2.2. Mathematical Model
Defines the following symbols and variables at first:
I nn = {0,1, 2, , , 1 + } : set of oil depot and gas stations. In order to establish the model conveniently, we use
two points to represent the oil depot, 0 represents the oil depot that tanker starts from, n + 1 represents the oil
depot that tanker returns to; 1, 2, , n represent gas stations;
i q : demand of gas station i;
T K = {1, 2, , } : set of tankers;
k p : capacity of tanker k;
ik d : the amount of refined oil unload at gas station i by tanker k;
ijk x : binary variable, 1 ijk x = , if tanker k passes through the path ( ,i j v v ); 0 ijk x = , otherwise; a
i t : the earliest time of gas station i to receive service; b
i t : the latest time of gas station i to receive service;
ik r : the time that tanker k starts to serve for gas station i;
0k r : the time that tanker k sets out from oil depot;
n k 1, r + : the time that tanker k returns to oil depot n + 1;
i s : the required time of gas station i for unloading oil;
ij t : the time that a tanker travels from gas station i to j;
y: the maximum time that all the tankers return to the oil depot after the tasks is finished;
The mathematical model can be described as follows: