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How Lean is Too Lean? Using Simulation-based Experiments to Assess the Impact of Supply

Side Supply Chain Disruptions on “Lean” Supply Chains

Alexandre M. Rodrigues* George A. Zsidisin

& Steven A. Melnyk

Department of Marketing and Supply Chain Management N370 North Business Complex

The Eli Broad Graduate School of Management Michigan State University

East Lansing, MI 48824-1122 rodrigues@bus.msu.edu

December 17, 2006

*author for correspondence

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How Lean is Too Lean? Using Simulation-based Experiments to Assess the Impact of Supply

Side Supply Chain Disruptions on “Lean” Supply Chains

Abstract How “lean” is too lean? What are the performance implications for a supply chain that is

managed using lean principles, practices, and tactics of a significant disruption to the

upstream flow of product? Addressing these two questions forms the major focal point

of this working paper. Specifically, this paper uses a series of experiments involving a

computer-based simulation of a supply chain to evaluate the impact of supply

disruptions on supply chain performance. The experiment draws on two factors – the

level of inventory (a major buffer and the target of many lean system implications) and

the presence/absence of a supply side supply chain disruption. Using a combination of

graphic analysis, conventional statistics, and time series analysis (with outlier

detection), the results show that relatively minor changes in inventory buffers can and

do have major implications of the supply chain to cope with disruptions. As inventory

buffers fall, the impact of the supply side supply chain disruptions is amplified in terms

of the time that it takes for performance to regain stability. The working paper explores

these and other issues in detail with the goal of operationally defining such terms as

system robustness and system resilience.

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Introduction Lean principles, practices and techniques have attracted a great deal of attention from

the business practitioner community (Trunick, 2000; Goldsby et al., 2006). Increasingly,

managers are recognized that lean principles and practice, when properly used, can

generate significant benefits in terms of reducing costs, improving quality, reducing lead

times, and improving flexibility. Lean systems are now so widespread that one

practitioner publication (World Trade)considers lean logistics (the result of applying lean

principles and practices to logistics) and the continued reduction in inventory levels

(another effect of the application of lean) a “mega-trend” (sic) in logistics (Gordon,

2004).

One of the major traits of any lean system, whether it is applied at the corporate or

supply chain level, is its focus on identifying and attacking waste and variance. By

attacking waste and reducing variance, lean systems enable management to reduce its

reliance on buffers. There are three types of buffers – inventory buffers, capacity

buffers and lead time buffers. All three types of buffers can be reduced through the

correct application of lean practices. By reducing the reliance on these buffers, the firm

can potentially reduce costs and increase the level of supply chain customer value

generated by the system.

Yet, there exists a hidden danger in reducing the reliance on these buffers. Buffers

exist to protect systems from uncontrolled or unanticipated problems. By reducing

buffers, the supply chain became more susceptible to unforeseen disruptions occurring

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anywhere within the supply chain. Such systems can become “fragile” – systems that

work well as long as there is no disruption in flows but systems that can collapse once

they encounter a disruption.

The objective of this study is to investigate the combined impact of lean inventory

strategies and supplier disruptions on supply chain performance. Specifically, this article

attempts to explore the following research question: How lean is too lean? The

intention of this paper is to emphasize the concept that depending on the supply chain

environment (customer requirements, lead time uncertainties, production constraints,

etc.) lean strategies may not have a good fit and, in fact, detrimentally effect

performance (Jones et al., 1997).

This study emphasizes the notion that comprehensive approaches such as lean are not

appropriate in all supply chain environments (Hayes, Pisano, Upton, & Wheelwright,

2005). In some situations, the benefits of lean strategies will outweigh its shortcomings

as evaluated by the total system performance. In other situations, inventory may be

necessary to protect against uncertainties and buffer against imbalances and

constraints. The implementation of lean systems and processes in situations of high

uncertainty, imbalances, and constraints, can lead to disastrous outcomes.

