Table 1 Parameter interpretation.

C

The aggregation of supply reserve centers, \(\:C=\left\{0\right\}\)

D

The aggregation of affected sites, \(\:D=\left\{\text{1,2},\dots\:,n\right\}\)

K

The aggregation of transport vehicles, \(\:K=\left\{\text{1,2},\dots\:,k\right\}\)

U

The aggregation of all nodes, \(\:U=C\cup\:D\)

\(\:{x}_{j}\)

Actual supply at disaster site \(\:j\:(j\in\:D)\)

\(\:{b}_{j}\)

Demand per unit of population at disaster site \(\:j\:(j\in\:D)\)

\(\:{r}_{j}\)

Total population of affected point \(\:j\:(j\in\:D)\)

\(\:{p}_{j}\)

Dependency function of the affected point \(\:j\:(j\in\:D)\)

\(\:{y}_{j}\)

Actual demand at disaster site \(\:j\:(j\in\:D)\)

\(\:\gamma\:\)

Minimum needs satisfaction rate

\(\:S\)

Stocks at the Supply Reserve Center

\(\:n\)

The number of affected sites

\(\:m\)

The number of transport vehicles

\(\:E\)

Maximum loading capacity of transport vehicles

\(\:{t}_{ij}\)

Vehicle travelling time from node \(\:i(i\in\:U)\) to node \(\:j(j\in\:U)\)

\(\:{t}_{ij}^{{\prime\:}}\)

Corrected vehicle travelling time from node \(\:i(i\in\:U)\) to node \(\:j(j\in\:U)\)

\(\:{d}_{ij}\)

Distance of road section \(\:ij\)

\(\:{v}_{ij}\)

Average speed on road section \(\:ij\)

\(\:L\)

Maximum mileage that a transport vehicle can travel

\(\:{z}_{ij}^{k}\)

0–1 variable, taking 1 means that vehicle \(\:k(k\in\:K)\) drives from node \(\:i(i\in\:U)\) to node \(\:j(j\in\:U)\); otherwise it takes 0

\(\:{f}_{j}^{k}\)

0–1 variable, taking 1 means that vehicle \(\:k(k\in\:K)\) serves the affected point \(\:j(j\in\:U)\); otherwise it takes 0

\(\:{h}_{j}^{k}\)

0–1 variable, taking 1 means that vehicle \(\:k(k\in\:K)\) travels from the distribution center to node \(\:j(j\in\:U)\); otherwise it takes 0