The impact of simultaneous continuous improvement ...

International Journal of Production Research Vol. 51, No. 2, 15 January 2013, 447–464

The impact of simultaneous continuous improvement in setup time and repair time on manufacturing cycle times under uncertain conditions Moacir Godinho Filhoa and Reha Uzsoyb* a

Universidade Federal de Saõ Carlos, Departamento de Engenharia de Produçaõ, Saõ Carlos-SP, Brazil; b Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27607, USA (Received 23 October 2010; final version received 9 December 2011)

We develop a system dynamics model to examine the cumulative effects of continuous improvement programmes for repair and setup times on the cycle time of a simple single-stage production system. The relationship between system performance and repair and setup times is captured using the Factory Physics approach. We find that modest rates of improvement in multiple areas in parallel yield cumulative benefits over time comparable with those obtained by a large reduction in a single parameter, especially when there is significant uncertainty in the degree of improvement that can be obtained, or in the degree to which improvements can be sustained over time. These results provide an insight into the success of the Toyota Production System and related lean manufacturing approaches where continuous improvement is an ongoing activity across the work environment. Keywords: continuous improvement; setup time; repair time; manufacturing; cycle times; system dynamics

1. Introduction Since the earliest days of the Industrial Revolution, the continuous improvement of products and processes has been a major source of competitive advantage for manufacturing firms. In recent years, manufacturing management philosophies such as the Toyota Production System (Liker 2004), Six Sigma (Pande et al. 2000), Lean Six Sigma (Chen and Lyu 2009), and the Theory of Constraints (Goldratt and Cox 1992) have aimed at achieving long-term competitive advantage in manufacturing operations by programmes of small, incremental improvements sustained over a period of many years. These have led to a number of approaches addressing specific aspects of operations and emphasising different tools and techniques. Among these are Total Preventive Maintenance (TPM) (Nakajima 1988), which focuses on improving machine availability; quality-management initiatives such as Quality Circles, which emphasise the tools of statistical quality control and employee participation; setup time reduction efforts such as Single Minute Exchange of Die (SMED) (Shingo 1986); Six Sigma (Pande et al. 2000), which emphasises the tools of statistical experimental design; and a wide range of others. However, despite the extensive literature describing and advocating continuous improvement programmes, we still lack a clear understanding of how continuous improvement efforts directed at different parameters of the manufacturing system, such as machine downtime, setup times, and processing time variability, interact to affect system performance measures such as cycle time, especially in terms of the cumulative effect of numerous small improvements over an extended period. Mauri et al. (2010) discuss the importance of such understanding to ensuring the success of continuous improvement initiatives. In this paper, we use the Factory Physics perspective (Hopp and Spearman 2001) to construct a system dynamics model of the cumulative effects of continuous improvement in machine repair and setup times over an extended period on the average cycle time. We are well aware that the problem of how to improve the cycle time of production systems whose behaviour can be modelled as queues has been extensively addressed in the literature over several decades, using queuing models, discrete-event simulation and a variety of optimisation techniques. Our objective in this paper is not to supplant this literature, but rather to use system dynamics to examine the evolution of system performance over time under different improvement programmes. This issue could also be studied using discreteevent simulation; but a detailed simulation model of system behaviour over a long period of time, such as several years, is likely to be time-consuming both to build and to run. Our objective is more modest: to present a simple *Corresponding author. Email: [email protected] ISSN 0020–7543 print/ISSN 1366–588X online ß 2013 Taylor & Francis http://dx.doi.org/10.1080/00207543.2011.652261 http://www.tandfonline.com

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modelling tool that is easy to explain to practitioners and students, and captures the basic qualitative behaviour of the system under different conditions. Our approach requires no more data than are needed to describe a simple queuing system, facilitating a rapid, rough-cut analysis. In addition, clear and transparent justification of the adoption of an improvement methodology is very important, especially to help those who must deploy it, to understand the expected results of improvement initiatives (Miller and Hartwick 2002, Thawesaengskulthai and Tannock 2008). Our paper aims to contribute in this direction. After describing the model for a simple single-stage production system, we demonstrate its use by investigating the cumulative effect over time of major improvements in one specific parameter as opposed to modest but continuous improvements in multiple parameters over time. Our results shed some light on the sustained success of the Just in Time/TPS (Toyota Production System)/Lean Manufacturing approach, where a continuous improvement in all aspects of manufacturing operations is part of everyone’s job (Drew et al. 2004, Hines et al. 2004, Liker 2004, Holweg 2007, Yamamoto and Bellgran 2010). This approach involves a process of collective learning, leading to a higher chance of achieving cultural change in a learning organisation. On the other hand, it presents a somewhat unstructured transformation process, so it is difficult to know exactly what outcome will be obtained after the improvement or when a particular desired outcome will be obtained. The uncertainty in the outcomes of improvement efforts is one issue we examine in this paper. Our experiments indicate that a sustained programme of very modest improvements in multiple parameters of the manufacturing system yields results, over time, that are comparable, and sometimes even superior to, those from a major improvement in one parameter that would very likely require a major capital investment. The advantage of multiple parallel improvements becomes even greater when the amount of improvement that can be obtained is subject to uncertainty. There are two mutually reinforcing reasons for this behaviour. The first is that improvements in setup or repair times have a multiplicative effect on the expected cycle time, as suggested by queuing theory; they not only reduce the mean effective processing time, but also the utilisation, bringing additional benefits. The second is that when the amount of improvement that can be obtained and the firm’s ability to sustain an improvement in that parameter are uncertain, working on improving multiple parameters simultaneously increases the probability of an improvement occurring somewhere in the system, while a programme focused on a single aspect may yield little or no improvement for extended periods if major difficulties are encountered. In the following section, we give a brief review of the related literature on continuous improvement, particularly on cycle-time reduction, and the use of system dynamics to model these aspects of manufacturing systems. We then present the system dynamics model based on the Factory Physics equations in Section 3. Section 4 presents the experimental design. Section 5 presents the experimental results. We conclude in Section 6 with a summary and some future directions.

2. Literature review Continuous improvement has been recognised for many years as a major source of competitive advantage, and is inherent in many recent movements such as the Theory of Constraints (Goldratt and Fox 1986) and Six Sigma (Pande et al. 2000). The strong emphasis of the Toyota Production System on elimination of waste (Sugimori et al. 1977) has attracted considerable interest, especially the Kaizen approach to continuous improvement (Imai 1986) and the Total Productive Maintenance (TPM) programme for maintenance and equipment management (Shingo 1986, Nakajima 1988). Inability to implement continuous improvement programmes effectively is seen by many scholars and practitioners as one of the reasons why Western firms have not benefited fully from Japanese management concepts (Berger 1997). Based on Imai (1986), Berger (1997) presents the core principles of CI: (1) Process orientation: management attention should be directed towards creating sound processes; this requires that a process be understood in detail, such that variability and interdependence in the activities are identified and controlled. (2) Incremental improvement of work standards over time: small ongoing improvements accumulate to make a significant contribution to organisational performance. (3) People orientation: continuous improvement should involve everyone in the organisation from top managers to workers on the shop floor. However, this aspect may differ from one approach to another; the Theory of Constraints, for instance, emphasises process improvements in bottleneck areas, while the Toyota Production System takes a much broader view that CI is part of everyone’s job. However, it is well recognised that CI is a complex process that involves considerable learning and fine tuning of the mechanisms used (Savolainen 1998, Bessant and Francis 1999).

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Despite its importance, there are still significant gaps in our understanding of this important area of manufacturing management. In particular, there are few studies that deal with prioritising or selecting among different improvement projects (Voss 2005). Several recent papers and their relationship to our proposed model are addressed below. Heijnen and Lukszo (2006) propose a decision-support framework for batch processing industries aiming at supporting continuous improvement in operational and management tasks. An important aspect of this framework is the selection of improvement projects. The authors argue that to take the right decision regarding different improvement alternatives, it is important to have a complete overview of the causal relationships between the candidate improvement projects and the firm’s performance criteria. Thawesaengskulthai and Tannock (2008) propose a multi-criteria decision aid to help managers to select improvement projects. This model uses brainstorming, weighting, and rating techniques to assess the expected results of improvement initiatives. Our paper, in contrast, uses established quantitative relationships between the shop-floor variables to be improved and the expected cycle time. Hu et al. (2008) develop a decision support system that uses a multi-objective formulation for projectimprovement selection in companies. The system is based on a goal-programming approach in which the expected results and weight of each project are inputs determined by group discussion and brainstorming. The model in this paper can be used to improve the understanding of decision-makers by illustrating the effects of different improvement programmes over time without becoming immersed in highly specific operational details. Barad and Dror (2008) propose a strategy map for locating and prioritising the improvement needs of an enterprise. The map starts from improvement needs at the corporate level that are translated into prioritised improvement objectives at lower levels. These objectives are then translated into performance measures to be improved. Although the model represents an important contribution, the authors note some limitations: (1) it does not involve any improvement activity in an explicit way; and (2) it does not consider eventual interactions between system elements that may affect the outcomes. The model developed in this paper addresses both these limitations. Storck (2010) proposes a framework aiming at developing insight into what manufacturing capabilities are required to reach the firm’s strategic goals and applies it to a case from the steel industry. They found that that the company should invest in setup reduction and dynamic scheduling in order to reduce cost and increase diversification. Although this framework provides improvement trajectories, it does not provide quantitative relationships between variables, which our model does. Mauri et al. (2010) propose a structured methodology for process improvement in manufacturing systems that can help companies to identify areas to be improved through constraint removal. Selected areas can be improved by frequent, small improvements or by infrequent actions such as investment in new capacity or radical changes in technology. In summary, although the research community is addressing the question of how to prioritise and select improvement projects, there is still a need for tools to establish a clear quantitative relationship between improvement options and performance measures such that managers can assess the probable outcomes of an improvement initiative. Hopp et al. (2007) take a significant step in this direction by structuring the relationship between different shop-floor parameters in the form of a diagnostic tree. Our paper contributes in this direction by developing simple models with modest data requirements that can give managers intuition as to the potential outcomes of improvement projects. While the use of simulation models to support CI activities is not new (Adams et al. 1999), we believe this model is the first to try to link a quantitative model of the behaviour of manufacturing systems with a system dynamics model to examine interactions between different CI activities over time. A model-based approach of this type can yield insight into how to prioritise/select continuous improvement efforts for different aspects of a production system based on system parameters, across a wide range of production environments. It also has potential as an instructional tool in both academic and industrial environments. We have chosen cycle time as the primary performance measure for our study owing to the widespread recognition of its importance to effective manufacturing operations. Time-based competition or Responsive Manufacturing (Stalk and Hout 1990, Kritanchai and MacCarthy 1998) focuses on cycle-time reduction as a primary manufacturing goal. Reduced cycle times allow companies to operate with lower work in process inventory (WIP) levels, and thus less operating capital (Jayaram et al. 1999). They also allow firms to adapt more easily to changes in the marketplace, and have been shown in several cases, such as the semiconductor industry, to help improve process yields (Akcali et al. 2000). Cycle-time reduction is also an important part of the Toyota Production System (Liker 2004), which has motivated the Lean Manufacturing literature (Womack et al. 1990).

