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Table 1 CAM and ADM notation

From: Evaluation of port disruption impacts in the global liner shipping network

Sets Subsets Indices
A All legs \( {A}_k^{+} \) Legs entering port k a Legs
K All ports \( {A}_k^{-} \) Legs leaving port k k Ports
S Destination ports A n Legs on service n y Corridors
R Origin ports L y Links on corridor y l Links
Y All corridors L n Links on service n n Liner services
L All links    r Origin ports
N All liner services    s Destination ports
J Disrupted components    j Disruption strategies
I Defended components    i Defence strategies
     f Loaded containers
     e Empty containers
Parameters
\( {B}_k^f \) Net flow of loaded containers at each port k
\( {B}_k^e \) Net flow of empty containers at each port k
Ca Sailing time on leg a, including loading and unloading times at ports (e.g. days)
CHCan Container handling cost per loaded container on leg a using liner service n
CR Rental cost per unit time per loaded or empty containers
\( {TD}_{rs}^f \) Demand for loaded containers to be transported from origin r to destination s in the defined planning horizon
\( {TD}_{rs}^e \) Demand for empty containers to be transported from origin r to destination s in the defined planning horizon
DV Depreciation cost per unit time per loaded container (inventory cost)
 τaln 1 if leg a uses link l on liner service n, and 0 otherwise
 τaly 1 if leg a uses link l on maritime corridor y, and 0 otherwise
Fa Frequency of sailings on leg a
PTk Throughput capacity of port k
LSn Throughput capacity of liner service n
MCy Throughput capacity of maritime corridor y
δi Defender flow diversion percentage in strategy i (please refer to Attacker-defender model section)
αj Attacker disruption percentage in strategy j (please refer to Attacker-defender model section)
\( {\hat{\delta}}_i \) Defender capacity multiplier for network components with flow diversion in strategy i
\( {\hat{\alpha}}_j \) Attacker capacity multiplier for disrupted network components in strategy j
PCf Penalty cost for loaded containers not transported
PCe Penalty cost for empty containers not transported
Decision variables
\( {t}_{rs}^f \) Serviced demand of loaded containers shipped from origin r to destination s
\( {t}_{rs}^e \) Serviced demand of empty containers shipped from origin r to destination s
\( {x}_{as}^f \) Flow of loaded containers on leg a en route to destination s
\( {x}_{as}^e \) Flow of empty containers on leg a en route to destination s
\( {w}_{ks}^f \) Expected dwell time at port k for all loaded containers en-route to destination s
\( {w}_{ks}^e \) Expected dwell time at port k for all empty containers en-route to destination s
pi Probability defender diverts flows from component i
qj Probability attacker disrupts component j
v Value of the game for the defender (routing costs)
z Value of the game for the attacker (disruption costs)