In addition to the previous discussion, this article’s primary objective is to study through

the use of computer based simulations how supplier disruptions are “felt” by the firm

operating in a supply chain when buffers in the form of inventories are simply too low

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(i.e., the system is too lean). Specifically, this study will address the following

questions:

• How do changes in inventory levels affect the overall performance of the supply

chain?

• How long does it take for the supply chain to return to stability once it has

experienced a disruption? How does the inventory level affect the time that it

takes for the system to regain steady-state?

• How sensitive are the results to changes in the inventory levels (which is a proxy

for the degree of leanness of the system)?

As previously noted, these questions will be addressed using data generated from a

computer simulation of a multi-tier supply chain. Driving the simulation model will be a

two factor experimental design consisting of level of inventory and presence/absence of

a supply side supply chain disruption.

Although tools such as supply continuity planning (Zsidisin et al. 2005) can be

implemented to manage this risk, there may still be negative organizational effects

experienced from such disruptions. This study will identify and explore these negative

effects.

Literature Review

It can be argued that the first application of lean principles and practices to the supply

chain involved the introduction and use of lean logistics. The term lean logistics was

proposed as an extension of the traditional lean production concepts (Womack & Jones,

1994; Jones et al., 1997). The concept presents a systematic approach for supply chain

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analysis by directing managerial attention on issues of process activities,

responsiveness of the chain, production variety, quality, demand amplification, decision

points, and industry structure. Since the initial proposition of the concept, several

researchers have highlighted the benefits of adopting lean strategies. Lean concepts

were found to be well fit to new product launch strategies (Bowersox, Stank, &

Daugherty, 1999), the automotive industry (Wu, 2002; Gilligan, 2004), health care

organizations (Palkon, 2001), and grocery distribution (Kerr, 2006).

Some studies highlight that a lean strategy will not be necessarily desirable in all

situations (Christopher & Towill, 2000; Cox & Chicksand, 2005; Agarwal, Shankar, &

Tiwari, 2006; Goldsby et al., 2006). These studies include as an alternative to leanness

the concept of agility. Whereas lean is about doing more with less, the term agility is

defined as a business-wide capability that promotes supply chain flexibility (Agarwal et

al., 2006). It is emphasized that although lean systems can positively affect markets

where cost is the primary order winning criteria; there are many other markets where

the order winner is product availability (Christopher & Towill, 2001). In addition, lean

concepts would better be applied in environments where demand is relatively stable and

hence predictable and where product variety is low. The key differentiation between the

two concepts is that whilst leanness may be an element of agility in certain

circumstances, by itself it will not enable the supply chain to meet the precise needs of

the customer more rapidly (van Hoek, Harrison, & Christopher, 2001). As a result, some

authors suggest a fit between market characteristics/performance objectives and the

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choice for a lean, agile, or even a combination of these two strategies - leagile (Naylor,

Naim, & Berry, 1999; Bruce, Daly, & Towers, 2004; Goldsby et al., 2006).

Hypotheses

Product availability is the primary measure of service in this present study. It is

important to highlight that costs are not explicitly considered in this analysis. We are

interested primarily in the impact of disruptions and inventory buffer policies on the

variability of the service measures. Our goal is to provide support to the points

presented by previous research: when service (product availability) is the primary

customer driver (order winner), lean systems can result in detrimental performance.

This research attempts to demonstrate two issues. The first is that any type of supply

chain system has inherent variability in its performance outcomes. This performance

variability is affected by uncertainties and imbalances naturally present in the business

environment and supply chain constraints that the company operates. The traditional

role of inventory is to buffer and protect against these uncertainties (variations in lead

times, supplier availability, production availability, information quality, etc). In addition,

inventory is generally used to buffer imbalances between supply and demand (different

geographic locations, different throughput rates, different lead times, etc). Therefore the

first issue is that as companies adopt lean strategies they can increase performance

variability if the amount of inventory in the system is below the minimum required to

protect against these inherent uncertainties and imbalances.

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H1: The implementation of lean systems can significantly reduce product

availability.

The second issue concerns disruptions in the supply base, named Supplier Side -

Supply Chain Disruptions (SS-SCDs). There are different ways to protect against such

types of disruptions, such as using multiple suppliers, extending customer lead-times,

and increasing supply chain inventory levels. In addition, firms can create plans that

facilitate awareness, focus on prevention, quickly remediate interruptions, and garner

knowledge that reduces the current and future likelihood these disruptions have on firm

performance (Zsidisin et al., 2005). Further, activities such as early supplier involvement

and strategic alliances (Smeltzer and Siferd, 1998) can reduce the chance of

disruptions occurring in the first place.

This article considers the utilization of inventory buffers to protect against such

disruptions. Although there are alternative options, as discussed above, that can be

used to protect against disruptions, inventory buffers are often the most typically used

management technique (Zsidisin and Ellram, 2003). As inventory buffers are

increasingly reduced, by the utilization of lean strategies, the system is more

susceptible to the negative impacts of supplier disruptions.

H2: The implementation of lean systems can result in significant detrimental

outcomes when supply disruptions occur.

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Methodology

One way of studying the interaction between inventory reductions and supplier

disruptions is to build a computer simulation model of a supply chain and expose it,

through controlled experimentation, to a series of disruption. Computer simulation is the

process of designing and building a model of a real or representative system and then

using this system as an environment for carrying out controlled experiments (Law &

Kelton, 2000). Simulation models have been extensively used to study operations

management and supply chain related problems (Bowersox & Closs, 1989; Levy, 1995;

Parlar, 1997; Ridall, Bennet, & Tipi, 2000; van der Vorst, Beulens, & van Beek, 2000;

Holweg & Bicheno, 2002; Shafer & Smunt, 2004; Terzi & Cavalieri, 2004;

Venkateswaran & Son, 2004; Allwood & Lee, 2005).

The Simulated Supply Chain Described The supply chain model is presented on Figure 1. The focal point is the manufacturing

firm. This sample supply chain considers the first tier supplier level and at the first tier

customer level. Such models have been previously used to study supply chain-related

problems (Jeuland & Sugan, 1983; Moorthy, 1987; Weng & Zeng, 2001; Qi, Bard, & Yu,

2004).

***** Insert Figure 1 about here *****

The simplified conceptual model is a dynamic multi-echelon structure (Figure 2) that

considers production and distribution functions, product and information flows, and

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customer demand. The model assumes independent policy and inventory operations for

each facility. Retail facilities (customers) obtain inventory supply from the plant facility,

which in turn replenishes inventory from three different suppliers. Each supplier

provides a different type of component for the finished good. One part from each

supplier is required to build a finished product at the plant.

***** Insert Figure 2 about here *****

Experimental Design Within the experiment, the researcher must specify and incorporate the parameters, and

the experimental factors. Parameters are those elements that describe elements

exogenous to the simulation model and outside of the control of the researcher and/or

manager. That is, for a particular experiment, parameters represent the “givens” or the

system constraints under which the simulation model operates. In contrast,

experimental factors are those elements that are under the control of the researcher

and/or manager.

Parameters In this study, the parameters considered are: customer demand, replenishment

strategy, initial inventory, bill of materials, transit lead time, and production strategy.

Daily customer demands are created using stochastic distributions. For each customer,

the daily demand pattern follows a Triangular distribution with minimum value of 20,

average of 35, and maximum of 50 units. Replenishment orders from the plant to each

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individual supplier are created after inventory is evaluated on a daily basis. Maximum

and minimum inventory target levels are defined at the plant. These target levels are

defined in days of demand. During every review period, the average daily forecast is

recalculated (smoothed) and then it is multiplied by the defined target (in days) to obtain

a specific quantity in units to be maintained at the facility. Initial inventory at the plant is

also set to the maximum target. Because the minimum and maximum targets are equal,

the system will always try to order up to the maximum level. This procedure allows the

system to dynamically adapt to changing demand trends. Inventory requirements are

then evaluated taking into account not only current inventory position, but also transit

inventory. If the planned inventory is below the maximum target, a replenishment order

is created. The order quantity is the necessary amount of products needed to build the

maximum target. Inventory requirements of finished goods are then exploded into

requirements of individual components, following the Bill of Materials (1:1 proportion for

all 3 components). Finally, individual orders for components are placed to suppliers.