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However, as De Treville et al. (2004) have pointed out, much of the literature on cycle-time reduction is anecdotal or exploratory. A number of authors (Suri 1998, Hopp and Spearman 2001) have proposed approaches to cycle-time reduction based on queuing theory, which involve building mathematical models linking the total expected waiting and processing time of a part at a workstation to the mean and variance of system parameters such as the time to repair, time between failures, and setup time. In this paper, we use System Dynamics (SD) simulation as a tool to accomplish our goals. The basic approach of system dynamics is to define a set of state variables whose values describe the state of a system at a given point in time. A set of equations that describe the evolution of these state variables over time, as a function of each other and other ancillary variables and parameters, is then developed and used to simulate the behaviour of the system starting from a predefined set of initial conditions. The mathematical methodology underlying the approach is that of representing a dynamic system as a set of simultaneous differential equations that are solved numerically. However, the long time periods used in our model render the explicit use of differential equations unnecessary. Extensive tutorials on system dynamics models and their application to manufacturing systems are given by Forrester (1962) and Sterman (2000). Despite many applications in a variety of areas, there are relatively few applications of SD to manufacturing systems. SD was first applied to supply-chain management in the pioneering work of Forrester (1962), and extensive examples are given in the excellent book by Sterman (2000). Extensive reviews of this work are provided by Angerhofer and Angelides (2000) and Bhushi and Javalagi (2004). Several papers (Coyle 1977, Towill 1982, Gupta and Gupta 1989, Byrne and Roberts 1994, Haslett and Osborne 2000, Huang et al. 2007) use SD to model production control mechanisms such as Constant Work in Process (CONWIP) and kanban. The computer simulation of manufacturing systems is most commonly carried out using discrete-event simulation (Law and Kelton 1991). Baines and Harrison (1999) review the status of SD application to manufacturing systems, and conclude that manufacturing system modelling represents a missed opportunity for SD. Our choice of SD as a modelling technique is based on its ability to describe the evolution of system behaviour over time, since we are interested in the cumulative effects over time of different continuous improvement policies. While these issues could probably be investigated just as well with discrete-event simulation, the SD approach provides a compact, computationally efficient model suitable for rough-cut analysis and building intuition through its highly graphic output where the high level of detail involved in discrete event models is unnecessary and often, in fact, confusing. The linkage of the SD model to the Factory Physics approach of describing manufacturing systems using queuing makes the technique easy to explain to practitioners and highly visual. In the following section, we describe our modelling approach and its motivation. We then discuss the different CI policies examined, our experimental design, and the conclusions from each experiment.

3. Modelling and analysis 3.1 Integrating system dynamics and factory physics The use of the Factory Physics concepts in a system dynamics model may, at first glance, appear to be somewhat contradictory. The Factory Physics approach as presented in chapters 8 and 9 of Hopp and Spearman (2001) is based on long-run steady-state analysis of the production system using the methods of queuing analysis. System dynamics, on the other hand, usually emphasises the dynamic behaviour of complex systems that are not in steady state. However, our objective in this paper is to study the cumulative effect of continuous improvement in repair and setup times of the performance of the system over a long period of time. The Factory Physics equations provide a mathematical model linking the mean and variance of system parameters such as setup and repair times to performance measures such as cycle time. In order to use the Factory Physics equations in a system dynamics model, we assume that the time increments used in the system dynamics model are quite long, of the order of several months. This is a reasonable assumption in our context, since it generally takes some time to identify opportunities for improvements in repair and setup times, implement the necessary changes, and obtain results. We thus assume that within each time period, the queue representing the manufacturing system will be in steady state, allowing us to use the Factory Physics equations to describe the behaviour of the system. The assumption of long time periods also allows us to neglect the transient behaviour at the boundaries between time periods. However, as we examine the behaviour of the system over a period of several years, the time increments are still small relative to the overall horizon studied.


