Keywords

1 Introduction

Systemic approaches to risk management in the supply chain (SC) became a visible research topic over the past decade. Fires, explosions, tsunami, and strikes at production plants, distribution centers, and transportation channels are typical disruptions in supply chains (SC). The ripple effect in the SC occurs if a disruption cannot be localized and cascades downstream impacting SC performance (Ivanov et al. 2014a). Methodical elaborations on the evaluation and understanding of low-frequency-high-impact disruptions are, therefore, vital for understanding and further development of network-based supply concepts (Tomlin 2006; Stecke and Kumar 2009; Liberatore et al. 2012; Sawik 2016; Ivanov and Rozhkov 2017).

It has been extensively documented in literature that severe disruptions may ripple quickly through global SCs and cause losses in SC performance that can be measured by such KPIs (key performance indicators) as revenues, sales, service level, and total profits (Schmitt and Singh 2012; Simchi-Levi et al. 2015; Snyder et al. 2016; Schmitt et al. 2017; Ivanov 2018). Such risks are a new challenge for research and industry who face the ripple effect that arises from vulnerability, instability, and disruptions in SCs (Liberatore et al. 2012; Ivanov et al. 2014a, b; Ho et al. 2015; Ivanov et al. 2017a, b, c). As an opposite to the well-known bullwhip effect that considers high-frequency-low-impact operational risks, the ripple effect describes low-frequency-high-impact disruptive risks (Ivanov et al. 2014a; Simchi-Levi et al. 2015; Sokolov et al. 2016; Snyder et al. 2016; Han and Shin 2016, Ivanov et al. 2017b; Sawik 2017; Cavalcantea et al. 2019; Hosseini et al. 2019a, b).

Recent studies have extensively considered disruption risks in light of the impact of disruption propagation (Wilson 2007; Lim et al. 2013; Ivanov et al. 2013, 2014b; Paul et al. 2014; Ivanov 2017). Previous studies also suggested several measures for quantifying disruption risks (Zobel 2011; Basole and Bellamy 2014; Han and Shin 2016; Lin et al. 2017). However, single-stage disruptions have mostly been considered. Disruption propagation has been ignored and a method for ripple effect quantification has not yet been developed. In addition, there are only a few studies that incorporate the recovery stage into the performance impact assessment. We are not aware of any published research that considers ripple effect quantification with SC recovery considerations.

The objective of this study is to quantify the ripple effect in the SC with recovery considerations. The remainder of this paper is organized as follows. Section 2 analyzes recent literature. Section 3 considers the methodology and modeling approach. Section 4 is devoted to the model presentation and experimental calculation. Section 5 considers the performance impact assessment and managerial insights. The paper concludes by summarizing the most important findings and outlining future research needs.

2 Literature Review

We structure the literature review according to performance impact assessment techniques and engineering methodologies to model severe SC disruptions. Two engineering methodologies—optimization and simulation—dominate studies on SC performance impact assessment in light of severe disruptions (Blackhurst et al. 2018; Ivanov 2019; Pavlov et al. 2019; He et al. 2018; Talluri et al. 2013; Käki et al. 2015; Hosseini and Barker 2016; Dolgui et al. 2019; Ojha et al. 2018; Pavlov et al. 2018). Petri nets have been applied to analyze disruption propagation through the SC and to evaluate the performance impact of disruptions (Wu et al. 2007). They allow the study of how changes disseminate through a SC and calculate the impact of the attributes by determining the states that are reachable from a given initial marking in a SC. Wilson (2007) considered transportation disruptions in a multistage SC in order to reveal the ripple effect’s impact on fulfilment rate and inventory fluctuations. The findings suggest that transportation disruptions between the Tier-1 supplier and the warehouse have the greatest performance impact.

Tuncel and Alpan (2010) extended the body of knowledge by incorporating multiple disruption scenarios (disruptions in demand, transportation, and quality). In addition, this study also considers recovery actions and the performance impact of such mitigation strategies. Carvalho et al. (2012) presented a simulation study for a four-stage automotive SC. Focusing on the research question of how different recovery strategies influence SC performance in the event of disruptions, the authors analyzed two recovery strategies and six disruption scenarios. The scenarios differ in terms of presence or absence of a disturbance and presence or absence of a mitigation strategy. The performance impact was analyzed according to the lead time ratio and total SC costs.