Suppliers are initially considered to have infinite capacity.

Replenishment orders are processed at each individual supplier. The quantity to be

shipped to the plant depends on the Allocation Factor utilized. If the factor is set to

100%, then all the quantity requested on the replenishment order from the plant is

shipped. If the factor is lower than 100%, for example 90%, then the shipped quantities

are reduced accordingly. This factor is introduced to represent sourcing constraints

without explicitly defining particular production logic and scheduling issues at the

supplier level. After the supplier shipment is sent, a transit lead time is applied.

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Shipments from suppliers to the factory assume a delay that follows a Triangular

distribution with minimum of 5, average of 7, and maximum of 10 days. Therefore, the

model considers variation in the lead times from suppliers to plant.

Production occurs at the plant facility on a daily basis. This illustration assumes that

assembly of components occurs inside a simulation day (hours) and no production lead

time is explicitly modeled. This means that on a daily basis, before any other decision

and after receipt of replenishment orders, the model automatically converts component

inventory into finished goods.

The parameters modeled provide inherent uncertainty and constraints to the system.

Both demand and transportation lead times are stochastic, providing uncertainty. The

fact that three different parts are needed to build a product and that individual shipments

from suppliers are independent from each other brings constraints to the system.

Experimental Factors The experimental design used for this study consists of two factors: (1) supply chain

disruption; and, (2) inventory buffers. The first factor consists of two levels: 1 – no

disruption; and 2 – disruption present. Disruptions are modeled to occur in one of the

suppliers (Supplier 1) at week 18 of the second year. The disruption lasts for 2 weeks,

and assumes a total supply loss over the triggering event time horizon (capacity at

supplier 1 is reduced to 0%). Orders received during that period are cancelled by the

supplier. The second factor, inventory buffers, consists of six levels (5 days of inventory,

6 days, 7 days, 8 days, 9 days, and 10 days of inventory), serves as a proxy for the

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degree of system “leanness.” That is, it is assumed that the lower the inventory buffer,

the more lean the system is. A full factorial design is used, resulting in 12 cells (2 levels

of supply chain disruptions X 6 levels of inventory buffers).

To assess the potential impact of supply chain disruptions on a lean system, the impact

is captured using two performance measures: product availability (as measured by Fill

Rate – the quantity provided in the customer order divided by the quantity requested)

and plant inventory (as measured by the end of each period). Data is recorded in two

forms: end-of-simulation results (what is typically done) and time series data. Since a

disruption generates a transient response and since the transient response is often that

portion of the data of greatest interest to researchers, this response is best captured

through the use of time series data.

Results

Figure 3 and Figure 4 present examples of scenario plots for each one of the 12

different scenarios. The upper part of these graphs presents the weekly Fill Rate (our

measure of service), and the lower part presents the weekly plant inventory.

***** Insert Figure 3 and Figure 4 about here *****

Figure 3 presents sample plots for the situation where no supplier disruption occurs in

the system. As inventory targets are increased, the weekly inventory at the plant

increases accordingly. What is interesting in these plots is to visually identify that as

inventory buffer is placed in the system (moving from 5 days to 10 days of targets) the

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variation on service is reduced. With 8 days of inventory targets, the system has little

variability, with service level close to 100% most of the time. With 9 days of targets, the

uncertainties and constraints are balanced, and the system provides 100% service all

the time. The increase to 10 days of target is a perfect example of inventory as waste.

