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Framework for Simulation-based Performance Assessment and Resilience Improvement
IFAC Conference on Manufacturing Modelling, IFAC Manufacturing Management and on Control IFAC Conference Conference on Manufacturing Modelling, Modelling, IFAC Conference on Manufacturing Modelling, Management and Control Available online at www.sciencedirect.com June 28-30, 2016. Troyes, France Management and Control Management and Control June June 28-30, 28-30, 2016. 2016. Troyes, Troyes, France France June 28-30, 2016. Troyes, France
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Framework for Simulation-based Framework for Simulation-based Framework for Simulation-based Performance Assessment and Resilience Performance Assessment Performance Improvement Assessment and and Resilience Resilience Improvement Improvement Moritz Schattka, Alena Puchkova, Duncan McFarlane Moritz Schattka, Alena Puchkova, Duncan McFarlane Moritz Moritz Schattka, Schattka, Alena Alena Puchkova, Puchkova, Duncan Duncan McFarlane McFarlane Institute for Manufacturing, Cambridge, CB3 0FS United Kingdom Institute Manufacturing, 0FS Institute for for(e-mails: Manufacturing, Cambridge, CB3 0FS United United Kingdom Kingdom mms61,Cambridge, ap823, dcmCB3 @cam.ac.uk) Institute for Manufacturing, Cambridge, CB3 0FS United Kingdom (e-mails: mms61, ap823, dcm @cam.ac.uk) (e-mails: mms61, ap823, dcm @cam.ac.uk) (e-mails: mms61, ap823, dcm @cam.ac.uk) Abstract: This paper presents a framework to assess and improve the resilience of a production Abstract: This paper presents framework to assess and improve the resilience of a production Abstract: This framework to and the of system by identifying the idealaa between disruption mitigation and associated cost. Abstract: This paper paper presents presents a trade-off framework to assess assess and improve improve the resilience resilience of aa production production system by identifying the ideal trade-off between disruption mitigation and associated cost. system by identifying the ideal trade-off between disruption mitigation and associated Through its modular structure, the developed framework is able to generate a simulation for an system by identifying the ideal trade-off between disruption mitigation and associated cost. cost. Through modular developed is simulation for Through its its modular structure, structure, the developed framework framework is able able to to generate generate simulationparallel for an an arbitrary production line, with the all disruption relevant properties. Based onaaarepeated, Through its modular structure, the developed framework is able to generate simulation for an arbitrary with relevant Based on parallel arbitrary production line, with all all disruption relevant properties. properties. Based on repeated, repeated, parallel runs of theproduction simulationline, generated, thedisruption overall economically efficient level of disruption mitigation arbitrary production line, with all disruption relevant properties. Based on repeated, parallel runs of the simulation generated, the overall economically efficient level of disruption mitigation runs of simulation generated, the overall economically efficient of mitigation can identified. In this first stage the research this concerns the locations for buffers and runsbe of the the simulation generated, the of overall economically efficient level level of disruption disruption mitigation can be identified. In this first stage of the research this concerns the locations for buffers and can be identified. In this first stage of the research this concerns the locations for buffers their respective sizes. The ability to identify such optimal level of resilience may allow companies can be identified. In this first stage of the research this concerns the locations for buffers and and their respective The ability to such level may allow companies their respective sizes. The ability to identify identify such optimal level of of resilience resilience may into allowaccount companies to alleviate the sizes. impact that disruptions have on optimal their operations while taking the their respective sizes. The ability to identify such optimal level of resilience may allow companies to the that have to alleviate alleviate the impact impact of that disruptions have on on their their operations operations while while taking taking into into account account the the economic effectiveness thedisruptions measures taken. to alleviate the impact that disruptions have on their operations while taking into account the economic effectiveness of the measures taken. economic effectiveness of the measures taken. economic effectiveness of the measures taken. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: resilience, production system, disruption, simulation, genetic algorithm Keywords: resilience, production system, disruption, simulation, genetic algorithm Keywords: Keywords: resilience, resilience, production production system, system, disruption, disruption, simulation, simulation, genetic genetic algorithm algorithm 1. INTRODUCTION resilience improvements that are more directly transferable 1. INTRODUCTION resilience improvements that are more directly transferable 1. resilience improvements that into industrial application. 1. INTRODUCTION INTRODUCTION resilience improvements that are are more more directly directly transferable transferable into industrial application. into industrial application. into industrial application. In this paper a method to assess the performance of a When production systems break down, companies are un- In this paper aa method to assess the and performance aa In to assess of production system in face of to identifyof When production systems break down, companies are unIn this this paper paper a method method to disruptions assess the the performance performance ofthe a When production systems break down, companies are under distress. Every minute a line is at a hold, businesses When production systems break down, companies are un- production system in face of disruptions and to identify the production system in face of disruptions and to identify the overall effective level of resilience for a production system der distress. Every minute aa line is at aa hold, businesses production system in face of disruptions and to identify the der distress. Every minute line is at hold, businesses miss out on revenue and particularly when margins are der distress. Every minute a line is at a hold, businesses overall effective of resilience for a production system overall effective level of for system is presented. A level framework is introduced, consisting of a miss out on revenue and particularly margins are overall effective level of resilience resilience for aa production production system miss out and when margins are thin, a production line running when can decide on winmiss keeping out on on revenue revenue and particularly particularly when margins are is presented. A framework is introduced, consisting of is presented. A framework is introduced, consisting of stochastic simulation and an optimisation method. Outaaa thin, keeping a production line running can decide on winis presented. A framework is introduced, consisting thin, keeping aa production line can decide ning loosing in competition. However, break-downs are stochastic simulation and an optimisation method. of thin, or keeping production line running running can decide on on winwinOut stochastic simulation and an optimisation method. Out of a structured description of any arbitrary production ning or loosing in competition. However, break-downs are stochastic simulation and an optimisation method. Out ning or in However, are aning common occurrence in production linesbreak-downs and the causes or loosing loosing in competition. competition. However, break-downs are of a structured description any arbitrary production of structured description of arbitrary production line framework generatesof detailed simulation of it. aaarecommon occurrence in production lines and the causes of aa the structured description ofa any any arbitrary production common occurrence in production lines and the causes often enough minor. Machines fail, suppliers do not a common occurrence in production lines and the causes line the framework generates a detailed simulation of it. line the framework generates a detailed simulation of it. This simulation represents the production line in all releare often enough minor. Machines fail, suppliers do not line the framework generates a detailed simulation of it. are enough minor. fail, suppliers do deliver or quality are not With increasare often often enough specifications minor. Machines Machines fail,met. suppliers do not not This simulation represents the production line in all releThis simulation represents the production line in all relevant properties and incorporates disruptions as stochastic deliver or quality specifications are not met. With increasThis simulation represents the production line in all reledeliver or specifications are With increasingly production systems andmet. external delivercomplex or quality quality specifications are not not met. Withpartners increas- vant properties and incorporates disruptions stochastic vant and disruptions as influences. A genetic algorithm was selectedas perform ingly complex production systems and external partners vant properties properties and incorporates incorporates disruptions astostochastic stochastic ingly production systems external partners closely integrated, such disruptions become continuously ingly complex complex production systems and and external partners influences. A genetic algorithm was selected to perform influences. A genetic algorithm was selected to perform the optimisation in this work. The algorithm evolves the closely integrated, such disruptions become continuously influences. A genetic algorithm was selected to perform closely such disruptions become harder to predict and through much wider the optimisation in this work. The algorithm evolves closely integrated, integrated, suchpropagate disruptions becomea continuously continuously the the optimisation in this work. The algorithm evolves the most effective configuration of the line through repeated, harder to predict and propagate through a much wider the optimisation in this work. The algorithm evolves the harder to and propagate aa much wider and complex network. result through is a firm’s inability to most effective configuration of the line through repeated, harder to predict