Catastrophe insurance and flexible planning for supply chain disruption management: a stochastic simulation case study

Figures & data

Figure 1. SC structure.

The structure of the multi-echelon global supply chain network and flows of materials, parts, and finished products from upstream supply chain nodes to downstream supply chain nodes.

Figure 2. The global SC network.

A Google maps depiction of part of the SC network. Links between nodes only represent connections, not routes.

Figure 3. Stages and timeline.

Stages and timeline of the two-stage stochastic programming model.

Table 1. Sets.

Set	Definition
$\mathcal{I}$	Set of nodes, $\mathcal{I}={\mathcal{I}}^{Sup}\cup {\mathcal{I}}^{Port}\cup {\mathcal{I}}^{Asm}\cup {\mathcal{I}}^{Dem}$
${\mathcal{I}}^{Sup}$	Set of supply nodes, ${\mathcal{I}}^{Sup}\subset \mathcal{I}$
${\mathcal{I}}^{Port}$	Set of ports, ${\mathcal{I}}^{Port}\subset \mathcal{I}$
${\mathcal{I}}^{Asm}$	Set of assembly centres, ${\mathcal{I}}^{Asm}\subset \mathcal{I}$
${\mathcal{I}}^{Dem}$	Set of demand nodes/sellers, ${\mathcal{I}}^{Dem}\subset \mathcal{I}$
$\mathcal{A}$	Set of transportation links, $\mathcal{A}\subseteq \mathcal{I}\times \mathcal{I}$
$\mathcal{M}$	Set of transportation modes
${\mathcal{P}}^F$	Set of finished products
${\mathcal{P}}^C$	Set of components/parts
$\mathcal{P}$	Set of all products, $\mathcal{P}={\mathcal{P}}^F\cup {\mathcal{P}}^C$
${\mathcal{P}}_i$	Set of products produced/processed at node $i\in \mathcal{I}$
$\mathcal{T}$	Set of periods in the considered time horizon (see Figure 3), $\mathcal{T}={\mathcal{T}}^{Pre}\cup {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$
${\mathcal{T}}^{Pre}$	Set of periods before the first stage, ${\mathcal{T}}^{Pre}\subset \mathcal{T}$
${\mathcal{T}}^{1st}$	Set of periods in the first stage, ${\mathcal{T}}^{1st}\subset \mathcal{T}$
${\mathcal{T}}^{2nd}$	Set of periods in the second stage, ${\mathcal{T}}^{2nd}\subset \mathcal{T}$
Ω	Set of scenarios
${\mathcal{T}}_{i\omega }^{Cata}$	Set of time periods when node $i\in \mathcal{I}$ is interrupted in scenario $\omega \in \mathrm{\Omega }$
${\mathcal{T}}_{i\omega }^{Loss}$	Set of time periods constituting the time span within which all products at node $i\in \mathcal{I}$ will be destroyed in scenario $\omega \in \mathrm{\Omega }$ (see Figure 3)

Table 2. Parameters.

Parameter	Definition
$V_{pi}$	Value of products $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$
$C_{pi}$	External purchasing cost for per unit of product $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$
$C_{pi}^I$	Storage cost per unit of product $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$
$C^H$	Capital holding cost coefficient
$T_{pi}$	Processing time for product $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$
$T_{ijm}$	Transport time for transportation link $(i,j)\in \mathcal{A}$ with transportation mode $m\in \mathcal{M}$
$R_{pq}$	Number of part $p\in {\mathcal{P}}^C$ required to make one unit of product $q\in \mathcal{P}$
$C_{pi}^L$	Cost of producing/processing one unit of product $p\in {\mathcal{P}}_i$ at node $i\in {\mathcal{I}}^{Sup}\cup {\mathcal{I}}^{Asm}$
$C_{pijm}$	Shipping cost for transportation link $(i,j)\in \mathcal{A}$ with transportation mode $m\in \mathcal{M}$ for one unit of product $p\in {\mathcal{P}}_i\cap {\mathcal{P}}_j$
$L_{pi}$	Coefficient of capacity consumption to make one unit of product $p\in {\mathcal{P}}_i$ at location $i\in \mathcal{I}$
$L_i^{Cap}$	Capacity at node $i\in \mathcal{I}$ per time period
$D_{tpi\omega }$	Demand of product $p\in {\mathcal{P}}_i\cap {\mathcal{P}}^F$ at node $i\in \mathcal{I}$ in period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ in scenario $\omega \in \mathrm{\Omega }$
$C_{pi}^{-}$	Stockout cost per unit of product $p\in {\mathcal{P}}_i\cap {\mathcal{P}}^F$ at node $i\in \mathcal{I}$
$h_{tpi}^0$	Inventory of product $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$ in time period $t_0$
$V^{Res}$	The ratio of the residual value of products in inventory at the end of the plan horizon to the market value.
$I^{Back}$	The ratio of damage costs that would be compensated by the insurer.
$R_{\omega }$	Probability of scenario $\omega \in \mathrm{\Omega }$
$T_{tpi\omega }^F$	Time period where products $p\in {\mathcal{P}}_i$, previously scheduled to be processed in time period $t\in \mathcal{T}$ at node $i\in \mathcal{I}$, will be finished in scenario $\omega \in \mathrm{\Omega }$
$t_0$	The beginning of the first stage (see Figure 3)
$t_1$	The end of the first stage (see Figure 3)
$t_f$	The end of the second stage (see Figure 3)

Table 3. Variables.