The additional inventory from 9 to 10 days of target is not necessary to provide 100%

service levels. Therefore, the simulation results provide valuable information on the

impact of inventory target manipulation on system performance. The key point here is

that, assuming that inventory and warehousing costs are lesser than stockout costs

(service is the primary driver), by reaching 6 and 5 days of inventory targets (lean

concept) the service performance is severely hurt. Not only does it reach points below

60% in some weeks, but also the variability of weekly Fill Rates is substantially

increased.

Figure 4 presents sample plots for the situation where a single supplier disruption

shocks the system. Because of the characteristic of the modeled disruption (it shut

downs the first supplier entirely), the system performance is hurt when the disruption is

present. Further, the impact on service is more pronounced as inventory targets are

reduced. It is interesting to note that, in the situation of no disruptions, the target of 10

days would not be considered. However, if disruptions are expected in the system, this

scenario would provide better protection against the supplier’s lack of availability.

Another interesting point on Figure 4 is that the targets of 9 and 10 days (non-lean

situations) allow the system to quickly recover to its 100% weekly level without any

additional managerial action. As targets are reduced, this does not happen. In the

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extreme lean case (target = 5 days) the impact not only is pronounced at the moment of

the disruption, but also appears a second time. What these sample plots demonstrate is

that during situations when inventory buffers are low, the system is not only unable to

protect against inherent uncertainties and constraints, but also is unable to protect

against unexpected situations (disruptions).

***** Insert Table 1 about here *****

Table 1 presents descriptive statistics of weekly average, standard deviation, and

coefficient of variation (CV) for each scenario considered in this study (summary of 30

replications in each). The CV is calculated as the standard deviation divided by the

mean. The table shows that the average Fill Rate decreases as inventory targets are

reduced (towards leaner situations) in both set of experiments (non-disruption vs. single

disruption). By using the CV as a measure of variability, it is also clear that as leaner

situations are used, the variability of the system performance (as measured by Fill Rate)

increases substantially. Confidence intervals at the 95% level are presented on Table 2.

***** Insert Table 2 about here *****

There are statistical differences in the average fill rates as the inventory targets are

manipulated. Therefore, leaner situations provide not only a reduction on the average

performance but also an increase in the system variability. Therefore, H1 is supported

by the results.

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To evaluate the second hypothesis, Univariate Analysis of Variance is utilized. The

model considered the direct effects of inventory targets and the presence of the supplier

disruption as well as their interactive effect. The results of the ANOVA procedure are

presented on Table 3.

***** Insert Table 3 about here *****

The model is significant at p<0.01. The direct effects of the presence of supplier

disruption (SS_SCD) as well as inventory targets (INV_TGT) are also significant.

Finally, the interaction effect between the two experimental variables (SS_SCD *

INV_TGT) is also found to be significant at p<0.01. Further information about the direct

effects and interaction is provided on Figure 5, which consists of the profile plots of

estimated marginal means, where the interactive effect on system performance is

presented.

***** Insert Figure 5 about here *****

As a conclusion, H2 is supported by the results. By increasingly reducing inventory

buffers, the system is more vulnerable to disruptions in the supplier side (SS-SCD).

There is indeed an interactive effect between the degree of leanness and the presence

of the disruption.

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Time Series Analysis – Outlier Detection In the completed paper to be presented at the workshop, the time series data previously

discussed will be analysis using time-series analysis techniques. Specifically, since the

disruption can be treated as essentially creating an outlier, a special type of time-series

analysis can be used – outlier detection. This technique will be used to precisely

address such questions as:

• From the onset of the disruption, how long will it take until the plant of interest to

be affected?

• How long will the system be affected by the disruption?

• Will the system return to the same pre-disruption of output after the disruption

has taken place and its effects allowed to transpire?

• How will the inventory levels affect the responses observed to the preceding

questions?

Conclusion

This study provides empirical validation to the fact that in some situations where service

is the primary market driver, lean strategies result in detrimental system performance.

