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) | ||||