Ivanov et al. (2014b) used a hybrid optimization-control model for simulation of SC recovery policies for multiple disruptions in different periods in a multistage SC. The developed approach allows simultaneous performance impact analysis of SC disruptions and recovery policies simulation. Basole and Bellamy (2014) used the measure “number of healthy nodes” to quantify the level of risk diffusion as the relation of the number of healthy nodes at time t to the network size.

With regards to robustness and resilience analysis, Nair and Vidal (2011) studied SC robustness against disruptions using graph-theoretical topology analysis. They studied twenty SCs which were subjected to random demand. The performances of the SCs were evaluated by considering varying probabilities of the random failures of nodes and targeted attacks on nodes. Furthermore, the analysis of the study also included the severity of these disruptions by considering the downtime of affected nodes. The results were obtained using multi-agent simulation. Furthermore, the authors went into detail on the impact of SC structural design on robustness in the presence of both demand and disruption uncertainty.

Zhao et al. (2011) quantified network connectivity and accessibility with the help of the largest connect component and average and maximum path length. Zobel (2011) computed predicted resilience assuming a sudden onset disruption and linear recovery behavior. Zobel (2014) extended to more generalized case considering nonlinearity and average loss per time unit.

Simchi-Levi et al. (2015) developed a risk-exposure index for the case of an automotive SC. The index computation is based on two models—time-to-recovery and time-to-survive—in order to the assess performance impact of a disruption in the SC. Raj et al. (2015) analyzed SC resilience based on a survival model to represent a time period from the system failure to operate to the time the system returns to its function (i.e., recovery). The input to the model is a failure event; the output of the model is the recovery time. The model allows a quantitative measurement of SC resilience in terms of recovery time.

Sokolov et al. (2016) quantified the ripple effect in the SC with the help of selected indicators from graph theory and developed a static model for performance impact assessment of disruption propagation in a distribution network. Han and Shin (2016) evaluated the structural robustness of the SC in random networks and compared this with the likelihood of network disruption resulting from random risk.

Ivanov et al. (2016) extended the performance impact assessment and SC plan reconfiguration with consideration of the duration of disruptions and the costs of recovery. They analyzed seven proactive SC structures, computed recovery policies to re-direct material flows in the case of two disruption scenarios, and assessed the performance impact for both service level and costs with the help of a SC (re)planning model containing elements of control theory and linear programming. This study reveals the impact of different parametrical and structural resilience measures on SC service level and efficiency. In the current paper, we use the basic model and the proactive strategies for SC design in Sect. 4 in order to analyze the performance impact of the ripple effect in Sect. 5.

The reliability of a multistage SC is evaluated by Lin et al. (2017) as the probability that market demand, and therefore sufficient commodity delivery, can be met by the SC through multiple stations of transit within the appropriate time frame. In this study, system reliability acts as the delivery performance index and is assessed by the number of minimal paths. Ivanov et al. (2018) developed a control-theoretic method to assess SC resilience with the consideration of recovery policies using attainable sets.

From the given literature, it can be observed that the scope of SC rippling and its impact on economic performance depends both on robustness reserves (e.g., redundancies like inventory or capacity buffers), flexibility in products and processes, disruption duration, and the speed and scale of recovery measures. Despite significant advancements in this research field, ripple effect assessment with SC recovery considerations is still an under-researched area and presents a promising field for future research.

3 Problem Statement and Research Methodology

We study a four-stage SC over time and consider both performance impact assessment and recovery decisions. The SCD comprises Tier 2 suppliers, Tier 1 suppliers, assembly plants, and markets. The disruptions and recovery policies are considered as given scenarios, the production and transportation quantities are the decision variables, and SC sales (revenue) is the KPI for measuring the estimated annual magnitude of the ripple effect.

The optimization model is developed to replan SC flows to maximize SC sales. The model aims to find the aggregate product flows to be moved from suppliers through the intermediate stages to the markets subject to revenue maximization (i.e., lost sales minimization) under (i) constrained capacities and processing rates, (ii) SC disruptions, and (iii) SC recovery for a multi-period case.

The modeling approach is the optimization-based simulation that allows simultaneous re-computing of the material flows in a multistage SC after a disruption and a comparison of the performance impact of different SCDs. Based on the optimization results, the performance impact of disruptions is computed.

For the computation of performance impact, we suggest introducing an index of performance impact (PI) that represents the relation between the planned KPI in a disruption-free mode and the real KPI in the disruption case (Eq. 1):

$$ PI = \frac{{ KPI_{plan} }}{{KPI_{disruption} }} $$
(1)

Such an index can be computed for each i-node in the SC, i = 1,…. N. Subsequently, we can compute a product of the i-PIs in order to calculate the overall PI in the SC (Eq. 2):

$$ PI_{general} = \mathop \prod \limits_{i = 1}^{N} PI $$
(2)

The organization of the rest of this manuscript is as follows. First, we compute optimal SC replanning for two disruption scenarios and KPI. In order to make the PI analysis more depictive, we restrict ourselves to the analysis of estimated annual magnitude in terms of the revenue at markets. Second, we perform the first step for six proactive strategies in SC design. Finally, we compare the PI of seven SC designs (i.e., the initial SC design and six proactive strategies) and draw conclusions on the ripple effect in these SC designs along with recommendations on the proactive strategy.

4 Mathematical Model

The SC design model can be represented as follows (Table 1).

Table 1 Supply chain design formalization
Full size table

Objective function

$$ J_{\chi 2} = \sum\limits_{\rho = 1}^{p} {\lambda_{\rho } \sum\limits_{i = 1}^{{n_{\chi } }} {\sum\limits_{k = 1}^{{L_{\chi } }} {g_{\chi i\rho k}^{ - } } } } ; $$
(3)

The objective function describes throughput maximization (i.e., sales indicator).

Constraints:

$$ \begin{aligned} I_{\chi i\rho k} + y_{\chi i\rho (k - 1)} + \sum\limits_{{j \in N_{\chi ik}^{ - } }} {\omega_{\chi ji\rho k} \cdot u_{\chi ji\rho k} } + \phi_{\chi i\rho k}^{ + } \cdot \vartheta_{\chi i\rho k}^{ + } = \hfill \\ = \phi_{\chi i\rho k}^{ - } \cdot \vartheta_{\chi i\rho k}^{ - } + \sum\limits_{{j \in N_{\chi ik}^{ + } }} {\omega_{\chi ij\rho k} \cdot u_{\chi ij\rho k} } + y_{\chi i\rho k)} + z_{\chi i\rho k} \hfill \\ \end{aligned} $$
(4)
$$ (\sum\limits_{{j \in N_{\chi ik}^{ + } }} {x_{\chi ij\rho k} - } \sum\limits_{{j \in N_{\chi ik}^{ - } }} {x_{\chi ji\rho k} } ) + (y_{\chi i\rho k)} - y_{\chi i\rho (k - 1)} ) + (g_{\chi i\rho k}^{ - } - g_{\chi i\rho k}^{ + } ) + z_{\chi i\rho k} = I_{\chi i\rho k} $$
(5)
$$ \begin{aligned} & 0 \le x_{\chi ij\rho k} \le \omega_{\chi ij\rho k} \cdot (t_{k} - t_{k - 1} ),0 \le \sum\limits_{\rho = 1}^{p} {y_{\chi i\rho k)} \le V_{\chi i} } ,0 \le g_{\chi i\rho k}^{ - } \le \phi_{\chi i\rho k}^{ - } \cdot (t_{k} - t_{k - 1} ), \\ & 0 \le g_{\chi i\rho k}^{ + } \le \phi_{\chi i\rho k}^{ + } \cdot (t_{k} - t_{k - 1} ),z_{\chi i\rho k} \ge 0. \\ \end{aligned} $$
(6)

Equations (4) and (5) describe the flow balances of the product ρ subject to the node Aχi and ensure that the sum of the outgoing flow (subscript (-)), inventory, and return flow should equal the incoming flow (subscript (+)). Equation (6) contains capacity and nonnegativity constraints.

5 Experimental Results

We consider a four-stage SC in the automotive industry. Two Tier 2 suppliers deliver speedometers to a Tier 1supplier that supplies two assembly plants with cockpits. The assembly plants deliver cars to one of two markets. SC structural elements can become fully or partially unavailable for a certain period of time. This capacity reduction may have performance impact on sales in the markets.