predict and The propagate through much wider most effective configuration of the line through repeated, parallel cycles of simulation. This particularly, but not exand complex network. The result is a firm’s inability to most effective configuration of the line through repeated, and complex network. The result is a firm’s inability to meet delivery network. dates. and complex The result is a firm’s inability to parallel cycles of simulation. This not exparallel cycles of simulation. This particularly, but not exclusively, concerns the optimal sizeparticularly, and locationbut of buffers. meet delivery dates. parallel cycles of simulation. This particularly, but not exmeet delivery dates. meet delivery dates. the ability to withstand such disrup- clusively, concerns the optimal size and location of buffers. ’Resilience’ describes clusively, concerns the optimal size and location of buffers. clusively, concerns the optimal size and location of buffers. To provide an optimisation for any production line and ’Resilience’ describes the ability to withstand such disrup’Resilience’ describes the to such tion and operate smoothly in a volatile environment (Hu, ’Resilience’ describes the ability ability to withstand withstand such disrupdisrupprovide optimisation any production line and To an optimisation for any production and industry, thean simulation has afor generic is based tion and operate smoothly in aa isvolatile environment (Hu, To To provide provide an optimisation for any structure. productionItline line and tion and operate smoothly in volatile environment 2013). A high level of resilience traditionally established tion and operate smoothly in a volatile environment (Hu, (Hu, industry, the simulation has a generic structure. It is based industry, the simulation has a generic structure. It is based on modular components which are composed according to 2013). A high level of resilience is traditionally established industry, the simulation has a generic structure. It is based 2013). high of traditionally through increased levelsis stock. Withestablished the broad on modular components which are composed according to 2013). A A keeping high level level of resilience resilience isof traditionally established on modular components which are composed according to a formal description of the production line. This modularthrough keeping increased levels of stock. With the broad on modular components which are composed according to through increased levels of With adaptation of Lean principles, management dis- a formal description of the production line. This modularthrough keeping keeping increased levelssuch of stock. stock. With the theofbroad broad a formal description of the production line. This modularity allows to model and simulate any arbitrary production adaptation of Lean principles, such management of disa formal description of the production line. This modularadaptation of Lean principles, such management of disruptions hasofbecome problematic (Bicheno and Holweg, adaptation Lean principles, such management of dis- ity allows to model and simulate arbitrary production ity to and any arbitrary production line, recreating its behaviour in any all its disruption-related ruptions become problematic and Holweg, ity allows allows to model model and simulate simulate any arbitrary production ruptions has become (Bicheno and Holweg, 2008). Ashas a consequence, the more (Bicheno systematic analysis of line, ruptions has become problematic problematic (Bicheno and Holweg, recreating its behaviour in all its disruption-related line, recreating its behaviour in all its disruption-related properties. Out of the simulation created, artificial be2008). As a consequence, the more systematic analysis of line, recreating its behaviour in all its disruption-related 2008). consequence, the disruption paramount. 2008). As As aabecomes consequence, the more more systematic systematic analysis analysis of of properties. Out of the simulation created, artificial beproperties. Out of the simulation created, artificial behaviour data for the line in different configurations can disruption becomes paramount. properties. Out of the simulation created, artificial bedisruption becomes disruption becomesofparamount. paramount. for the different configurations can The identification an overall effective balance between haviour haviour data for the line in different configurations can then be data gathered andline be in systematically compared. The haviour data for the line in different configurations can The identification an overall effective between be gathered and be systematically compared. The The of overall balance between resilience and costof required, to make balance businesses com- then then be and compared. The data is processed through the genetic algorithm. The identification identification ofis an an overall effective effective balance between then obtained be gathered gathered and be be systematically systematically compared. The resilience and cost is required, to make businesses comdata obtained is processed through the genetic algorithm. resilience is to businesses petitive thecost market place while ensuring their comabil- data obtained is processed the genetic algorithm. Through repeated cycles ofthrough simulation and learning this resilienceinand and cost is required, required, to make make businesses comdata obtained is processed through the genetic algorithm. petitive in the market place while ensuring their abilrepeated of simulation learning this petitive in place while their ity to react to market unexpected (Starr al., Through Through repeated cycles of simulation and learning this algorithm identifiescycles an optimal resilienceand configuration for petitive in the the market placecircumstances while ensuring ensuring theiretabilabilThrough repeated cycles of simulation and learning this ity to react to unexpected circumstances (Starr et al., identifies an optimal resilience configuration for ity to unexpected circumstances (Starr et al., 2003). A great of analytical approaches algorithm identifies an optimal resilience configuration for the production system. This optimisation considers not ity to to react react to number unexpected circumstances (Starr to et imal., algorithm algorithm identifies an optimal resilience configuration for 2003). A great number of analytical approaches to improduction optimisation considers not 2003). A of analytical to prove have been These however re- the the production system. This optimisation considers not just the output, system. but the This overall financial performance of 2003). resilience A great great number number of developed. analytical approaches approaches to imimthe production system. This optimisation considers not prove resilience have been developed. These rethe output, but the overall performance of prove resilience have These however require make substantial abstractions and however simplifying just the output, but the overall financial performance of the line. The algorithm trades offinancial the costs of an action prove to resilience have been been developed. developed. These however re- just just the output, but the overall financial performance of quire to make abstractions and simplifying line. The algorithm trades the costs quire substantial abstractions and assumptions in substantial order to model the production line and the the line. The algorithm increase trades of ofand the identifies costs of of an an action against its performance theaction most quire to to make make substantial abstractions and simplifying simplifying the line. The algorithm trades of the costs of an action assumptions in order to model the production line and its promising performance increase and identifies most assumptions in order to model the line and the disruptions a consequence of this coarse against increase identifies the financially configuration of the line. the assumptions in with order it. to As model the production production line and against against its its performance performance increase and and identifies the most most the disruptions with it. As a consequence of this coarse financially promising configuration of the line. the with it. consequence coarse representation, the results promising configuration of the line. the disruptions disruptions the withindustrial it. As As aa applicability consequence of of this this coarse financially financially promising configuration of the line. This paper is structured as follows: Section 2 reviews representation, the industrial applicability of thethe results representation, the applicability of the methods find limited. This work explores pos- This representation, theis industrial industrial applicability of the the results results paper ismethods structured as follows:mitigation Section 22discussed reviews This paper as the of disruption the methods find is limited. This work explores the posThisdifferent paper is is structured structured as follows: follows: Section Section 2 reviews reviews the methods find is limited. This work explores the possibilities to overcome such abstraction in order to find the methods find is limited. This work explores the pos- the different methods of disruption mitigation discussed the different methods of disruption mitigation discussed sibilities to overcome such abstraction in order to find the different methods of disruption mitigation discussed sibilities to overcome such abstraction in order to find sibilities to overcome such abstraction in order to find Copyright 2016 IFAC 289 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 289 Peer review© of International Federation of Automatic Copyright © 2016 IFAC 289 Copyright ©under 2016 responsibility IFAC 289Control. 10.1016/j.ifacol.2016.07.619
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in literature. In Section 3 the simulation is introduced that is used to evaluate the resilience of a particular production system. Section 4 describes the optimization of the production system’s configuration in order for it to be resilient. In Section 5 an example of a production system is given and the application of the optimization framework is presented. Section 6 concludes this paper. 2. REVIEW OF PRODUCTION DISRUPTION MITIGATION APPROACHES The literature on disruption mitigation was found to be clustered in four chronological categories. The first category is the paradigms on which the production system is founded, the later three categories sort strategies by whether they are executed before, during or after a disruption occurs (figure 1).
Fig. 1. Types of disruption mitigation strategies ’Paradigms’ describe a system’s inherent reactivity to change. Holonic Manufacturing System’s (HMS) approach of self-reliant, reconfigurable units has been researched by Covanich and McFarlane (2009) and Bal and Hashemipour (2009). ’Ex-ante’ strategies are strategies implemented preventively to avoid a negative impact of disruptions. Buffers as a mean to balance these variations have been studied by Giglio and Minciardi (2008), Battini et al. (2009), Puchkova et al. (2015), Tezcan and Gosavi (2001), Shi and Gershwin (2014), Demir et al. (2012) and Ouazene et al. (2014). Disruptions through quality defects and their mitigation through integration of inspection stations have been investigated by Galante and Passannanti (2007) and Shiau (2002). Machine break-downs can be reduced through preventive maintenance. Gharbi and Kenne (2000) describe a method to determine the cost-minimal rate of it. ’Ex-Nunc’ strategies aim at recovering from disruptions. Once the disruption has had an impact on the line they try to re-balance the line and avoid the disruption propagating further downstream through the production network. Koren and Shpitalni (2010), Yamada (2006) and Bruccoleri et al. (2003, 2006) explored disruption mitigation through re-configuration of the production system. The importance of leveled schedules as a mean to remove instability from a line (Muri and Mura) where stressed by Schonberger (1982). McMullen and Tarasewich (2005) have introduced Mixed Model Scheduling as a method of balancing the production schedule. Balanced schedules depend on the right combination of jobs and resources. Re-scheduling of resources has been researched by Kohl et al. (2007), Clausen et al. (2001), Darmoul et al. (2013) and Yang et al. (2005) based on findings from the airline industry. 290
The optimal sequence of jobs to enter a production line has recently been considered by Tamura et al. (2011) and Akg¨ und¨ uz and Tunal (2010). Although their work is concerned with solving scheduling problems ex-ante, they provide the necessary groundwork for developing reactive on-line scheduling methods. ’Ex-Post’ strategies allow to learn from previous disruptions and make sure such disruptions can be avoided in the future. Ex-post therefore represents a feedback cycle to Ex-ante. Simchi-Levi et al. (2014) have introduced a paradigm of systematically hardening the most vulnerable spots in a supply chain. In an equivalent way this idea can be applied to hardening resources and links within a production system. Another important step in ex-post mitigation is the collection of data to accurately determine the characteristics of the production line (e.g. MTBF) and feed them back into the other strategies. Most of the research in the field, including Yang et al. (2005), Shiau (2002), Hu (2013) and Puchkova et al. (2015), applies mathematical methods that are closedform solutions. They allow for a very accurate solving, however, they require a drastically abstracted and simplified representation of the production line in order for the method to be applied. As a result they optimize quite coarse representations of reality. The approach in this work deliberately chooses a different trade-off. It prioritizes accuracy of modelling over accuracy and simplicity of solving. The discrete simulation allows to model a production line in great detail. Detailed simulations of production systems, see, for example, Battini et al. (2009), Tezcan and Gosavi (2001), McNamara et al. (2013), are used frequently in industry, however they are used to test only a number of pre-selected configurations and identify weaknesses. This work in contrast runs a very high number of different configurations. It uses the results to systematically improve the configuration and iterate further. Another weakness of simulation is often structurally inherent. Most simulations are designed in an integrated fashion, which does not allow for the configuration of the line itself to be a variable. This work in contrast structures the simulation into distinct modules, to allow for the comparison of different configurations. Also, the modularity allows to separate the code development from the application of the software, which allows for the use in highly confidential systems. The identification of the optimal solution through repeated cycles of details simulation is significantly slower and potentially less accurate than solving problems in the closed-form solutions. The motivation for this deviating approach is, that it reduces abstraction to a minimum. It allows for a significantly better representation of reality, to a degree, where an actual transferability into industrial use is plausible. For the optimization the speed of finding solutions is prioritized to the optimality of the solution. Therefore, good solutions to a very detailed problem can be found in feasible time. The optimization over large simulations is very complex, but the use of a fuzzy optimization logic accelerates the process of finding good or even near-optimal solutions. This potentially allows to solve problems of industrial scale and hardness in a level
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of detail, that can not be reached through any of the other means in academia. The feasibility of the trade-off this work picked is very much a consequence of recent technological developments. While the kind of approach used to make problems unsolvable once they got to an industry-scale, the situation has changed. The availability and price of large scale parallel computing capabilities through cloud infrastructure enable this approach. In the initial stage of development of the framework, that is presented in this paper, this work focuses on finding ideal locations and sizes for buffers (ex-ante). As the genetic algorithm learns from iterations, the framework also represents certain characteristics associated with expost mitigation. 3. APPROACH TO SIMULATION OF PRODUCTION DISRUPTIONS 3.1 Production Simulation Approach The implementation of disruption mitigation strategies in the simulated production line requires the simulation setup to be re-configurable. Since in an industrial application the simulation potentially contains a large amount of confidential data, it is required that the code-development and the actual data it runs on are separated from each other. Only this way can the software be applied in different companies without having to change the source code. This work’s algorithmic implementation of the simulation is based on biological stem-cells. Stem-Cells are basic, undeveloped cells, that can be turned into any kind of body cell (e.g. muscle-, blood-, brain-cell) through a process called specialisation (Mitalipov and Wolf, 2009). Accordingly in this work’s simulation, the code of the simulation is contained in one generic, self-sufficient element. This element is able to resemble the behaviour of any cell-type in the production (e.g. production-cells, buffer-cells) and can be connected to other specialised copies of the stemcell. This way, the whole production line can be based on just a single object of programmed code. A construction code then creates, specialises and connects the required numbers of cells according to a adjacency matrix. Compared to a totally integrated simulation code this has three major advantages: (1) The information of the production’s layout is isolated from the code development, which allows companies to use the software without having to share confidential data. (2) The simulation can continuously be reconfigured, whether to experiment with different layouts or to assess different production lines. (3) The modularity allows the algorithm to only create a simulation for part of the tree and then solve the large problem through optimization of less complex sub-trees (Divide & Conquer). These algorithmic properties are reached through ObjectOriented Programming.
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processes. Common Causes is the description of a variation created by a great number of individual factors influencing the value measured. Each of these factors has an independent statistical distribution and aggregated, they can be described by one distribution. They can be considered the noise e.g. the deviation of a product specification from its norm. Special Causes are variations that can be directly assigned to factors, such as single machines or processes. Based on this theorem, the simulation considers two types of defects to a product. Random Defects: A random defect is a Common Cause. It is assumed it can be detected from a certain point on in the production line, but is not causally related to any particular entity (e.g. poor machine calibration) within it. Defects occur randomly based on a set probability. The probability is constant and independent of the last time a defect occurred (memorylessness). The defect creation is therefore described as a repeated Bernoulli-experiment in the simulation. Its occurrence therefore follows a geometric distribution. Systematic Defects: These Special Causes occur, when e.g. a machine is out of calibration or its components degrade. These defects therefore occur in clusters. Their occurrence is correlated to the frequency of maintenance. Subjects to these defects are either products or machines. Product defects do not stop production and can be detected at inspection stations. Defect products detected at an inspection station will be scraped. Machine breakdowns occur randomly and behave according to the two parameters Mean-Time-Between-Failures (MTBF) and Mean-Timeto-Repair (MTTR). MTBF and MTTR are modelled as stochastic processes based on Bernoulli-experiments and are therefore the sum of the products of a geometric distribution’s value pair. 4. OPTIMIZATION The framework tries to identify a good balance between resilience of the production and the cost required to establish it. An illustration for such optimization is given in figure 2. The figure shows the impact the size of a buffer has to the total cost. It illustrates the impact of the different sizes a particular buffer in a production line can have. The buffer is assumed to have a fix-cost and a constant variable-cost for the number of spaces available. The larger the buffer is, the larger the variations in the production line it can mitigate. The down-time of a production line is described by a cost (e.g. lost revenue). The larger the buffer is, the less down-time will occur and thus the cost for down-time decreases. However, the marginal utility of a buffer decreases with its size. Therefore, a point exists at which the sum of the buffercost and the down-time cost is minimal. This point is referred to as the optimum. Alternatively, the optimum can be described as the point, where the marginal buffercost equals the marginal down-time cost. This point the framework is trying to identify.
3.2 Disruption Simulation Approach 4.1 Problem Definition According to Shewhart and Deming (1939), who developed the foundations of what is later known as Statistical Process Control (SPC), there is two sources of variation in 291
Finding the optimal configuration for the production line can be described as a non-linear integer-programming
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4.3 Procedure
Fig. 2. Example: Cost curve for variable buffer sizes problem, where e.g. buffer-sizes are the variables. The function value is discontinuous between the values zero and one, for many of the input variables. For example, the cost incurred by the size of a buffer, lets the function value be discontinuous between zero and one because there is a fixed-cost for buffers. Another example is the defects an inspection station can detect, which only have binary values. This discontinuity makes the problem have properties of a 0-1 integer-programming problem, which severely affects the complexity of the problem. The optimisation problem is a multi-dimensional, nonlinear discrete function with multiple local optima and potentially more than one global optimum. Therefore the optimisation algorithm needs to be (1) applicable to nondifferentiable functions (2) and capable of finding global optima, which excludes direct application of gradientdescent methods. (3) The algorithm needs to be sensitive to changes of the target function in the interval zero to one. (4) the optimisation algorithm has to find solutions with a small number of function evaluations, to reduce the computational effort. 4.2 Genetic Algorithm
The first step of the optimisation is the definition of an initial configuration of the variables that are being optimised. For existing production lines the current parameters can be used. If either the production line does not yet exist or there is plausible doubt on the effectiveness of the existing configuration, ways to artificially create an initial configuration exist. The optimisation can be warm-started through one of the algorithms that describe the problem as a closed-form problem, as discussed in the literature review or be approximated through analytical methods determining the configuration for a balanced line under the assumption of regular and recurring disruption. The use of these warm-start methods relies on the assumption that the higher degree of abstraction they rely on changes the optimal result just gradually, compared to the less abstracted simulation model. If this assumption holds to be true, computational effort can be drastically reduced, compared to a random start-configuration. In the second step the optimisation algorithm defines a set of values for the variables, evaluates the target function and derives a set of values for the next iteration. In this work, each evaluation of the target function means running the simulation with the respective values as parameters. The result of the target function then is based on a costfunction. Finally, results of the optimisation can be tested for sensitivity through a Monte Carlo simulation. This is a very valuable test, since it can determine how strongly a modelling error would affect the optimality of the result. If a simulation shows very high sensitivity to the respective variable around the point of the optimum, a slight inaccuracy in the parameter definition would render the simulation results useless. If however the sensitivity is low, the simulation results are reliable and robust to inaccuracies in the modelling process or measuring errors on the exogenous variables. 5. ILLUSTRATIVE EXAMPLE
A genetic algorithm was selected to perform the optimisation in this work, since it is robust to remote optima and can be configured to efficiently handle 0-1 integer variables. Another advantage is that it can easily be warm-started, if an approximate value and an expected variance are known, which is advantageous in this work, since algorithms of this type are available. Genetic algorithms can be executed in a highly parallel fashion, which accelerates the computation. Also, genetic algorithms are considered efficient at solving problems with a complex fitness landscape. Their combinatoric evolution make them capable of moving away from local optima, which gradient methods tend to converge towards. The algorithm starts from an initial population of sets of variables (’individuals’). It inputs each of these sets into the function and determines their respective function value (fitness). The best sets of values (individuals) are then identified (selection) and crossovers of them are generated. Additionally, random mutations occur to some of the new generations of individuals. The algorithm keeps producing generations until a defined termination-condition is met. 292
In this section the proposed framework is illustrated on an arbitrary production system of industrial scale. 5.1 Simulation Development
Fig. 3. Example Tree: 23 production nodes and 23 potential buffer locations Figure 3 shows a random tree representing a production line. It contains 23 production cells (squares). In order
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to identify both, the best location for buffers and their respective optimal size, there a 23 nodes in the network (circles) representing potential positions for buffers in the production line. If the result of the optimisation equals zero for one of the buffers, this then means, that in a production line no buffer should be placed in that position. Of the 23 buffer nodes 11 are known to have an optimal size of zero. These are the buffers in the first level. Since in this example all disruptions originate from break-downs of production cells, rather than from external influences, these buffers have no disruption to mitigate. Although they do not contribute to the resilience of the production, these cells allow to make a judgment on the optimality of the results found by the algorithm. If the genetic algorithm returns a solution where one of these buffers has a size that is not zero, it is proven that the solution found is not optimal. The basis for the optimization is the definition of an objective function. It depicts the overall profit of the production line π (see (1)) and is being maximized in the optimization. For the sake of simplicity in this example, only one type of revenue and two types of cost are considered. Every produced unit is assumed to generate a revenue of α. The number of total output of the production system P (b1 , ..., bn ) is a function of the sizes of the buffers bi for every possible location i. A buffer in a certain location incurs a fixed cost component βf ix and a variable cost component βvar depending on the size of the buffer installed. n (βf ix · max (bi , 1) + βvar · bi ) (1) π = α · P (b1 ...bn ) − i=1
5.2 Solution for Optimal Resilience The optimization problem contained 23 variables. The genetic algorithm was configured to operate in parallel on a population of 48 and evolved this population over 200 cycles until it came to a hold. The development of the function value over the course of the optimization is shown in figure 4. It shows a seemingly convergent trend.
Fig. 4. Function value improvement over the simulation cycles Table 1 shows the three solutions the algorithm has found. Each of the solutions was found to generate the same profit. The 11 nodes (B1-B21) that were know to have an optimal value of zero, returned the value of zero as necessary. The results are promising. The algorithm finds solutions that, with the means available, can not be proven wrong and the function value shows seemingly convergent behaviour during the optimization. These two factors suggest that a good if not near-optimal solution can be found through the algorithm. 293
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Table 1. Best buffer-size configuration found by the genetic algorithm Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
Output Profit
Optimum 1 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 7 0 12 13 16 14 16
Optimum 2 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 7 0 12 13 15 14 16
Optimum 3 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 7 0 12 13 14 14 16
133 110.83
133 110.83
133 110.83
6. CONCLUSION The paper presented a framework that tries to assess the performance of a production system and to improve the resilience through repeated cycles of detailed simulation and the application of a genetic algorithm. The developed framework is able to generate a simulation of the operation of an arbitrary production line in face of disruptions. Compared to the mathematical models in academia this paper shifts the balance towards a high detail in the modelling and a more fuzzy optimisation logic. First results suggest that the genetic algorithm is able to find improved solutions that can alleviate the impact that disruptions have on a production and that an economically efficient level of disruption mitigation can be found. The significant abstraction, that mathematical closed-form analysis imposes can be overcome in favour of the detail and applicability of the results. For industry, the method presented offers a way to harden production system in an overall economically efficient way. In the increasingly complex environment businesses operate in and under the continuous pressure for reduction of resources, such optimisation can mean a competitive advantage. The method presented in this work shows promising results of being applicable in an industrial environment. Future research will have to show whether the abstraction, complexity and computational power will allow for an application on problems of industrial scale and hardness. REFERENCES Akg¨ und¨ uz, O.S. and Tunal, S. (2010). An adaptive genetic algorithm approach for the mixed-model assembly line
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McMullen, P.R. and Tarasewich, P. (2005). A beam search heuristic method for mixed-model scheduling with setups. International Journal of Production Economics, 96(2), 273–283. McNamara, T., Shaaban, S., and Hudson, S. (2013). Simulation of unbalanced buffer allocation in unreliable unpaced production lines. International Journal of Production Research, 51 (6), 1922–1936. Mitalipov, S. and Wolf, D. (2009). Totipotency, pluripotency and nuclear reprogramming. Advances in biochemical engineering/biotechnology, 114, 185–99. Puchkova, A., Srinivasan, R., Mcfarlane, D., and Thorne, A. (2015). Towards Lean and Resilient Production. Proceedings of the 15th IFAC Symposium on Information Control in Manufacturing:2467-2472. Ouazene, Y., Yalaoui, A., Yalaoui, F., and Chehade, H. (2014). Non-linear Programming Method for Buffer Allocation in Unreliable Production Lines. InAnalytical and Stochastic Modeling Techniques and Applications, 80–94. Schonberger, R. (1982). Japanese manufacturing techniques: Nine hidden lessons in simplicity. Shewhart, W. and Deming, W. (1939). Statistical method from the viewpoint of quality control. Courier Corporation. Shi, C. and Gershwin, S.B. (2014). A segmentation approach for solving buffer allocation problems in large production systems. International Journal of Production Research, 1–21. Shiau, Y.R. (2002). Inspection resource assignment in a multistage manufacturing system with an inspection error model. International Journal of Production Research, 40(June 2001), 1787–1806. Simchi-Levi, D., Schmidt, W., and Wei, Y. (2014). From superstorms to factory fires: Managing unpredictable supply-chain disruptions. Harvard Business Review, (JAN-FEB). Starr, R., Newfrock, J., and Delurey, M. (2003). Enterprise resilience: managing risk in the networked economy. Strategy and Business, 70–79. Tamura, T., Okumura, T., Singh Dhakar, T., and Ohno, K. (2011). Optimal production sequencing problem to minimise line stoppage time in a mixed-model assembly line. International Journal of Production Research, 49(14), 4299–4315. Tezcan, T. and Gosavi, A. (2001). Optimal buffer allocation in production lines using an automata search. Proceedings of the 2001 Institute of Industrial Engineering Research Conference. Yamada, Y. (2006). Dynamic reconfiguration of reconfigurable manufacturing systems using particle swarm optimization. In Robotics and Automation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on, 1444–1449. Yang, J., Qi, X., and Yu, G. (2005). Disruption management in production planning. Naval Research Logistics, 52, 420–442.
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Framework for Simulation-based Framework for Simulation-based Framework for Simulation-based Performance Assessment and Resilience Performance Assessment Performance Improvement Assessment and and Resilience Resilience Improvement Improvement Moritz Schattka, Alena Puchkova, Duncan McFarlane Moritz Schattka, Alena Puchkova, Duncan McFarlane Moritz Moritz Schattka, Schattka, Alena Alena Puchkova, Puchkova, Duncan Duncan McFarlane McFarlane Institute for Manufacturing, Cambridge, CB3 0FS United Kingdom Institute Manufacturing, 0FS Institute for for(e-mails: Manufacturing, Cambridge, CB3 0FS United United Kingdom Kingdom mms61,Cambridge, ap823, dcmCB3 @cam.ac.uk) Institute for Manufacturing, Cambridge, CB3 0FS United Kingdom (e-mails: mms61, ap823, dcm @cam.ac.uk) (e-mails: mms61, ap823, dcm @cam.ac.uk) (e-mails: mms61, ap823, dcm @cam.ac.uk) Abstract: This paper presents a framework to assess and improve the resilience of a production Abstract: This paper presents framework to assess and improve the resilience of a production Abstract: This framework to and the of system by identifying the idealaa between disruption mitigation and associated cost. Abstract: This paper paper presents presents a trade-off framework to assess assess and improve improve the resilience resilience of aa production production system by identifying the ideal trade-off between disruption mitigation and associated cost. system by identifying the ideal trade-off between disruption mitigation and associated Through its modular structure, the developed framework is able to generate a simulation for an system by identifying the ideal trade-off between disruption mitigation and associated cost. cost. Through modular developed is simulation for Through its its modular structure, structure, the developed framework framework is able able to to generate generate simulationparallel for an an arbitrary production line, with the all disruption relevant properties. Based onaaarepeated, Through its modular structure, the developed framework is able to generate simulation for an arbitrary with relevant Based on parallel arbitrary production line, with all all disruption relevant properties. properties. Based on repeated, repeated, parallel runs of theproduction simulationline, generated, thedisruption overall economically efficient level of disruption mitigation arbitrary production line, with all disruption relevant properties. Based on repeated, parallel runs of the simulation generated, the overall economically efficient level of disruption mitigation runs of simulation generated, the overall economically efficient of mitigation can identified. In this first stage the research this concerns the locations for buffers and runsbe of the the simulation generated, the of overall economically efficient level level of disruption disruption mitigation can be identified. In this first stage of the research this concerns the locations for buffers and can be identified. In this first stage of the research this concerns the locations for buffers their respective sizes. The ability to identify such optimal level of resilience may allow companies can be identified. In this first stage of the research this concerns the locations for buffers and and their respective The ability to such level may allow companies their respective sizes. The ability to identify identify such optimal level of of resilience resilience may into allowaccount companies to alleviate the sizes. impact that disruptions have on optimal their operations while taking the their respective sizes. The ability to identify such optimal level of resilience may allow companies to the that have to alleviate alleviate the impact impact of that disruptions have on on their their operations operations while while taking taking into into account account the the economic effectiveness thedisruptions measures taken. to alleviate the impact that disruptions have on their operations while taking into account the economic effectiveness of the measures taken. economic effectiveness of the measures taken. economic effectiveness of the measures taken. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: resilience, production system, disruption, simulation, genetic algorithm Keywords: resilience, production system, disruption, simulation, genetic algorithm Keywords: Keywords: resilience, resilience, production production system, system, disruption, disruption, simulation, simulation, genetic genetic algorithm algorithm 1. INTRODUCTION resilience improvements that are more directly transferable 1. INTRODUCTION resilience improvements that are more directly transferable 1. resilience improvements that into industrial application. 1. INTRODUCTION INTRODUCTION resilience improvements that are are more more directly directly transferable transferable into industrial application. into industrial application. into industrial application. In this paper a method to assess the performance of a When production systems break down, companies are un- In this paper aa method to assess the and performance aa In to assess of production system in face of to identifyof When production systems break down, companies are unIn this this paper paper a method method to disruptions assess the the performance performance ofthe a When production systems break down, companies are under distress. Every minute a line is at a hold, businesses When production systems break down, companies are un- production system in face of disruptions and to identify the production system in face of disruptions and to identify the overall effective level of resilience for a production system der distress. Every minute aa line is at aa hold, businesses production system in face of disruptions and to identify the der distress. Every minute line is at hold, businesses miss out on revenue and particularly when margins are der distress. Every minute a line is at a hold, businesses overall effective of resilience for a production system overall effective level of for system is presented. A level framework is introduced, consisting of a miss out on revenue and particularly margins are overall effective level of resilience resilience for aa production production system miss out and when margins are thin, a production line running when can decide on winmiss keeping out on on revenue revenue and particularly particularly when margins are is presented. A framework is introduced, consisting of is presented. A framework is introduced, consisting of stochastic simulation and an optimisation method. Outaaa thin, keeping a production line running can decide on winis presented. A framework is introduced, consisting thin, keeping aa production line can decide ning loosing in competition. However, break-downs are stochastic simulation and an optimisation method. of thin, or keeping production line running running can decide on on winwinOut stochastic simulation and an optimisation method. Out of a structured description of any arbitrary production ning or loosing in competition. However, break-downs are stochastic simulation and an optimisation method. Out ning or in However, are aning common occurrence in production linesbreak-downs and the causes or loosing loosing in competition. competition. However, break-downs are of a structured description any arbitrary production of structured description of arbitrary production line framework generatesof detailed simulation of it. aaarecommon occurrence in production lines and the causes of aa the structured description ofa any any arbitrary production common occurrence in production lines and the causes often enough minor. Machines fail, suppliers do not a common occurrence in production lines and the causes line the framework generates a detailed simulation of it. line the framework generates a detailed simulation of it. This simulation represents the production line in all releare often enough minor. Machines fail, suppliers do not line the framework generates a detailed simulation of it. are enough minor. fail, suppliers do deliver or quality are not With increasare often often enough specifications minor. Machines Machines fail,met. suppliers do not not This simulation represents the production line in all releThis simulation represents the production line in all relevant properties and incorporates disruptions as stochastic deliver or quality specifications are not met. With increasThis simulation represents the production line in all reledeliver or specifications are With increasingly production systems andmet. external delivercomplex or quality quality specifications are not not met. Withpartners increas- vant properties and incorporates disruptions stochastic vant and disruptions as influences. A genetic algorithm was selectedas perform ingly complex production systems and external partners vant properties properties and incorporates incorporates disruptions astostochastic stochastic ingly production systems external partners closely integrated, such disruptions become continuously ingly complex complex production systems and and external partners influences. A genetic algorithm was selected to perform influences. A genetic algorithm was selected to perform the optimisation in this work. The algorithm evolves the closely integrated, such disruptions become continuously influences. A genetic algorithm was selected to perform closely such disruptions become harder to predict and through much wider the optimisation in this work. The algorithm evolves closely integrated, integrated, suchpropagate disruptions becomea continuously continuously the the optimisation in this work. The algorithm evolves the most effective configuration of the line through repeated, harder to predict and propagate through a much wider the optimisation in this work. The algorithm evolves the harder to and propagate aa much wider and complex network. result through is a firm’s inability to most effective configuration of the line through repeated, harder to predict predict and The propagate through much wider most effective configuration of the line through repeated, parallel cycles of simulation. This particularly, but not exand complex network. The result is a firm’s inability to most effective configuration of the line through repeated, and complex network. The result is a firm’s inability to meet delivery network. dates. and complex The result is a firm’s inability to parallel cycles of simulation. This not exparallel cycles of simulation. This particularly, but not exclusively, concerns the optimal sizeparticularly, and locationbut of buffers. meet delivery dates. parallel cycles of simulation. This particularly, but not exmeet delivery dates. meet delivery dates. the ability to withstand such disrup- clusively, concerns the optimal size and location of buffers. ’Resilience’ describes clusively, concerns the optimal size and location of buffers. clusively, concerns the optimal size and location of buffers. To provide an optimisation for any production line and ’Resilience’ describes the ability to withstand such disrup’Resilience’ describes the to such tion and operate smoothly in a volatile environment (Hu, ’Resilience’ describes the ability ability to withstand withstand such disrupdisrupprovide optimisation any production line and To an optimisation for any production and industry, thean simulation has afor generic is based tion and operate smoothly in aa isvolatile environment (Hu, To To provide provide an optimisation for any structure. productionItline line and tion and operate smoothly in volatile environment 2013). A high level of resilience traditionally established tion and operate smoothly in a volatile environment (Hu, (Hu, industry, the simulation has a generic structure. It is based industry, the simulation has a generic structure. It is based on modular components which are composed according to 2013). A high level of resilience is traditionally established industry, the simulation has a generic structure. It is based 2013). high of traditionally through increased levelsis stock. Withestablished the broad on modular components which are composed according to 2013). A A keeping high level level of resilience resilience isof traditionally established on modular components which are composed according to a formal description of the production line. This modularthrough keeping increased levels of stock. With the broad on modular components which are composed according to through increased levels of With adaptation of Lean principles, management dis- a formal description of the production line. This modularthrough keeping keeping increased levelssuch of stock. stock. With the theofbroad broad a formal description of the production line. This modularity allows to model and simulate any arbitrary production adaptation of Lean principles, such management of disa formal description of the production line. This modularadaptation of Lean principles, such management of disruptions hasofbecome problematic (Bicheno and Holweg, adaptation Lean principles, such management of dis- ity allows to model and simulate arbitrary production ity to and any arbitrary production line, recreating its behaviour in any all its disruption-related ruptions become problematic and Holweg, ity allows allows to model model and simulate simulate any arbitrary production ruptions has become (Bicheno and Holweg, 2008). Ashas a consequence, the more (Bicheno systematic analysis of line, ruptions has become problematic problematic (Bicheno and Holweg, recreating its behaviour in all its disruption-related line, recreating its behaviour in all its disruption-related properties. Out of the simulation created, artificial be2008). As a consequence, the more systematic analysis of line, recreating its behaviour in all its disruption-related 2008). consequence, the disruption paramount. 2008). As As aabecomes consequence, the more more systematic systematic analysis analysis of of properties. Out of the simulation created, artificial beproperties. Out of the simulation created, artificial behaviour data for the line in different configurations can disruption becomes paramount. properties. Out of the simulation created, artificial bedisruption becomes disruption becomesofparamount. paramount. for the different configurations can The identification an overall effective balance between haviour haviour data for the line in different configurations can then be data gathered andline be in systematically compared. The haviour data for the line in different configurations can The identification an overall effective between be gathered and be systematically compared. The The of overall balance between resilience and costof required, to make balance businesses com- then then be and compared. The data is processed through the genetic algorithm. The identification identification ofis an an overall effective effective balance between then obtained be gathered gathered and be be systematically systematically compared. The resilience and cost is required, to make businesses comdata obtained is processed through the genetic algorithm. resilience is to businesses petitive thecost market place while ensuring their comabil- data obtained is processed the genetic algorithm. Through repeated cycles ofthrough simulation and learning this resilienceinand and cost is required, required, to make make businesses comdata obtained is processed through the genetic algorithm. petitive in the market place while ensuring their abilrepeated of simulation learning this petitive in place while their ity to react to market unexpected (Starr al., Through Through repeated cycles of simulation and learning this algorithm identifiescycles an optimal resilienceand configuration for petitive in the the market placecircumstances while ensuring ensuring theiretabilabilThrough repeated cycles of simulation and learning this ity to react to unexpected circumstances (Starr et al., identifies an optimal resilience configuration for ity to unexpected circumstances (Starr et al., 2003). A great of analytical approaches algorithm identifies an optimal resilience configuration for the production system. This optimisation considers not ity to to react react to number unexpected circumstances (Starr to et imal., algorithm algorithm identifies an optimal resilience configuration for 2003). A great number of analytical approaches to improduction optimisation considers not 2003). A of analytical to prove have been These however re- the the production system. This optimisation considers not just the output, system. but the This overall financial performance of 2003). resilience A great great number number of developed. analytical approaches approaches to imimthe production system. This optimisation considers not prove resilience have been developed. These rethe output, but the overall performance of prove resilience have These however require make substantial abstractions and however simplifying just the output, but the overall financial performance of the line. The algorithm trades offinancial the costs of an action prove to resilience have been been developed. developed. These however re- just just the output, but the overall financial performance of quire to make abstractions and simplifying line. The algorithm trades the costs quire substantial abstractions and assumptions in substantial order to model the production line and the the line. The algorithm increase trades of ofand the identifies costs of of an an action against its performance theaction most quire to to make make substantial abstractions and simplifying simplifying the line. The algorithm trades of the costs of an action assumptions in order to model the production line and its promising performance increase and identifies most assumptions in order to model the line and the disruptions a consequence of this coarse against increase identifies the financially configuration of the line. the assumptions in with order it. to As model the production production line and against against its its performance performance increase and and identifies the most most the disruptions with it. As a consequence of this coarse financially promising configuration of the line. the with it. consequence coarse representation, the results promising configuration of the line. the disruptions disruptions the withindustrial it. As As aa applicability consequence of of this this coarse financially financially promising configuration of the line. This paper is structured as follows: Section 2 reviews representation, the industrial applicability of thethe results representation, the applicability of the methods find limited. This work explores pos- This representation, theis industrial industrial applicability of the the results results paper ismethods structured as follows:mitigation Section 22discussed reviews This paper as the of disruption the methods find is limited. This work explores the posThisdifferent paper is is structured structured as follows: follows: Section Section 2 reviews reviews the methods find is limited. This work explores the possibilities to overcome such abstraction in order to find the methods find is limited. This work explores the pos- the different methods of disruption mitigation discussed the different methods of disruption mitigation discussed sibilities to overcome such abstraction in order to find the different methods of disruption mitigation discussed sibilities to overcome such abstraction in order to find sibilities to overcome such abstraction in order to find Copyright 2016 IFAC 289 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 289 Peer review© of International Federation of Automatic Copyright © 2016 IFAC 289 Copyright ©under 2016 responsibility IFAC 289Control. 10.1016/j.ifacol.2016.07.619
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in literature. In Section 3 the simulation is introduced that is used to evaluate the resilience of a particular production system. Section 4 describes the optimization of the production system’s configuration in order for it to be resilient. In Section 5 an example of a production system is given and the application of the optimization framework is presented. Section 6 concludes this paper. 2. REVIEW OF PRODUCTION DISRUPTION MITIGATION APPROACHES The literature on disruption mitigation was found to be clustered in four chronological categories. The first category is the paradigms on which the production system is founded, the later three categories sort strategies by whether they are executed before, during or after a disruption occurs (figure 1).