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Our basic approach, then, is to model the performance of the system over a time horizon of several years using time increments of the order of several months. Continuous improvement policies are modelled as a reduction in the mean or variance of the parameters of interest, in our case the repair or setup time realised in each period. In each period, the new parameter values are calculated based on the improvements implemented in the previous period and the Factory Physics equations used to estimate the effects of these improvements on the expected cycle time. We thus obtain the trajectory of improvements in cycle time owing to the improvements in repair and setup time. We assume a stochastic model of the effects of continuous improvement on cycle time represented as a Markov chain that allows us to examine the effects of different levels of uncertainty in the firm’s ability to improve different parameters, and its ability to sustain those improvements over time. The effects of variability in the operation of the production system are captured by the variances used in the Factory Physics equations. The limitations of our approach must be noted at the outset. Our purpose is not to provide specific guidance for detailed planning and implementation of continuous improvement activities in a specific setting. This goal is far better achieved either by a detailed, discrete-event simulation model of the production system, or, when appropriate, a deterministic or stochastic optimisation model. Our objective is to provide a high-level, aggregate modelling tool that requires a few basic parameters and can be used to explore the quantitative relationship between system performance and improvements in different system parameters. In this sense, our approach has much in common with queuing models of manufacturing systems, except that the latter provide long-run steady-state results describing the behaviour of the system under a fixed set of parameter values, whereas our model is aimed at studying the cumulative effects of improvements over time. Surprisingly, given the extensive discussion of continuous improvement and cycle-time reduction in both the academic and the trade literature, there seems to be very little industrial data publicly available on the rates of improvement realised over time in different industries, which makes it difficult to calibrate models of this type. We thus take the approach of examining the behaviour of number of different scenarios to provide insight into the most appropriate improvement policy in each situation.

3.2 SD model The quantitative relationships expressed in the SD model are shown in Figure 1. We consider a manufacturing system modelled as a single server with arbitrary interarrival and processing time distributions that can be represented as a G/G/1 queue. We assume that the natural processing time, the time required to process a job without any detractors other than the variability natural to the production process, has a mean of t0 and a standard deviation of 0. We shall denote the mean effective time to process one part, which is the natural processing time modified by the impacts of disruptions such as setups and machine failures, as te, and its coefficient of variation as ce. We assume that work arrives at this station in lots consisting of L parts on average, and the interarrival time between lots has mean ta and coefficient of variation ca. The arrival rate of lots is the inverse of the time between arrivals, giving ¼ 1/ta. If we denote the mean annual demand by D parts/year, since the system must be in a steady state to avoid unbounded accumulation of jobs in the queue, the mean arrival rate to the system must equal the mean demand rate, implying ta ¼ LH/D, where H denotes the total number of hours worked in a year (Suri 1998). The mean time to process a lot of L parts is then given by Lte, and the mean utilisation of the server by u¼

Lte Dte : ¼ ta H

ð1Þ

The primary performance measure of interest in this study is the expected cycle time. For the G/G/1 queue, no exact analytical expression exists, but the following approximation, where Lte is the mean time to process one lot, is recommended by Hopp and Spearman (2001): 2 ca þ c2e u CT¼ ð2Þ Lte þ Lte : 1u 2 The effective time to make one part is constructed from the natural processing time by incorporating first the effects of pre-emptive disruptions, in our case machine failures, and then the effects of non-pre-emptive outages, in our case setups. Both the mean and the variance of the effective processing time must be calculated in order to reflect these effects. Following Hopp and Spearman’s treatment, we shall assume that the time between failures is

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M.G. Filho and R. Uzsoy MARKOV CHAIN SIMULATOR Number of pieces on queue

Arrival rate Improvement function on mean setup time

TIME WORKED DURING THE YEAR

Coefficient of variation for effective processing time

AUXILIARY 9

Throughput Production rate

ANNUAL DEMAND Utilization

setup time Lot Size COEFFICIENT OF VARIATION FOR ARRIVAL TIMES

Utilization term of Kingsman's equation

Variability term of Kingsman's equation

setup Time with improvement

Mean of effective processing time with nonpreemptive and preemptive outages

Variance of setup time

Queue Time Total WIP

Variance of effective processing NATURAL time with nonpreemptive andPROCESS TIME premptive outages

AUXILIARY 3

AUXILIARY 1

Variance of effective processing time with preemptive outage (machine failure)

AUXILIARY 2

Cycle Time

Availability VARIANCE OF NATURAL PROCESS TIME

Variance of repair time with improvement

MEAN TIME TO FAILURE Mean repair time with improvement Mean repair time

Variance of repair time AUXILIARY 7 AUXILIARY 500

MARKOV CHAIN SIMULATOR 0

Improvement function on mean repair time

Figure 1. Factory physics relationships used in system dynamics.

exponentially distributed with mean mf, and that the time to repair has mean mr and variance r2 . Then, the mean availability of the server is given by A ¼ mf/(mf þ mr), yielding tef ¼ t0/A, and 2 f 2 02 mr þ r2 ð1 AÞt0 e ¼ 2 þ : ð3Þ A Amr We now incorporate the effects of setups, assuming, as in Hopp and Spearman (2001), that a setup is equally likely after any part is processed, with the expected number of parts between setups equal to the specified lot size L. The mean setup time is denoted by ts, and its variance by s2 . We thus obtain the overall mean effective processing time as te ¼ tef þ ts/L, and 2 2 L 1 2 t : e2 ¼ ef þ s þ L s L

ð4Þ

Figure 1 shows these relationships in a causal loop diagram that forms the basis of our model. In this paper, we address two aspects of uncertainty in the realisation of continuous improvement programmes. The first is the magnitude of the improvement in the parameter of interest that a firm will be able to obtain in a given time period. In practice this is affected, among other factors, by the availability of personnel capable of leading and


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implementing continuous improvement efforts, and the technological complexity of the process to be improved. The other is the ability of the firm to sustain this improvement over time. In practice, this is determined by the ability to diffuse improvements among the workforce and incorporate them into standard operating procedures. To capture the effects of these uncertainties, we modify the exponential improvement model commonly used in the SD literature (Sterman 2000) to include the effects of uncertainty. We assume the production system evolves over time through a discrete set of states I ¼ {1, . . . , Q}, which represent the different levels of improvement in a given parameter of interest that can be obtained in a given time period. Transitions between states are governed by a time-stationary discrete-state discrete-time finite horizon Markov chain fxt : t ¼ 1, . . . , Tg, so the probability of a transition from state xt–1 ¼ i to state xt ¼ j is given by pij. Uncertainty in the amount of improvement that can be obtained in a given state i 2 I is reflected by associating with each state a continuous random variable q(i) with probability density function fi(x) that denotes the fraction of the possible deterministic improvement that will be realised in a given time period when the production system is in state i in that period. In our implementation, we assume that q(i) will be uniformly distributed over the R interval [ai, bi]. We can now define a stochastic process fqðxt Þ : t 2 f1, . . . , Tg, xt 2 Ig such that Pfqðxt Þ g ¼ 1 fxt ð yÞdy where q(x0) ¼ 1 by definition. The value A(t) of the parameter being improved at a given time t is given by AðtÞ ¼ G þ qðxt ÞðA0 GÞet= ,

ð5Þ

where A0 denotes the initial value of the parameter A before any improvement, G the minimum level to which the parameter can be reduced over an infinite time period, and the time constant of the improvement. Note that when qi ¼ 1, A(0) ¼ A0, and Að1Þ ¼ G. The probability distribution of the amount of improvement obtained in one period can be controlled by the choices of A0 and G, the limits ai and bi of the uniform distributions associated with each state i 2 I, and the transition probabilities. Appropriate choices of these parameters and the transition probabilities pij can be used to represent a wide variety of possible environments. Let us assume that lower numbered states represent a higher likelihood of improvements over higher numbered ones. Different degrees of difficulty in obtaining and maintaining improvements are then modelled using different state-transition matrices. A situation where improvements are easy to obtain can be represented with high probabilities of transition from a high numbered state to a low numbered state. Similarly, a situation where improvements are hard to sustain can be represented by high probabilities of transition from low numbered to high numbered states. This type of approach has been used extensively in the inventory literature to model demand (Zipkin 2000), being referred to in that context as Markov-modulated demand or world-driven demand. Similar Markov chain approaches have also been used to model the degradation of equipment performance over time in the maintenance literature, e.g. (Sloan and Shanthikumar 2000). A review of Markov chains and the underlying theory can be found in the book by Cinlar (1975). In practice, a firm could estimate the transition probabilities related to improvements by examining historical data on the evolution of the values of the parameters of interest over time, and fitting an appropriate Markov model. This would require a sustained longitudinal data collection activity over the course of several improvement projects for the estimates to be representative. Estimates collected across different firms in the same industry group might also provide useful estimates of such probabilities. However, the purpose of the model provided here is to allow management to explore different scenarios at an aggregate level of detail, rather than provide precise estimates of parameter values at a given point in time. Hence, the examination of several different transition matrices representing what management perceives to be interesting scenarios is likely to be sufficient. This is the approach we take in this paper. To illustrate the mechanism used to model improvements over time, assume the system can pass through three states i 2 f1, 2, 3g. Recalling that fi(x) denotes the probability density function of the improvement fraction q(i) when the production system is in state i in a given period, and denoting a continuous uniform distribution over the interval [ai, bi] by U[ai, bi], let f1(x) ¼ U[0.7, 0.8], f2(x) ¼ U[0.8, 0.9], and f3(x) ¼ U[0.8, 1.0]. When the production system is in state 1 in period t, i.e. xt ¼ 1, the improvement obtained in that period is a fraction q(xt) of the deterministic improvement that would have been obtained in period t, and that fraction is uniformly distributed over the interval [0.7, 0.8]. The reader will observe that lower numbered states have lower expected values of q(i), representing a larger improvement over the deterministic improvement. The state transition diagram for this example is shown in Figure 2, where each arc from state i to state j is labelled with the associated transition probability pij, and the notation ‘qt(xt) U[ai, bi]’ should be interpreted as ‘the random variable qt(xt) follows a continuous uniform distribution over the interval [ai, bi]’.

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Figure 2. Illustrative state transition diagram for stochastic model of improvement.