Variable	Definition	Note
$x_{tpi\omega }$	Production quantity of product $p\in {\mathcal{P}}_i$ at location $i\in \mathcal{I}\setminus {\mathcal{I}}^{Dem}$ started in time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	non-negative
$z_{tpijm\omega }$	Quantity of product $p\in {\mathcal{P}}_i\cap {\mathcal{P}}_j$ transported on transportation link $(i,j)\in \mathcal{A}$ with transportation mode $m\in \mathcal{M}$, launched in time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	non-negative
$x_{tpi}$	Production quantity of product $p\in {\mathcal{P}}_i$ at location $i\in \mathcal{I}\setminus {\mathcal{I}}^{Dem}$ started in time period $t\in {\mathcal{T}}^{1st}$	first-stage variable
$z_{tpijm}$	Quantity of product $p\in {\mathcal{P}}_i\cap {\mathcal{P}}_j$ transported on transportation link $(i,j)\in \mathcal{A}$ with transportation mode $m\in \mathcal{M}$ started in time period $t\in {\mathcal{T}}^{1st}$	first-stage variable
$h_{tpi\omega }$	Inventory of product $p\in {\mathcal{P}}_i$ at node $i\in \mathcal{I}$ at the end of time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	non-negative auxiliary variable
$h_{tpi\omega }^{Dem}$	Inventory of final product $p\in {\mathcal{P}}^F\cap {\mathcal{P}}_i$ at seller $i\in {\mathcal{I}}^{Dem}$ in time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	non-negative auxiliary variable
$h_{tpi\omega }^{-Dem}$	Stockout of final product $p\in {\mathcal{P}}^F\cap {\mathcal{P}}_i$ at seller $i\in {\mathcal{I}}^{Dem}$ in time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	non-negative auxiliary variable
$h_{tpi\omega }^{Loss}$	Destroyed inventory of final product $p\in {\mathcal{P}}^F\cap {\mathcal{P}}_i$ at seller $i\in {\mathcal{I}}^{Dem}$ in time period $t\in {\mathcal{T}}^{1st}\cup {\mathcal{T}}^{2nd}$ for scenario $\omega \in \mathrm{\Omega }$	auxiliary variable
$C_{t\omega }^{SC}$	SC costs for time period $t\in \mathcal{T}$ in scenario $\omega \in \mathrm{\Omega }$	dependent variable
$V_{ti\omega }^{Loss}$	Damage costs in time period $t\in \mathcal{T}$ at node $i\in \mathcal{I}$ caused by a catastrophe in scenario $\omega \in \mathrm{\Omega }$	dependent variable

Table 4. Experiment results.

Solutions	$I^{Back}$	$V^{Res}$	$T{C}^{SC}$ ${}^{}$	$C_{1st}$	$C_{2nd}$	$V_{Loss}$	$V_{Loss}\mathrm{\%}$ ${}^{}$	$\mathrm{\Delta }T{C}^{SC}\mathrm{\%}$ ${}^{}$	$\mathrm{\Delta }{C}_{1st}\mathrm{\%}$ ${}^{}$	CPU Time	Wall-clock Time
EF-100${}^{}$	0	0	172323	113173	59150	0	0	7.2%	28.3%	–	17901
	0	80%	101926	139832	−37906	0	0	7.7%	25.6%	–	16657
	80%	0	171782	115476	56306	4638	2.7%	6.9%	30.9%	–	18666
	80%	80%	101733	145317	−43583	5646	5.5%	7.5%	30.5%	–	17427
EF-40${}^{}$	0	0	175928	109514	66414	278	0.2%	9.5%	24.1%	–	3780
	0	80%	104714	135234	−30520	0	0	10.7%	21.4%	–	3805
	80%	0	175839	110754	65085	4946	2.8%	9.4%	25.6%	–	3495
	80%	80%	103402	139329	−35927	5953	5.8%	9.3%	25.1%	–	3710
EVS	0	0	291401	87984	203417	0	0	81.3%	−0.3%	100	–
	0	80%	216122	110944	105178	0	0	128.4%	−0.4%	101	–
	80%	0	291401	87984	203417	0	0	81.3%	−0.3%	101	–
	80%	80%	216122	110944	105178	0	0	128.4%	−0.4%	96	–
HCS	0	0	238320	102279	136041	0	0	48.3%	15.9%	20604	2183
	0	80%	165829	122942	42887	0	0	75.3%	10.4%	25516	2634
	80%	0	238320	102279	136041	0	0	48.3%	15.9%	25070	2575
	80%	80%	165829	122942	42887	0	0	75.3%	10.4%	22980	2344
WS${}^{}$	0	0	160685	88212	72473	0	0	–	–	–	–
	0	80%	94606	111361	−16755	0	0	–	–	–	–
	80%	0	160685	88212	72472	0	0	–	–	–	–
	80%	80%	94606	111361	−16755	0	0	–	–	–	–

${}^{}$$T{C}^{SC}$: expected SC costs (including both the first and the second stage) of the 1000-scenario

${}^{}$$V_{Loss}\mathrm{\%}$: the ratio of damage costs in SC costs (calculated by $V^{Loss}/T{C}^{SC}$)

${}^{}$$\mathrm{\Delta }T{C}^{SC}\mathrm{\%}$: the gaps between the expected SC costs of EF-100/EF-40/EVS/HS solutions and the wait-and-see solutions (WS)

${}^{}$$\mathrm{\Delta }{C}_{1st}\mathrm{\%}$: gaps

${}^{}$EF-100: extensive form solutions with 100 scenarios

${}^{}$EF-40: extensive form solutions with 40 scenarios

${}^{}$WS: expected SC costs of wait-and-see solutions.

Data availability statement

The data that support the findings of this article are available from the corresponding author, Y. Fan. upon reasonable request.