Fig. 1. Types of disruption mitigation strategies ’Paradigms’ describe a system’s inherent reactivity to change. Holonic Manufacturing System’s (HMS) approach of self-reliant, reconfigurable units has been researched by Covanich and McFarlane (2009) and Bal and Hashemipour (2009). ’Ex-ante’ strategies are strategies implemented preventively to avoid a negative impact of disruptions. Buffers as a mean to balance these variations have been studied by Giglio and Minciardi (2008), Battini et al. (2009), Puchkova et al. (2015), Tezcan and Gosavi (2001), Shi and Gershwin (2014), Demir et al. (2012) and Ouazene et al. (2014). Disruptions through quality defects and their mitigation through integration of inspection stations have been investigated by Galante and Passannanti (2007) and Shiau (2002). Machine break-downs can be reduced through preventive maintenance. Gharbi and Kenne (2000) describe a method to determine the cost-minimal rate of it. ’Ex-Nunc’ strategies aim at recovering from disruptions. Once the disruption has had an impact on the line they try to re-balance the line and avoid the disruption propagating further downstream through the production network. Koren and Shpitalni (2010), Yamada (2006) and Bruccoleri et al. (2003, 2006) explored disruption mitigation through re-configuration of the production system. The importance of leveled schedules as a mean to remove instability from a line (Muri and Mura) where stressed by Schonberger (1982). McMullen and Tarasewich (2005) have introduced Mixed Model Scheduling as a method of balancing the production schedule. Balanced schedules depend on the right combination of jobs and resources. Re-scheduling of resources has been researched by Kohl et al. (2007), Clausen et al. (2001), Darmoul et al. (2013) and Yang et al. (2005) based on findings from the airline industry. 290
The optimal sequence of jobs to enter a production line has recently been considered by Tamura et al. (2011) and Akg¨ und¨ uz and Tunal (2010). Although their work is concerned with solving scheduling problems ex-ante, they provide the necessary groundwork for developing reactive on-line scheduling methods. ’Ex-Post’ strategies allow to learn from previous disruptions and make sure such disruptions can be avoided in the future. Ex-post therefore represents a feedback cycle to Ex-ante. Simchi-Levi et al. (2014) have introduced a paradigm of systematically hardening the most vulnerable spots in a supply chain. In an equivalent way this idea can be applied to hardening resources and links within a production system. Another important step in ex-post mitigation is the collection of data to accurately determine the characteristics of the production line (e.g. MTBF) and feed them back into the other strategies. Most of the research in the field, including Yang et al. (2005), Shiau (2002), Hu (2013) and Puchkova et al. (2015), applies mathematical methods that are closedform solutions. They allow for a very accurate solving, however, they require a drastically abstracted and simplified representation of the production line in order for the method to be applied. As a result they optimize quite coarse representations of reality. The approach in this work deliberately chooses a different trade-off. It prioritizes accuracy of modelling over accuracy and simplicity of solving. The discrete simulation allows to model a production line in great detail. Detailed simulations of production systems, see, for example, Battini et al. (2009), Tezcan and Gosavi (2001), McNamara et al. (2013), are used frequently in industry, however they are used to test only a number of pre-selected configurations and identify weaknesses. This work in contrast runs a very high number of different configurations. It uses the results to systematically improve the configuration and iterate further. Another weakness of simulation is often structurally inherent. Most simulations are designed in an integrated fashion, which does not allow for the configuration of the line itself to be a variable. This work in contrast structures the simulation into distinct modules, to allow for the comparison of different configurations. Also, the modularity allows to separate the code development from the application of the software, which allows for the use in highly confidential systems. The identification of the optimal solution through repeated cycles of details simulation is significantly slower and potentially less accurate than solving problems in the closed-form solutions. The motivation for this deviating approach is, that it reduces abstraction to a minimum. It allows for a significantly better representation of reality, to a degree, where an actual transferability into industrial use is plausible. For the optimization the speed of finding solutions is prioritized to the optimality of the solution. Therefore, good solutions to a very detailed problem can be found in feasible time. The optimization over large simulations is very complex, but the use of a fuzzy optimization logic accelerates the process of finding good or even near-optimal solutions. This potentially allows to solve problems of industrial scale and hardness in a level
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of detail, that can not be reached through any of the other means in academia. The feasibility of the trade-off this work picked is very much a consequence of recent technological developments. While the kind of approach used to make problems unsolvable once they got to an industry-scale, the situation has changed. The availability and price of large scale parallel computing capabilities through cloud infrastructure enable this approach. In the initial stage of development of the framework, that is presented in this paper, this work focuses on finding ideal locations and sizes for buffers (ex-ante). As the genetic algorithm learns from iterations, the framework also represents certain characteristics associated with expost mitigation. 3. APPROACH TO SIMULATION OF PRODUCTION DISRUPTIONS 3.1 Production Simulation Approach The implementation of disruption mitigation strategies in the simulated production line requires the simulation setup to be re-configurable. Since in an industrial application the simulation potentially contains a large amount of confidential data, it is required that the code-development and the actual data it runs on are separated from each other. Only this way can the software be applied in different companies without having to change the source code. This work’s algorithmic implementation of the simulation is based on biological stem-cells. Stem-Cells are basic, undeveloped cells, that can be turned into any kind of body cell (e.g. muscle-, blood-, brain-cell) through a process called specialisation (Mitalipov and Wolf, 2009). Accordingly in this work’s simulation, the code of the simulation is contained in one generic, self-sufficient element. This element is able to resemble the behaviour of any cell-type in the production (e.g. production-cells, buffer-cells) and can be connected to other specialised copies of the stemcell. This way, the whole production line can be based on just a single object of programmed code. A construction code then creates, specialises and connects the required numbers of cells according to a adjacency matrix. Compared to a totally integrated simulation code this has three major advantages: (1) The information of the production’s layout is isolated from the code development, which allows companies to use the software without having to share confidential data. (2) The simulation can continuously be reconfigured, whether to experiment with different layouts or to assess different production lines. (3) The modularity allows the algorithm to only create a simulation for part of the tree and then solve the large problem through optimization of less complex sub-trees (Divide & Conquer). These algorithmic properties are reached through ObjectOriented Programming.
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processes. Common Causes is the description of a variation created by a great number of individual factors influencing the value measured. Each of these factors has an independent statistical distribution and aggregated, they can be described by one distribution. They can be considered the noise e.g. the deviation of a product specification from its norm. Special Causes are variations that can be directly assigned to factors, such as single machines or processes. Based on this theorem, the simulation considers two types of defects to a product. Random Defects: A random defect is a Common Cause. It is assumed it can be detected from a certain point on in the production line, but is not causally related to any particular entity (e.g. poor machine calibration) within it. Defects occur randomly based on a set probability. The probability is constant and independent of the last time a defect occurred (memorylessness). The defect creation is therefore described as a repeated Bernoulli-experiment in the simulation. Its occurrence therefore follows a geometric distribution. Systematic Defects: These Special Causes occur, when e.g. a machine is out of calibration or its components degrade. These defects therefore occur in clusters. Their occurrence is correlated to the frequency of maintenance. Subjects to these defects are either products or machines. Product defects do not stop production and can be detected at inspection stations. Defect products detected at an inspection station will be scraped. Machine breakdowns occur randomly and behave according to the two parameters Mean-Time-Between-Failures (MTBF) and Mean-Timeto-Repair (MTTR). MTBF and MTTR are modelled as stochastic processes based on Bernoulli-experiments and are therefore the sum of the products of a geometric distribution’s value pair. 4. OPTIMIZATION The framework tries to identify a good balance between resilience of the production and the cost required to establish it. An illustration for such optimization is given in figure 2. The figure shows the impact the size of a buffer has to the total cost. It illustrates the impact of the different sizes a particular buffer in a production line can have. The buffer is assumed to have a fix-cost and a constant variable-cost for the number of spaces available. The larger the buffer is, the larger the variations in the production line it can mitigate. The down-time of a production line is described by a cost (e.g. lost revenue). The larger the buffer is, the less down-time will occur and thus the cost for down-time decreases. However, the marginal utility of a buffer decreases with its size. Therefore, a point exists at which the sum of the buffercost and the down-time cost is minimal. This point is referred to as the optimum. Alternatively, the optimum can be described as the point, where the marginal buffercost equals the marginal down-time cost. This point the framework is trying to identify.
3.2 Disruption Simulation Approach 4.1 Problem Definition According to Shewhart and Deming (1939), who developed the foundations of what is later known as Statistical Process Control (SPC), there is two sources of variation in 291
Finding the optimal configuration for the production line can be described as a non-linear integer-programming
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4.3 Procedure
Fig. 2. Example: Cost curve for variable buffer sizes problem, where e.g. buffer-sizes are the variables. The function value is discontinuous between the values zero and one, for many of the input variables. For example, the cost incurred by the size of a buffer, lets the function value be discontinuous between zero and one because there is a fixed-cost for buffers. Another example is the defects an inspection station can detect, which only have binary values. This discontinuity makes the problem have properties of a 0-1 integer-programming problem, which severely affects the complexity of the problem. The optimisation problem is a multi-dimensional, nonlinear discrete function with multiple local optima and potentially more than one global optimum. Therefore the optimisation algorithm needs to be (1) applicable to nondifferentiable functions (2) and capable of finding global optima, which excludes direct application of gradientdescent methods. (3) The algorithm needs to be sensitive to changes of the target function in the interval zero to one. (4) the optimisation algorithm has to find solutions with a small number of function evaluations, to reduce the computational effort. 4.2 Genetic Algorithm
The first step of the optimisation is the definition of an initial configuration of the variables that are being optimised. For existing production lines the current parameters can be used. If either the production line does not yet exist or there is plausible doubt on the effectiveness of the existing configuration, ways to artificially create an initial configuration exist. The optimisation can be warm-started through one of the algorithms that describe the problem as a closed-form problem, as discussed in the literature review or be approximated through analytical methods determining the configuration for a balanced line under the assumption of regular and recurring disruption. The use of these warm-start methods relies on the assumption that the higher degree of abstraction they rely on changes the optimal result just gradually, compared to the less abstracted simulation model. If this assumption holds to be true, computational effort can be drastically reduced, compared to a random start-configuration. In the second step the optimisation algorithm defines a set of values for the variables, evaluates the target function and derives a set of values for the next iteration. In this work, each evaluation of the target function means running the simulation with the respective values as parameters. The result of the target function then is based on a costfunction. Finally, results of the optimisation can be tested for sensitivity through a Monte Carlo simulation. This is a very valuable test, since it can determine how strongly a modelling error would affect the optimality of the result. If a simulation shows very high sensitivity to the respective variable around the point of the optimum, a slight inaccuracy in the parameter definition would render the simulation results useless. If however the sensitivity is low, the simulation results are reliable and robust to inaccuracies in the modelling process or measuring errors on the exogenous variables. 5. ILLUSTRATIVE EXAMPLE
A genetic algorithm was selected to perform the optimisation in this work, since it is robust to remote optima and can be configured to efficiently handle 0-1 integer variables. Another advantage is that it can easily be warm-started, if an approximate value and an expected variance are known, which is advantageous in this work, since algorithms of this type are available. Genetic algorithms can be executed in a highly parallel fashion, which accelerates the computation. Also, genetic algorithms are considered efficient at solving problems with a complex fitness landscape. Their combinatoric evolution make them capable of moving away from local optima, which gradient methods tend to converge towards. The algorithm starts from an initial population of sets of variables (’individuals’). It inputs each of these sets into the function and determines their respective function value (fitness). The best sets of values (individuals) are then identified (selection) and crossovers of them are generated. Additionally, random mutations occur to some of the new generations of individuals. The algorithm keeps producing generations until a defined termination-condition is met. 292
In this section the proposed framework is illustrated on an arbitrary production system of industrial scale. 5.1 Simulation Development
Fig. 3. Example Tree: 23 production nodes and 23 potential buffer locations Figure 3 shows a random tree representing a production line. It contains 23 production cells (squares). In order
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to identify both, the best location for buffers and their respective optimal size, there a 23 nodes in the network (circles) representing potential positions for buffers in the production line. If the result of the optimisation equals zero for one of the buffers, this then means, that in a production line no buffer should be placed in that position. Of the 23 buffer nodes 11 are known to have an optimal size of zero. These are the buffers in the first level. Since in this example all disruptions originate from break-downs of production cells, rather than from external influences, these buffers have no disruption to mitigate. Although they do not contribute to the resilience of the production, these cells allow to make a judgment on the optimality of the results found by the algorithm. If the genetic algorithm returns a solution where one of these buffers has a size that is not zero, it is proven that the solution found is not optimal. The basis for the optimization is the definition of an objective function. It depicts the overall profit of the production line π (see (1)) and is being maximized in the optimization. For the sake of simplicity in this example, only one type of revenue and two types of cost are considered. Every produced unit is assumed to generate a revenue of α. The number of total output of the production system P (b1 , ..., bn ) is a function of the sizes of the buffers bi for every possible location i. A buffer in a certain location incurs a fixed cost component βf ix and a variable cost component βvar depending on the size of the buffer installed. n (βf ix · max (bi , 1) + βvar · bi ) (1) π = α · P (b1 ...bn ) − i=1
5.2 Solution for Optimal Resilience The optimization problem contained 23 variables. The genetic algorithm was configured to operate in parallel on a population of 48 and evolved this population over 200 cycles until it came to a hold. The development of the function value over the course of the optimization is shown in figure 4. It shows a seemingly convergent trend.
Fig. 4. Function value improvement over the simulation cycles Table 1 shows the three solutions the algorithm has found. Each of the solutions was found to generate the same profit. The 11 nodes (B1-B21) that were know to have an optimal value of zero, returned the value of zero as necessary. The results are promising. The algorithm finds solutions that, with the means available, can not be proven wrong and the function value shows seemingly convergent behaviour during the optimization. These two factors suggest that a good if not near-optimal solution can be found through the algorithm. 293
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Table 1. Best buffer-size configuration found by the genetic algorithm Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer Buffer
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
Output Profit
Optimum 1 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 7 0 12 13 16 14 16
Optimum 2 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 7 0 12 13 15 14 16
Optimum 3 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 7 0 12 13 14 14 16
133 110.83
133 110.83
133 110.83
6. CONCLUSION The paper presented a framework that tries to assess the performance of a production system and to improve the resilience through repeated cycles of detailed simulation and the application of a genetic algorithm. The developed framework is able to generate a simulation of the operation of an arbitrary production line in face of disruptions. Compared to the mathematical models in academia this paper shifts the balance towards a high detail in the modelling and a more fuzzy optimisation logic. First results suggest that the genetic algorithm is able to find improved solutions that can alleviate the impact that disruptions have on a production and that an economically efficient level of disruption mitigation can be found. The significant abstraction, that mathematical closed-form analysis imposes can be overcome in favour of the detail and applicability of the results. For industry, the method presented offers a way to harden production system in an overall economically efficient way. In the increasingly complex environment businesses operate in and under the continuous pressure for reduction of resources, such optimisation can mean a competitive advantage. The method presented in this work shows promising results of being applicable in an industrial environment. Future research will have to show whether the abstraction, complexity and computational power will allow for an application on problems of industrial scale and hardness. REFERENCES Akg¨ und¨ uz, O.S. and Tunal, S. (2010). An adaptive genetic algorithm approach for the mixed-model assembly line
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