This mechanism for representing uncertainty in the improvements to be obtained in setup time, repair time, or both, is integrated into the system dynamics model shown in Figure 1.The Markov chain representing improvements in each parameter is simulated to obtain a realisation of the qi values associated with each parameter in each period. These are then read by the SD model through the locations indicated for Markov chain simulator input in Figure 1. One hundred independent realisations of the improvements for each parameter are used in the experiments, which are described in more detail in the following section. 4. Experimental design 4.1 Continuous improvement policies investigated We focus on the effects of improvements in two specific system parameters: the setup time required to begin processing each lot, and the time required to repair the machine after it fails. Reducing setup and repair time are prominent components of many manufacturing improvement programmes such as Lean Manufacturing (Womack et al. 1990), Quick Response Manufacturing (Suri 1998), and the Toyota Production System (Liker 2004), among others. Rapid setups were pioneered by Toyota in the 1950s and 1960s (Cusumano 1986), led by Shingo with his Single Minute Exchange of Die (SMED) system (Shingo 1986). The effect of such programmes should be to reduce the mean and the variability of setup times; in our model, we shall focus on their effect on the mean, as we wish to focus on the effect of improvements in one parameter alone, or several parameters simultaneously. In addition to the direct benefits of reduced setup times, a major benefit of setup reduction is that it allows parts to be processed in smaller lots, with the ultimate goal of one-piece flow. The reduction in lot sizes, in turn, has been shown to reduce cycle time significantly (Karmarkar 1987, Hopp and Spearman 2001). However, we shall not consider this effect in this paper, which renders our results conservative. Unplanned machine failures are a major source of variability in many manufacturing operations, especially hightechnology industries such as semiconductor manufacturing. A variety of studies (Kayton et al. 1997, Hopp and Spearman 2001) have shown that both the mean and the variability of machine down times have a significant effect on system performance. It is thus no surprise that many manufacturing management philosophies such as Six Sigma and Lean Manufacturing have devoted considerable effort to understanding and eliminating unplanned downtimes. One of the best recognised approaches to this problem is the Total Productive Maintenance (TPM) approach developed as part of the Toyota Production System (Nakajima 1988, Willmott 1997). 4.2 Parameters used We will vary individual parameters in different experiments to examine their effect on cycle times. The basic time period in the system dynamics model is assumed to be three months, or 12 weeks. This is a reasonable time increment for the purposes of this paper, since it is likely to require several months to develop and implement the improvements needed to make a significant reduction in repair or setup times. We simulate the operation of the system over a period of 10 years, or 40 quarters. Since our objective is to study the effects of continuous

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International Journal of Production Research Table 1. Parameter values used in experiments. Parameter Annual demand Lot size Hours of operation per year Mean of natural processing time Standard deviation of natural processing time Coefficient of variation of interarrival times Mean time between failures (assumed exponentially distributed) Mean time to repair (assumed exponentially distributed) Mean setup time

Table 2. Improvement easy to obtain and easy to sustain.

Notation

Value

D L H t0 0 ca mf mr ts

11,520 parts/year 200 parts 1920 h 6 min 6 min 1 9600 min 480 min 180 min

Table 3. Improvement easy to obtain and hard to sustain.

To state

From state

1 2 3

To state

1

2

3

0.8 0.5 0.3

0.1 0.4 0.5

0.1 0.1 0.2

Table 4. Improvement hard to obtain and hard to sustain.

From state

1 2 3

1

2

3

0.2 0.4 0.4

0.4 0.2 0.4

0.4 0.4 0.2

Table 5. Improvement very hard to obtain and very hard to sustain.

To state To state From state

1 2 3

1

2

3

0.2 0.1 0.05

0.5 0.2 0.15

0.3 0.7 0.8

From state

1 2 3

1

2

3

0.03 0.03 0.01

0.6 0.27 0.02

0.37 0.7 0.97

improvement in repair and setup times, the annual demand and lot size are held constant throughout the simulation; in particular, lot sizes are not reduced as setup time decreases, providing a conservative estimate of the impact of this improvement on the system cycle time. These parameter values result in a utilisation level of 0.72, based on the effective processing time under the initial operating conditions before any improvement is made. The parameter of the improvement process was chosen to give a half-life for the exponential decay of 1 year. The values of the parameters used for the system before any improvements take place are summarised in Table 1. We shall denote each scenario as a tuple (A, B, C | P, Q, R) where A denotes the relative difficulty of improving setup time, B that of repair time, and C that of improving both parameters simultaneously. The three parameters P, Q, and R denote the difficulty of sustaining the improvements in each of the three parameters (setup time, repair time, and both together, respectively). Tables 2–5 show the transition matrices used to model these different levels of difficulty; recall that lower numbered states permit larger improvements than higher numbered ones.

5. Experiments with uncertain process improvement outcomes In this section, we focus on three policies – improving setup time, improving repair time, and improving both simultaneously. We examine a number of scenarios based on the relative difficulty of obtaining and sustaining

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M.G. Filho and R. Uzsoy Table 6. Uncertainty scenarios for improvements. Distribution of qi ¼ uniform(ai, bi) Uncertainty level Low Medium High

State 1

State 2

State 3

(0.7, 0.8) (0.65, 0.85) (0.6, 0.9)

(0.8, 0.9) (0.75, 0.95) (0.7, 1.0)

(0.9, 1.0) (0.85, 1.05) (0.8, 1.1)

Table 7. Summary of the scenarios used in experiments.

Difficulty of obtaining improvements Scenario (figure)

Setup time

Repair time

1 2 3 4 5 6 7

Easy Easy Easy Easy Easy Easy Easy


(3) (4) (5) (6) (7) (8) (9)

Difficulty of sustaining improvements

Both

Setup time

Repair time

Easy Hard Very hard Hard Hard Hard Very hard



Uncertainty in obtaining the improvement (different state parameters)

Both

Setup time

Repair time

Both

Hard Hard Very hard Hard Hard Hard Very hard

Low Low Low Medium Low Low Low

Low Low Low Medium Low Low Low

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improvements in the different parameters and the uncertainty in obtaining these improvements using the approach described in Section 3. Therefore, each of the scenarios in this section is represented by a different set of parameters governing the continuous improvement in a given state, and different transition matrices governing the transitions between states as described in Section 3. The distributions associated with each state are given in Table 6, and the scenarios considered in Table 7. Owing to the uncertain nature of the realised improvements in the different scenarios, we simulate each scenario 100 times using independent random number streams to determine the realised transitions between states. Recall that each state determines the realised improvement from the continuous improvement programmes. We compute upper and lower 95% confidence limits as well as the average values of the cycle time for each time period and show these in the plots. We first study three scenarios. In the first, denoted by (E, E, E | E, E, H), improvement is easy to obtain for each parameter individually, as well as when improving both parameters simultaneously. However, it is hard to sustain improvement in both parameters over time, while improvements in individual parameters can be sustained easily. The second (E, E, H | E, E, H) and third (E, E, VH | E, E, VH) scenarios are even less favourable to simultaneous improvements in both parameters. Figures 3–5 show that over time, simultaneous improvement in both parameters (BOTH) rapidly outperforms improvement in individual parameters (SETUP and REPAIR) in both scenarios. In the figures, the upper and lower confidence limits and the average cycle time are plotted in the same colour. In Figure 3, by the time 4800 h has elapsed, the average cycle time from improvement in both parameters is lower than the lower confidence limit of SETUP and REPAIR; after 9600 h, the upper confidence limit of BOTH is almost always below the lower confidence limit of the other two policies. Throughout the simulations, the upper confidence limit from BOTH is competitive with the other approaches; by the end of the simulated horizon, it actually lies below the lower limits of the other two policies. In Figures 4 and 5, representing scenarios less favourable to BOTH, the BOTH policy still performs well but takes longer to outdistance SETUP and REPAIR. Under all three scenarios, by the end of the simulation period, the three policies are clearly separated, with non-overlapping confidence intervals: BOTH outperforms SETUP, which in turn outperforms REPAIR.

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Figure 3. Comparison of improvement policies for the (E, E, E | E, E, H) experiment.

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Figure 4. Comparison of improvement policies for the (E, E, H | E, E, H) experiment.

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Figure 5. Comparison of improvement policies for the (E, E, VH | E, E, VH) experiment.

These results suggest that a policy of working towards improving multiple parameters simultaneously can yield comparable or better results than improving one parameter at a time, even when improving two parameters simultaneously is significantly more difficult than improving one parameter. It also clearly shows that improvements in different parameters can yield quite different results – the SETUP policy significantly outperforms the REPAIR policy by the end of the simulations. There are two mutually reinforcing reasons for the superior performance of the BOTH policy. The first of these is inherent in the structure of the Factory Physics equations governing the effective processing time. The effective processing time involves the effects of both pre-emptive failures (repair times in our case) and non-pre-emptive failures, in our case setups. Thus the mean effective processing time is given by te ¼ t0 =A þ ts =L ¼ t0 ððmr þ mf Þ=mf Þ þ

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Thus, when L and t0 are fixed, the effects of improvements in mean setup time and mean repair time on the mean effective processing time are additive. Thus improving mean setup time and repair time simultaneously by a given amount will be more beneficial than reducing either one alone. However, improvement in te has a multiplicative effect on the mean cycle time, since reduction in te will reduce utilisation in addition to reducing te itself. To illustrate this effect, consider a system with c2a ¼ c2e ¼ 1 and te ¼ 8 min. With the other parameters taking the values specified in the previous section, this yields a utilisation of 0.8 and an expected cycle time of 8000 min. Reducing the mean effective processing time by 6.25% to 7.5 min yields a utilisation of 0.75 and an expected cycle time of 6000 min, a reduction of 25%. In addition to this effect, when the gains from continuous improvement are uncertain, working on multiple improvements in parallel maintains a ‘portfolio’ of improvement activities. While efforts to improve one parameter may fail in any given period, there is a non-zero probability that an improvement can be obtained in one of the others during that period, resulting in a non-zero improvement in system performance. When we work on one parameter alone, if we cannot succeed in obtaining an improvement in that parameter in a given period there is no possibility of system improvement in that period at all. Similarly, when the system’s ability to sustain improvements is uncertain, i.e. the benefit of an improvement may be lost in the future, a degradation in the value of one parameter may be offset by an improvement in another.

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Figure 6. Comparison of improvement policies for the (E, E, H | E, E, H) experiment under medium uncertainty.

