrence of the lowlevel string The state output is t2 if WP_at7 has occurred at every state as shown in Figure 19 and it becomes t7 if mv_Conv3 has occurred Step 5: The designed high-level plant Ghi ¼ Y½fðGlo Þvocal g Š has 14 states and 78 sub;1 SOCC transitions Step 6–0: The control data of K0hi;1 with respect to Ghi disables the uncontrollable event tuc,1 Tuc,1 which is not defined at each state This means that K0hi;1 does not satisfy the controllability because it disables t2 and t1 at the state and 3, respectively Therefore, let us redesign the high-level legal language Table Additional information map to satisfy the condition for OCC Low-level sequence t ¼ Y(s) mv_Conv3 WP_at1 mv_Conv3 WP_at7 t4 t5 as K1hi;1 by adding the self-loop of these events at all states Step 6–1: The control data of K1hi;1 satisfies the controllability because it disables the controllable event t3 at the state Step 7: K1hi;1 is non-blocking as shown in Figure 19 Step 8: K1hi;1 is non-conflicting with Ghi because K1hi;1 satisfies Lm ðGhi Þ ^ Lm ðK1hi;1 Þ ¼ LðGhi Þ ^ LðK1hi;1 Þ therefore, the high-level supervisor is designed as S0hi;1 ¼ K1hi;1 Ghi ^ K1hi;1 has 52 states and 287 transitions and S0 hi,1 has states and 59 transitions Step 9: The automaton of the supremal controllable sub-language of K1hi;1 has 52 states and 287 transitions with respect to Ghi This automaton is the solution of the SCP, Shi,1 Step 10: Finally, S0 hi,1, is the solution of the SCP with respect to ðK1hi;1 ; Ghi Þ which has less states and transitions than Shi,1 because it satisfies L(S0 hi,1 Ghi) ¼ L(Shi,1) The designed high-level supervisor S0 hi,1 makes the state transition only for the high-level events t1 and t2 And it disables mv_Conv1 at the states while it enables mv_Conv1 at the states 0, 1, and Therefore, only high-level events defined in Table have meaning Implementation 5.1 CMSSM transform In this article, the designed modular supervisors are transformed into the CMSSM for implementation purposes The CMSSM is a machine which has specific outputs for the current state, the input, and the clock (Wakerley 1990) The supervisor, which is transformed into the CMSSM, can be implemented as the PLC or the digital circuit (Brandin 1994) The CMSSM of the AGV collision avoidance supervisor for section is shown in Figure 20 In Figure 20, D0 * D2 represents the state of the CMSSM and mv_AGV1 and mv_AGV2 are the outputs of each state And the state output is operated as the edge trigger for the current input High-level event Controllable WP_at1 Controllable WP_at7 Table Additional information map to satisfy the condition for SOCC Low-level sequence t ¼ Y(s) High-level event s1s2 t7, t9, t11, t13, t15, t17 s1s2s3 t6, t8, t10, t12, t14, t16 Controllable event occur in G10 Uncontrollable event occur in G10 Figure 19 figure 18 vocal fðGlo Þvocal sub;1 gSOCC for fðGlo Þsub;1 gOCC shown in International Journal of Computer Integrated Manufacturing Figure 20 253 CMSSM of AGV collision avoidance supervisor for section CMSSM of the buffer size supervisor in the conveyor belt is shown in (14), (15), (16), (17), and (18) D2new ¼ ðD1 ^ D0 ^ AGV1 at17^ $ AGV2 at13Þ _ ðD2^ $ AGV2 at13Þ Figure 21 ð14Þ Event occurrence signal There is an issue which has to be considered when the supervisor is transformed into the CMSSM The event can be recognised into more than one event if the event occurrence time is longer than the CMSSM clock An example of this problem is as follows If WP_at1 has occurred at the initial state then the state will be state and it will go to the state after the additional occurrence of WP_at1 in the buffer size supervisor for the conveyor belt shown in Figure 11(a) However, if the event occurrence time of WP_at1 is longer than one clock of the CMSSM as shown in Figure 21, the CMSSM will recognise this event as several occurrences of WP_at1 As a result, the initial state will go to state even only one WP_at1 has occurred Therefore, the event which can make state transition continuously has to be differentiated when the supervisor is transformed into the CMSSM In the case of this example, the CMSSM has to be designed by differencing WP_at1 occurring at the initial state with WP_at1 occurring at the state In the CMSSM of the buffer size supervisor, the latter case of WP_at1 is redefined as WP_at1 as shown in Figure 22 Also, this means that the additional sensor for the new event WP_at1 is needed for the implementation The logic is designed for the inputs and the outputs of the CMSSM (Wakerley 1990) In the case of the CMSSM shown in Figure 22, the sensor signals WP_at1, WP_at10 , WP_at3, and WP_at30 are the inputs and the control signal for the conveyor belt mv_Conv1 is the output Finally, the logic for the D1new ¼ ð$ D1 ^ D0 ^ AGV2 at17^ $ AGV1 at13Þ _ ðD1^ $ D0^ $ AGV1 at13Þ Á Á Á ^ ð$ D2^ $ D1^ $ D0 ^ AGV2 at12Þ _ ðD1 ^ D0^ $ AGV1 at17^ $ AGV2 at13Þ ð15Þ D0new ¼ fð$ D2^ $ D1^ $ D0Þ ^ ðAGV1 at14_ $ AGV2 at12Þg Á Á Á _ ð$ D1 ^ D0^ $ AGV2 at17 ^ $ AGV1 at13Þ _ ðD1 ^ D0^ ð16Þ $ AGV1 at17^ $ AGV2 at13Þ mv AGV1 ¼$ D2 ð17Þ mv AGV2 ¼$ D1 _ D0 ð18Þ 5.2 Simulation The designed CMSSMs are verified using the circuit design and analysis software PSpice In simulation, the outputs are tested with the arbitrary input to the CMSSM All designed supervisors are simulated and the simulation result of the AGV collision avoidance supervisor for the section is shown in Figure 23 In Figure 23, AGV1_at12, AGV2_at12, AGV1_at13, AGV2_at13, AGV1_at17, and AGV2_at17 are the sensor signals which are used as the input and 254 Figure 22 H.I Son CMSSM of buffer size supervisor for conveyor belt Figure 23 Simulation result for AGV collision avoidance supervisor for section Figure 25 Experimental AGV collision avoidance system AGV1_at13 has occurred, the state goes back to and AGV2 will be enabled again This means that if a certain AGV enters the section and also if the other AGV enters the section before the previous AGV leaves the section, the supervisor will disable the latter AGV until the previous supervisor leaves the section We can see the same control action when the AGV2 enters the section at first, i.e when AGV2_at12 has occurred at the state in Figure 23 Figure 24 system Block diagram of AGV collision avoidance the output signals are AGV1 and AGV2 which are the control signals of the AGVs And D0, D1, and D2 are the states of the CMSSM Let us analyse the simulation result shown in Figure 23 In the beginning, all states are The state does not change even after the occurrence of AGV1_at17 because AGV1_at17 is the self-loop event at the initial state And then D0 becomes due to the occurrence of AGV1_at12 At the same time, if AGV2_at17 has occurred, D1 becomes while D0 becomes Therefore, the state of the CMSSM becomes and AGV2 is disabled If 5.3 Implementation The AGV collision avoidance supervisors for all sections are implemented and experimented as shown in Figure 24 These supervisors control the AGVs as follows The sensors located in the AGV lane will detect the AGV and and then these signals will be transmitted to the collision avoidance supervisors Each supervisor will output the control signal to the motor driver of the AGVs using the embedded logical circuits with the transmitted sensor signal The implemented AGV collision avoidance system is shown in Figure 25 The implanted collision avoidance supervisors are operated in an exactly similar manner as that of the simulation result Conclusion In this article, the decentralised supervisory control scheme is presented for large complex systems which International Journal of Computer Integrated Manufacturing are modelled as DESs The proposed decentralised control scheme is divided into the modular supervisory control and the high-level supervisory control The generalised solution for the modular SCP is presented with the concept of the sub-plant to reduce the computational complexity and it is also proved theoretically The modular supervisors, designed using the proposed solution, are the maximum permissible and controllable sub-language of the given legal languages with respect to the plant to be controlled For the high-level SCP, the generalised solution is also presented and then proved, which guarantees the hierarchical consistency The high-level supervisors are also the maximum permissible and controllable sub-language of the given high-level legal languages with respect to the high-level plant designed using the proposed Theorem The proposed decentralised control scheme is applied for the control of the experimental miniature CIM system The miniature CIM system is modelled as 31 automata The first eight and next six modular supervisors are designed using the proposed modular SCP solution procedure with respect to the legal languages for the production line and the AGV control respectively In addition, one high-level supervisor, which has 52 states and 287 transitions, is designed using the highlevel SCP solution procedure proposed in Theorem to control the buffer size of all conveyor belts The designed decentralised supervisors are transformed into the CMSSM in order to apply and verify the proposed control scheme for real-world problems The control logic is designed based on the transformed CMSSM and this logic is implemented and embedded 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