3. Heuristic Algorithm
The mathematical model of inventory routing problem based on the working time equilibrium is an integer programming
model. Lingo software can be used to solve small size problems directly, but it needs a long time to
get the solution of the large scale problems, so this paper will design a heuristic algorithm to solve this model.
Several definitions are given as follows.
Set of feasible successor gas stations: the set of feasible successor gas stations that can be served when a
tanker unload oil at a gas station. Every gas station has a fixed time window to accept the service, and tanker
needs a certain time to drive from current gas station to the successor one. If the arrival time to the successor gas
station just falls in its service time window, the gas station will be a feasible successor gas station. Since each
gas station has a time window, it is impossible that each gas station becomes a successor gas station.
According to the following rules, we can calculate the set of feasible successor gas stations.
Because we consider the calculation of the set of feasible successor gas stations with hard time window, in
order to avoid tankers waiting and gas station out of stock, it is necessary to calculate the feasible successor gas
stations of oil depot and every gas station in the heuristic algorithm calculation process.
Assumed Gib is the set of feasible successor gas stations of gas station i, Gob indicates the set of feasible
successor gas stations of oil depot. According to the time window calculation of gas station j, its revised time
window corresponding to gas station i is: