Table 2 Integrated overview of criteria,...

Table 2

Integrated overview of criteria, parameters, and notations applied in the model

Symbol	Description	Type/Unit
$i = 1, . . ., N$	Index and set of suppliers	Integer/Set
$j \in J$	Index and set of demand items (or locations/components, based on your model)	Integer/Set
$d_{j}$	Demand for item/component $j$	Units
$c_{i}$	Unit cost offered by the supplier $i$	Monetary units
$s_{i}$	Sustainability score of the supplier $i$	Dimensionless
$r_{i}$	Disruption risk level associated with the supplier $i$	Probability/Risk score
$x_{i}$	Quantity (or proportion) of demand allocated to supplier $i$	Real number [0,1] or units
$y_{i}$	Binary decision variable: 1 if supplier $i$ is selected; 0 otherwise	Binary ${0, 1}$
$B$	Total procurement budget	Monetary units
$E$	Maximum allowed environmental impact	Environmental units
$α$	Risk tolerance level (confidence level for VaR constraint)	Real number [0,1]
$V a R$	Value-at-Risk threshold	Probability-weighted loss
$λ_{1}, λ_{2}, λ_{3}$	Weighting coefficients for goals (cost, sustainability, risk)	Real numbers
$Z$	Objective function value	Composite/dimensionless

Symbol	Description	Type/Unit
$i = 1, . . ., N$	Index and set of suppliers	Integer/Set
$j \in J$	Index and set of demand items (or locations/components, based on your model)	Integer/Set
$d_{j}$	Demand for item/component $j$	Units
$c_{i}$	Unit cost offered by the supplier $i$	Monetary units
$s_{i}$	Sustainability score of the supplier $i$	Dimensionless
$r_{i}$	Disruption risk level associated with the supplier $i$	Probability/Risk score
$x_{i}$	Quantity (or proportion) of demand allocated to supplier $i$	Real number [0,1] or units
$y_{i}$	Binary decision variable: 1 if supplier $i$ is selected; 0 otherwise	Binary ${0, 1}$
$B$	Total procurement budget	Monetary units
$E$	Maximum allowed environmental impact	Environmental units
$α$	Risk tolerance level (confidence level for VaR constraint)	Real number [0,1]
$V a R$	Value-at-Risk threshold	Probability-weighted loss
$λ_{1}, λ_{2}, λ_{3}$	Weighting coefficients for goals (cost, sustainability, risk)	Real numbers
$Z$	Objective function value	Composite/dimensionless

Note(s): $W_{1}$ ⁠: The weight for the sustainability goal

$W_{2}$ ⁠: The weight for the risk goal

Decision variables

$x_{i} \in [0, 1]$ ⁠: A fraction of the whole quantity ordered from the provider i

$y_{i} \in [0, 1]$ ⁠: Takes 1 if supplier i is included in the portfolio, 0 otherwise

Parameters

${C v}_{i} \in R$ The selling price of supplier i (variable cost) per unit

${C f}_{i} \in R$ Fixed cost associated with sourcing from a supplier i

$\log_{i} \in [0, 1]$ ⁠: A measure of the logistical performance of supplier i

${s r s}_{i} \in [0, 1]$ ⁠: Sustainability performance of Supplier i (sustainability rating score)

${C A P}_{i} \in [0, 1]$ ⁠: The portion of the whole demand that can be sourced from the supplier's capacity i

${M O Q}_{i} \in [0, 1]$ ⁠: Minimum order quantity allocated the supplier i (as a % of the total demand)

${s t r a t}_{i} \in {0, 1}$ ⁠: Binary variable, 1 if supplier i is a “strategic” supplier, 0 otherwise

${r e g}_{i} \in {0; 1}$ Binary variable, 1 if supplier i is a regional supplier, 0 otherwise

$D \in R$ ⁠: Total Demand

$B \in R$ ⁠: Allocated Budget

$L \in [0, 1]$ ⁠: Minimum logistics service desired

$N_{\max} \in Z$ ⁠: The maximum of selected suppliers in the portfolio

$N_{s t r} \in Z$ ⁠: The number of strategic suppliers in the portfolio

$N_{r e g} \in Z$ ⁠: The number of regional suppliers in the portfolio

Source(s): Authors’ elaboration

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