For computational experiments, the following data set was used (Table 2).

Table 2 Input data
Full size table

In the first scenario, which we call “optimistic”, a disruption at assembly plant #2 happens in the second period and destroys the capacity of this plant 100%. This disruption lasts two periods. In period #4, the capacity of this production plant is recovered 100%. In addition, in period #3 a fire at the Tier 2 supplier #1 happens that makes deliveries from this supplier to the Tier 1 supplier in period #3 impossible. In the next period, deliveries can run in normal mode again. Finally, due to strikes at a railway company in periods #4 and #6, the transportation channels between the assembly plant #1 and market #1 and between the Tier 2 supplier #2 and the Tier 1 supplier become unavailable, respectively (see Fig. 1).

Fig. 1
figure 1

“Optimistic” disruption scenario

Full size image

In Fig. 1, the following parameters are represented:

  • Tier 2 supplier #1: node #1

  • Tier 2 supplier #2: node #2

  • Tier 1 supplier: node #3

  • Assembly plant #1: node #5

  • Assembly plant #2: node #6

  • Market #1: node #8

  • Market #2: node #9

Maximum processing throughput capacities are marked in rectangles, maximum transportation throughput capacities are presented on the arcs, and maximum storage capacities are depicted in triangles. The disruptions are marked red. In Fig. 2, the so-called “pessimistic scenario” is shown.

Fig. 2
figure 2

“Pessimistic” disruption scenario

Full size image

The following alternative proactive strategies for SC design can be considered:

  1. 1.

    Increase in the flexibility of supplier #2 so that it delivers, under normal conditions, 100 units in each period and can extend the quantity to 400 units if needed

  2. 2.

    New backup supplier is introduced at the Tier 1 stage

  3. 3.

    A backup assembly plant is introduced

  4. 4.

    Multiple sourcing strategy with alternative transportation channels

  5. 5.

    Increase in warehouse storage and processing capacity

  6. 6.

    Increase in transportation channel throughput capacity

The summary of these measures is shown in Fig. 3.

Fig. 3
figure 3

Possible extensions to SC structure (Ivanov et al. 2016)

Full size image

In regard to the processing and transportation throughput capacity of new SC design elements, we assume the following: throughput capacity of new transportation channels is 120% of the processing throughput capacity of the outgoing node; processing capacity at node #4 is 250 units in each period, and processing capacity at node #7 is 150 units in each period.

In Fig. 4, the result of optimal replanning for the initial SC design (cf. Figures 1 and 2) subject to the given data set (cf. Table 2) is presented.

Fig. 4
figure 4

Replanning results for optimistic scenario

Full size image

In Fig. 3, the production and shipment quantities of the speedometers, cockpits, and cars are depicted and marked green, red, and blue, respectively. The yellow triangles show the storage capacities and their actual utilization. The grey rectangles depict the manufacturing maximum and used processing capacity, respectively. The numbers on the arcs represent the maximum transportation capacities and their actual utilization. The red nodes and channels are disrupted. The yellow arrows at nodes #8 and #9 depict the delivered quantity of goods at the markets.

In Tables 3 and 4 and Figs. 5 and 6, the planning results are summarized for two scenarios.

Table 3 Performance impact of different proactive policies in optimistic scenario
Full size table
Table 4 Performance impact of different proactive policies in pessimistic scenario
Full size table
Fig. 5
figure 5

Revenue impact of disruptions

Full size image
Fig. 6
figure 6

Lost sales impact of disruptions

Full size image

It can be observed from Tables 3 and 4 and Figs. 5 and 6 that structural changes significantly impact SC performance. The highest revenue of $140,985 in the optimistic scenario can be achieved if we apply the SC design according to proactive strategy #5, i.e., an increase in warehouse storage and processing capacity is needed.

The highest revenue of $85,800 in the pessimistic scenario can be achieved if we apply the SC design according to proactive strategies #4 and #6, i.e., introduction of alternative transportation channels or/and increase in transportation capacity of the existing channels. To make a final decision, the costs of these proactive measures need to be analyzed.

Further, it can be observed that lost sales are much higher in the “pessimistic” scenario. Such a scenario comparison allows the drawing of conclusions on the performance impact of disruptions at different parts in the SC. For example, the Tier 2 supplier #1 (node #1), the production plant #1 (node #5), and the transportation channel between the node #5 and node #8 need to be considered as critical elements in the SC design. According to the study of Simchi-Levi et al. (2015), dual sourcing policies, risk-sharing contracts, and continuous capacity monitoring can be recommended for these SC elements.

6 Performance Impact of the Ripple Effect and Managerial Insights

Now, we use the computation results from Sect. 4 and compute the PI index using Eqs. 1 and 2. The diagrams with the computational results for seven SC design for both scenarios can be found in an online supplement. First, we compute PI for two markets individually using Eq. 1. In the next step, we aggregate these partial PI to general PI using Eq. 2. We consider SC sales (revenue) as the KPI for measuring the estimated annual magnitude of the ripple effect. To make the analysis more depictive, we restrict ourselves to the PI consideration at the markets without PI analysis at the intermediate stage in the SC. This is an admissible restriction since the revenue KPI is directly related to the market stage in the SC. The results of PI computation are shown in Table 5.

Table 5 PI computation results
Full size table

Let us present these results graphically and analyze their managerial implications (Figs. 7, 8 and 9).

Fig. 7
figure 7

PI computation for individual markets

Full size image
Fig. 8
figure 8

PI computation for individual markets and different SC designs

Full size image
Fig. 9
figure 9

Comparison of individual and total PI computation

Full size image

Table 5 and Figs. 7, 8 and 9 can be used as a dashboard for SC design comparison in regard to the ripple effect. The results can also help to analyze the disruption impact at different markets individually in order to derive recommendations for securing supplier and customer satisfaction. For the given data set it can be observed that the SC for market #2 (node #9) is much more resilient and was less exposed to the ripple effect compared to market #1 (node #8). In both scenarios, the PI in regard to market #2 (node #9) does not exceed 1.51 while the maximum PI in regard to market #1 (node #8) is 6.04.

In the case of the optimistic scenario, the lowest ripple effect can be observed in SC design #6 both at the market #1 (node #8) and at the market #2 (node #9), PI = 1.14284 and PI = 1.3744, respectively. In the case of the pessimistic scenario, the lowest ripple effect can be observed in the initial SC design at market #1 (node #8, PI = 3.295455), while at market #2 (node #9), minimum PI = 1.133929 for SC designs #4 and #6.

In total cumulative PI in the optimistic scenario, a large gap between the minimum PI (i.e., initial SCD) and PI for other SC designs can be observed in Fig. 9. At the same time, the total PI values in the pessimistic scenario are very close to each other with a small advantage for SC design #6.

Therefore, PI computation supports the results of the optimization model described in Sect. 4. For the considered example, it becomes obvious that market #1 (node #8) is highly exposed to the ripple effect in the negative scenario while market #2 (node #9) shows disruption-resistance and performs in the pessimistic scenario even better than in the optimistic one.

In the joint analysis of two markets, the initial SC design can be recommended since it exhibits the lowest ripple effect. At market #8, risk-sharing contracts can be recommended with the customers. In addition, storage capacity extensions and a higher safety stocks can be applied in this market.

7 Conclusions

The experiments with the optimization model and PI index analysis depict how disruption risks may result in the ripple effect and structure dynamics in the SC. From the developed model and experiments, it can be observed how the scope of the rippling and its performance impact depend on the SC design structure.

The results of this study are twofold. First, with the help of the developed approach, severe disruptions in the SC can be modeled subject to temporary unavailability of some SC elements and their recovery. Second, a method to compare SC designs with a performance impact assessment of the ripple effect has been developed.

The developed method of ripple effect evaluation helps to analyze effective ways to recover and reallocate resources and flows in the SC and to select a resilient SC design. As such, the model can be used by SC risk specialists to analyze the performance impact of different resilience and recovery actions and adjust mitigation and recovery policies with regard to critical SC design elements and SC planning parameters.

In the future, PI computation can be extended in regard to multiple objectives. In addition, PI can be evaluated individually at each SC echelon. Finally, markets can be modeled as heterogeneous entities allowing for competitive elements.