Uncertainty Modelling in Risk-averse
Supply Chain Systems Using
Multi-objective Pareto Optimization
Heerok Banerjee
University of Antwerp, Belgium
Heerok.Banerjee@student.uantwerpen.be
Abstract
Risk modelling along with multi-objective optimization problems have been at the
epicenter of attention for supply chain managers. In this paper, we introduce a dataset
for risk modelling in sophisticated supply chain networks based on formal mathematical models. We have discussed the methodology and simulation tools used to synthesize
the dataset. Additionally, the underlying mathematical models are discussed in granular
details along with providing directions to conducting statistical analyses or neural machine learning models. e simulation is performed using MATLAB ™Simulink and
the models are illustrated as well.
Keywords— Supply Chain Management (SCM), Supply Chain Risk Management (SCRM), Risk
Modelling, Time-series Analysis, Machine Learning
1 Summary
e emergence of business intelligence has broadly reinforced the interplay among business entities in
the digital realm. ese AI tools are undoubtedly powerful in employing self-learning paradigms to facilitate convenient services but such tools still remain inadequate to reduce the impact of inevitable risks
involved in business operations. In context to Supply Chain Risk Management (SCRM), it is therefore
an open problem to eliminate and more significantly, optimize the impact of such risky operations that
have been an evolutionary target for supply chain managers. is dataset is primarily targeted to support self-learning models and evolutionary algorithms for estimating non-linear functions and trends
in supply chain systems. e Time-series sequence consists of 6 Lakh timesteps of seven attributes
namely, Timestamp, RI_Supplier1, RI_Distributor1, RI_Manufacturer1, RI_Retailer1, Total_Cost,
SCMstability_category. e time-series sequence is generated by simulating a multi-echelon supply
chain network in MATLAB ™with three suppliers, one distributor, one manufacturer and one retailer.
An arbitrary demand is introduced to the supply chain model and selective features such as total cost and
risk index are calculated at each time-step. Section 2.2 describes the features and their mathematical
formulation extensively. Finally, the obtained results are tabulated and exported as a dataset.
2 Dataset for Modelling Risks in Supply Chain Systems
2.1 Scope of the Dataset
e purpose of this dataset is intended for academic purposes only. e dataset is not claimed to resemble the nature of a real-time supply chain networks. After a careful literature review, a set of succinctly
defined mathematical models were selected to formulate the attributes and yield an empirical dataset.
Hence, the dataset is generated based on limited assumptions on the underlying principles in supply
chain networks.
1
is dataset is suitable for training machine learning models for time-series analyses and estimation
of non-linear functions in risk-averse supply chain networks. It is thoroughly verified with absolute minimal outliers and could serve as an appropriate source for time-series analysis and evaluating non-linear
auto-regressive models. As described in section 2.2, the calculated risk indices of supplier, distributor, manufacturer and retailer are non-linear in nature due to intended disruptions in the supply chain.
Considering all the variables as cross-sectional data and performing trend analysis or regression analysis,
a broader investigation on the nature of the risks involved in supply chain networks can be carried out.
2.2 Mathematical Modelling
In this section, a deterministic mathematical model for each attribute in the supply chain network is
discussed.
For a given supply chain with 4 echelons: Supplier, Distributor, Manufacturer, Retailer and selective
activities such as sourcing or supplying raw material to each component, assembling final products and
delivering to destination markets, each component has its own cost, lead-time and associated risk.
1. e Risk Index (RI) is derived from the model proposed in [1], and can be mathematically
formulated as:
RIsupplier =
n
∑
αsij . βsij . (1 − (1 −
i=1
m
∏
P (S̃ij ))
j=1
(1)
where, αsij is the consequence to the supply chain if the ith supplier fails,
βsij is the percentage of value added to the product by the ith supplier,
P (S̃ij ) denotes the marginal probability that the ith supplier fails for j th demand,
Similarly, the risk indices for the rest of the components can be calculated as:
RIdistributor = αdriski . βmi . (1 − (1 − P (M̃j )))
(2)
RImanuf acturer = αmriski . βmi . (1 − (1 − P (M̃j )))
(3)
RIretailer = αrriski . βri . (1 − (1 − P (R̃j )))
(4)
2. For each set of demand, the cumulative risk index of the supply chain network can be calculated
as:
T RI = w1 . RIsupplier + w2 . RIdistributor + w3 . RImanuf acturer + w4 . RIretailer
where, w1 , w2 , w3 , w4 are arbitrary weights such that w1 + w2 + w3 + w4
(5)
=1
3. e risk fluctuation subjected to the supply chain network is generated by a sine-wave
generator, and is mathematically gives as :
δ˜r = A. sin(ωt + φ) + Bi
where, δ˜r denotes the absolute value of risk fluctuation,
A denotes the peak amplitude of disruption,
ω denotes the angular frequency, t denotes time,
φ denotes the phase and Bi denotes a bias
2
(6)
4. e total supply chain cost can be calculated as [2]:
TC = ξ ×
N
∑
i=1
( µi .