This result provides additional support to existing concepts in the literature related to

lean and agile supply chains (Agarwal et al., 2006; Goldsby et al., 2006). In addition,

this study also provides empirical support that lean strategies not only reduce the

system performance (as measured by product availability) but also increases the

variability of such outcomes. Finally, this study shows that when disruptions can occur

in the system, lean strategies amplify the detrimental effect on system performance (as

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measured by product availability). Therefore, there is an interaction effect between the

disruption and the degree of buffer protection in the system.

Managers should be careful to adopt lean strategies as “perfect mantras”. It becomes

imperative that firms carefully evaluate the environment characteristics and the

adequacy to lean strategies. As proposed in the academic literature, there is a natural fit

between system characteristics and the adequacy to use lean systems (Christopher and

Towill, 2000; Cox and Chicksand, 2005). Lean systems and processes can be used by

some firms to increase cash flow and reduce waste in the supply chain. However, a

balance needs to be determined by organizations to understand when those systems

are too lean, and hence become fragile and break when disruptions do occur.

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Table 1: Descriptive Statistics - Weekly Fill Rate Dependent Variable: Weekly Fill Rate (AVG)

Disruption Type Inventory Target Mean Std. Deviation Coefficient of Variation NDisruption 5 74.94 1.93 2.57% 30

6 83.96 1.84 2.19% 307 90.05 1.42 1.58% 308 94.00 1.41 1.50% 309 96.98 1.50 1.55% 3010 98.34 1.21 1.23% 30

No Disruption 5 80.36 1.34 1.67% 306 88.54 1.16 1.31% 307 93.25 0.79 0.85% 308 96.20 0.71 0.74% 309 98.74 0.46 0.47% 3010 99.83 0.13 0.13% 30

Total 5 77.65 3.19 4.11% 606 86.25 2.77 3.21% 607 91.65 1.98 2.16% 608 95.10 1.57 1.65% 609 97.86 1.41 1.44% 6010 99.09 1.14 1.15% 60

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Table 2: 95% Confidence Intervals - Weekly Fill Rate

Dependent Variable: Weekly Fill Rate (AVG)

74.939 .232 74.483 75.39583.959 .232 83.503 84.41590.054 .232 89.598 90.50994.000 .232 93.544 94.45696.981 .232 96.525 97.43698.341 .232 97.885 98.79680.361 .232 79.905 80.81788.538 .232 88.082 88.99393.253 .232 92.797 93.70996.195 .232 95.740 96.65198.738 .232 98.282 99.19399.831 .232 99.376 100.287

Inventory Target56789105678910

Disruption TypeDisruption

No Disruption

Mean Std. Error Lower Bound Upper Bound95% Confidence Interval

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Table 3: ANOVA Results Dependent Variable: Weekly Fill Rate (AVG)

20862.439b 11 1896.585 1177.589 .000 .974 12953.474 1.0002998596.755 1 2998596.755 1861827 .000 1.000 1861826.7 1.000

868.922 1 868.922 539.513 .000 .608 539.513 1.00019801.530 5 3960.306 2458.951 .000 .972 12294.757 1.000

191.986 5 38.397 23.841 .000 .255 119.204 1.000560.477 348 1.611

3020019.671 36021422.916 359

SourceCorrected ModelInterceptSS_SCDINV_TGTSS_SCD * INV_TGTErrorTotalCorrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Noncent.Parameter

ObservedPowera

Computed using alpha = .05a.

R Squared = .974 (Adjusted R Squared = .973)b.