To test these conclusions, Figure 5 simulates a situation where it is very hard both to obtain and sustain simultaneous improvement, using the transition matrix given in Table 5. After several runs examining different transition matrices, we found that even with only a 3% probability of obtaining improvements, simultaneous improvement outperforms improvement in mean setup time alone, although clearly it takes longer to achieve a statistically significant difference in expected cycle time. In Scenarios 4–6, represented in Figures 6–8, we examine the effect of the improvement programmes under different levels of uncertainty in obtaining the improvement. All scenarios studied here use the (E, E, H | E, E, H) transition matrix, which favours improvements in individual parameters over simultaneous improvements in both. Figure 6 compares improvement in only one parameter versus simultaneous improvement in both in a more uncertain environment. While the lower confidence limit for BOTH is significantly better than all others, it is striking that the average curve for BOTH lies below the lower limits of the setup and repair policies for the vast majority of the time periods. It also appears that the average rate of improvement over the simulated horizon obtained by both is higher than for setup or repair, despite the fact that improvement in the individual parameters is easier to obtain and to sustain than improvement in both. This can again be attributed to the portfolio effect mentioned above; low improvement, or even degradation, in one parameter in a given period can be offset by improvement in another. When the uncertainty in improvements in mean setup and mean repair time is low (per Table 6), and uncertainty in improvement in both parameters is medium, as shown in Figure 7, BOTH again pulls ahead by the end of the simulated horizon. Early in the horizon, the setup policy is more consistent, but still by about 10,000 h the BOTH average is ahead of the SETUP lower limit and remains so for the remainder of the horizon. Figure 8 simulates a scenario where uncertainty in improvement in mean setup and mean repair times is low, and that of improvement in both is high. Again the average curve for BOTH almost always outperforms the lower confidence limit for reduction in setup time. Pursuing this line of exploration, we ran another set of experiments where improvements in the individual parameters are easy to obtain and sustain, but it is very hard to obtain and sustain improvements in both parameters simultaneously (Scenario 7, shown in Figure 9). This scenario, represented by the (E,E,VH|E,E,VH) transition matrix given in Table 5, might represent a situation where the firm has limited resources to direct continuous improvement projects, resulting in a severe limitation of progress as resources are committed to too many different projects. Even in this adverse situation, BOTH remains the best performing option by the end of the horizon, although setup is now a closer contender.

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Figure 7. Comparison of improvement policies for the (E, E, H | E, E, H) experiment (improvement in mean setup time and mean repair have less uncertainty and BOTH improvement is medium uncertainty).

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Figure 8. Comparison of improvement policies for the (E, E, H | E, E, H) experiment (improvement in mean setup time and mean repair have less uncertainty and BOTH improvement is high uncertainty).

Taken together, these results make a powerful case for pursuing multiple improvements in parallel if the firm has resources to do so. The advantages of this simultaneous improvement approach become increasingly evident as the uncertainty in the realised improvements increases. This result also supports our ‘portfolio’ hypothesis, that when we work on multiple improvements, we reduce the probability of a period with no improvement at all.

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Figure 9. Comparison of improvement policies for the (E, E, VH | E, E, VH) experiment (improvement in mean setup time and mean repair have less uncertainty and BOTH improvement is high uncertainty).

Finally, it should be noted that the results so far are conservative for several reasons. First of all, in all the scenarios so far, the level of utilisation has been relatively low, beginning at 0.72. One would expect to see considerably greater improvements at higher utilisation levels. In order to see the effect of utilisation on the results, we simulate the (E, E, VH | E, E, VH) scenario with a 93% starting utilisation (natural processing time from 6 to 8 min). The results are shown in Figure 10. The results of this experiment closely parallel those shown in Figure 9, but the magnitude of the improvements is greater. Another factor rendering these results conservative is the fact that lot size is held constant throughout the simulations. In reality, a reduction in mean setup time would also allow lot sizes to be reduced, further reducing the mean cycle time.

7. Conclusions and future directions Our results indicate that the use of system dynamics combined with Factory Physics can yield interesting insights into the relative effectiveness of different continuous improvement policies and sheds some light on how the Toyota Production System achieves the results that it does. The results indicate that a modest but continuous improvement in multiple parameters over time can result in cumulative benefits that compare very favourably with major improvements in a single parameter that are likely to require significant investment. This is true even when uncertain conditions are present: even when the probability of improvement in any given parameter is quite small, pursuing simultaneous improvements can eventually outperform improvements in one parameter alone. This observation is consistent with the well-known history of continuous improvement at Toyota, where continuous improvement is part of everyone’s job and hence is worked on in multiple areas on an ongoing basis. The model used here is obviously subject to some limitations. It focuses on a single-stage system producing a single product, with differences between products represented by the variability in processing and setup times. The extension of the current model to multiple stage production systems is conceptually straightforward and opens the way for some interesting extensions. One such direction is to compare the long-term effect of continuous improvement policies focusing exclusively on the bottleneck station, as suggested by the Theory of Constraints, with a Toyota-style policy of constant but modest improvements at multiple areas. The incorporation of constraints on the resources available to implement continuous improvement activities is another direction to explore.

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Figure 10. Comparison of improvement policies for the (E, E, VH |E, E, VH) experiment, with 93% of utilisation.

The proposed modelling tools also have considerable potential as a teaching tool, facilitating the discussion and exploration of different continuous improvement policies under different environmental conditions. It is also necessary to interpret the results carefully, since the use of equations derived from steady-state queuing analysis requires that the time periods considered in the system dynamics model be long enough for steady state to be a reasonable assumption, and transient effects at the boundaries between periods to be negligible.

Acknowledgements The research of Reha Uzsoy was partially supported by the National Science Foundation under Grant No. DMI-0559136. Moacir Godinho Filho was supported by a Fellowship from the CAPES agency of Brazil during his visit to North Carolina State University. The authors would like to thank three anonymous referees for their helpful comments that greatly improved the original submission.

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