Ni
∑
Cij yij )
j=1
(7)
where, N is the number of components,
ξ denotes the period of interest,
µi is the average demand per unit time,
Cij is the cost of the j th resource option for the ith component,
yij is a binary variable denoting whether the ith component is a participant for the j th
resource option
5. For each couple of normalized risk index and total cost of the supply chain, the main
objective function Z is given as [2]:
Z = w1 . T Cn + w2 . T RIn
(8)
where, T Cn is the normalized total cost,
T RIn is the normalized total risk index,
w1 , w2 are the weights ; w1 + w2 = 1
3 Setup
In Quasi-experimental evaluations, a system is evaluated by intervening the model parameters with
reference to variable constraints. Particularly in context to supply chains, a supply chain model is subjected to either risk fluctuations or demand variations and the resiliency of the supply chain network
is recorded. For modelling this proposed scenario, we have used MATLAB ™simulink library. e
psuedo supply chain models are given below in fig. 1 and fig. 2:
Figure 1: Psuedo Supply Chain Model using linear Diophantine evaluator
In Fig. 1, A linear Diophantine evaluator model is illustrated to emulate simple supply chain networks. e demand is fed to the polynomial evaluator subsystem which determines the suitable coefficients for the Diophantine equation. Consequently, the residual, denoted by κ0 is determined by
3
subtracting the demand from the real value of the cost function. Additionally, the probability associated
with the risk is calculated by dividing the residual with the demand. e output is the risk magnitude.
Figure 2: Psuedo Supply Chain Model using Fuzzy Inference system
In Fig.2, A Fuzzy Inference System (FIS) is used to evaluate the risk factor. A FIS is a rule-based
system that operates on linguistic variables, which represents uncertainty or vagueness in the magnitude
of the input variables. e FIS input parameters are demand, residual loss, probability of risk and the
output is the risk magnitude.
Figure 3: Quasi-Experimental setup for Risk Analyses in Supply Chain Networks
As shown in Fig. 3, a sine-wave generator is used to synthesize a sinusuidol waveform expressed
in equation 6 with amplitude equal to ’A’. e value ’A’ denotes the peak magnitude of disruptions to
be introduced to the supply chain system in order to evaluate its resiliency. e demand is generated as
a discrete waveform with constant amplitude of value ’d’. Both the input signals are introduced to the
pseudo supply chain model, which then evaluates the risk factor.
4 Citing the Dataset
e dataset is available online in Mendeley Data library.
To manually add the dataset in the bibiliography, use the following :
”Banerjee, Heerok; Saparia, Grishma; Ganapathy, Velappa; Garg, Priyanshi; Shenbagaraman, V. M.
(2019), “Time Series Dataset for Risk Assessment in Supply Chain Networks”, Mendeley Data, v2
http://dx.doi.org/10.17632/gystn6d3r4.2”
4
References
[1] Neureuther, Brian D., and George Kenyon. ”Mitigating supply chain vulnerability.” Journal of
marketing channels 16.3 (2009): 245-263.
[2] Mastrocinque, Ernesto, et al. ”A multi-objective optimization for supply chain network using
the bees algorithm.” International Journal of Engineering Business Management 5.Godište 2013
(2013): 5-38.
[3] Banerjee, Heerok; Saparia, Grishma; Ganapathy, Velappa; Garg, Priyanshi; Shenbagaraman, V. M.
(2019), “Time Series Dataset for Risk Assessment in Supply Chain Networks”, Mendeley Data,
v2 http://dx.doi.org/10.17632/gystn6d3r4.2
[4] Banerjee, Heerok. ”A Comparative Study On Statistical And Neural Approaches for Optimizing
Supply Chain Management (SCM) Systems.” (2019).
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Uncertainty Modelling in Risk-averse Supply Chain Systems Using Multi-objective Pareto Optimization
Risk modelling along with multi-objective optimization problems have been at the epicenter of attention for supply chain managers. In this paper, we introduce a dataset for risk modelling in sophisticated supply chain networks based on formal mathematical models. We have discussed the methodology and simulation tools used to synthesize the dataset. Additionally, the underlying mathematical models are discussed in granular details along with providing directions to conducting statistical analyses or neural machine learning models. The simulation is performed using MATLAB ™Simulink and the models are illustrated as well. ...Read more
