Detection of operational quick-wins by time windows in Logistics
Logistics planning with time window constraints
Incompatibilities due to the use of time windows
One of the direct consequences of using time windows is that there is now the possibility of not being able to reach service point B on time from service point A. In other words, it will not be possible to reach B on time from A when:
tAini + tAs + tA-B > tBfin Eq. 1
Where the following time parameters have been considered:
- Time of arrival at point A (tA), with time window [tAini, tAfin], where tAini ≤ tA ≤ tAfin to be able to serve point A on time. If tA < tAini, there will be a waiting time of tAini – tA until point A is ready to receive the service.
- Time required to perform the service at point A, tAs.
- Time required to reach B from A, tA-B.
- Time of arrival at point B (tB), with time window [tBini, tBfin], where tBini ≤ tB ≤ tBfin to be able to serve point B on time. If tB < tBini, there will be a waiting time of tBini – tB until point B is ready to receive the service.
- It is not possible to reach B in time from A, even if A is reached just at the beginning of its time window (i.e. incompatibility of A with B).
- It is not possible to reach A in time from B, even if B is reached just at the beginning of its time window (i.e. incompatibility of B with A).
tAini + tAs + tA-B > tBfin, or when tBini + tBs + tB-A > tAfin Eq. 2.The detection of time window incompatibilities is essential for logistics planning because if two service points A and B are incompatible with each other in terms of time windows, these two service points cannot be served by the same vehicle. To determine the quality of a given time window configuration, visual representations of data can be used. A very useful visualization tool can be the histogram of the number of incompatibilities as a function of the distance between incompatible service points. An example of such a histogram is shown in Fig. 2, where the CDF (Cumulative Distribution Function) of the bins of the histogram itself has been included. The following useful information can be obtained from this representation:
- The histogram curve indicates how the number of incompatibilities increases and/or decreases with distance. With this, it can be deduced i) what is the number of incompatibilities for short, medium and long distance, ii) for which distance between incompatible nodes there is a significant number of incompatibilities and iii) whether or not there has already been previous work by logistics experts when configuring the time windows of the service points. Specifically, for the example in Fig. 2 the following can be observed:
- The number of incompatibilities does not increase progressively with distance but follows a curved approach with a maximum at around 145 km distance between incompatible nodes. This indicates that there is previous work in the configuration of the time windows between service points that are more than 150 km apart.
- There is an atypical set of incompabilities around 255 km.
- 90% of the incompabilities occur for a distance less than or equal to 175 km.