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Figure 1: Structure of the supply chain model considered

Factory(Focal Point)

SuppliersTier 1

SuppliersTier 2

DistributionEchelon 1

DistributionEchelon 2

Upstream Supply Chain Downstream Supply Chain

Information FlowProduct Flow(Regular Source)Product Flow(Alternative Source)

Factory(Focal Point)

SuppliersTier 1

SuppliersTier 2

DistributionEchelon 1

DistributionEchelon 2

Upstream Supply Chain Downstream Supply Chain

Information FlowProduct Flow(Regular Source)Product Flow(Alternative Source)

Information FlowProduct Flow(Regular Source)Product Flow(Alternative Source)

24

Figure 2: Illustrative supply chain - overall schematic

Supplier 1

Supplier 2

Supplier 3

Plant

Customer 1

Customer 2

Customer 3

1 Week Transit Time

1 Week Transit Time

Demand = 250 units / week

Product

Part 1 Part 2 Part 3

Transit Time

Information Time / Order Processing Time

(1)

(1) (1) (1)

5 7 10 Days

5 7 10 Days

20 35 50 units per day

Supplier 1

Supplier 2

Supplier 3

Plant

Customer 1

Customer 2

Customer 3

1 Week Transit Time

1 Week Transit Time

Demand = 250 units / week

Product

Part 1 Part 2 Part 3

Transit Time

Information Time / Order Processing Time

(1)

(1) (1) (1)

5 7 10 Days5 7 10 Days

5 7 10 Days5 7 10 Days

20 35 50 units per day

20 35 50 units per day

25

Figure 3: Examples of single scenario plots for the non-disruption case

Scenario: No Disruption, Inventory Target = 5 Days

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Fill

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e (%

)

-

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1,000

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Pla

nt In

vent

ory

(Uni

ts)

Fill RatePlant Inventory

Scenario: No Disruption, Inventory Target = 6 Days

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Week

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Rate

(%)

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t Inv

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ry (U

nits

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Fill RatePlant Inventory

Scenario: No Disruption, Inventory Target = 7 Days

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Week

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Rate

(%)

-

500

1,000

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3,000Pl

ant I

nven

tory

(Uni

ts)

Fill RatePlant Inventory

Scenario: No Disruption, Inventory Target = 8 Days

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Week

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Rate

(%)

-

500

1,000

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Pla

nt In

vent

ory

(Uni

ts)Fill Rate

Plant Inventory

Scenario: No Disruption, Inventory Target = 9 Days

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Week

Fill

Rat

e (%

)

-

500

1,000

1,500

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3,000

Plan

t Inv

ento

ry (U

nits

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Fill RatePlant Inventory

Scenario: No Disruption, Inventory Target = 10 Days

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Week

Fill

Rate

(%)

-

500

1,000

1,500

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t Inv

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ry (U

nits

)Fill RatePlant Inventory

26

Figure 4: Examples of single scenario plots for the disruption case

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity, Inventory Target = 5 Days

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Week

Fill

Rate

(%)

-

500

1,000

1,500

2,000

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3,000

Plan

t Inv

ento

ry (U

nits

)

Fill RatePlant Inventory

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity, Inventory Target = 6 Days

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Week

Fill

Rat

e (%

)

-

500

1,000

1,500

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Pla

nt In

vent

ory

(Uni

ts)

Fill RatePlant Inventory

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity,

Inventory Target = 7 Days

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Week

Fill

Rate

(%)

-

500

1,000

1,500

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3,000

Plan

t Inv

ento

ry (U

nits

)

Fill RatePlant Inventory

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity. Inventory Targets = 8 Days

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

Week

Fill

Rat

e (%

)

-

500

1,000

1,500

2,000

2,500

3,000

Pla

nt In

vent

ory

(Uni

ts)

Fill RatePlant Inventory

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity,

Inventory Target = 9 Days

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100.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

Week

Fill

Rate

(%)

-

500

1,000

1,500

2,000

2,500

3,000

Plan

t Inv

ento

ry (U

nits

)Fill RatePlant Inventory

Scenario: Single Disruption, Week 18, Duration 2 Weeks, 0% Capacity , Inventory Target = 10 Days

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100.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

Week

Fill

Rate

(%)

-

500

1,000

1,500

2,000

2,500

3,000

Plan

t Inv

ento

ry (U

nits

)Fill RatePlant Inventory

27

Figure 5: ANOVA Profile Plots