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Detection of operational quick-wins by time windows in Logistics

Logistics planning with time window constraints

One of the fundamental aspects to take into account when planning logistics for one or more vehicles is to know whether it is necessary to deliver and/or pick up orders within a time slot at each of the service points. These time slots are known as time windows and can be different for each service point, imposing complex constraints whose impact on logistics costs is greater as these windows are smaller and smaller and configured without having global knowledge of the logistics planning to be performed.

For example, Fig. 1 shows a possible case study in which each point on the map is assigned a certain time slot that has been assigned according to the delivery/pickup preferences of each customer.

Ejemplo de asignación de ventanas de tiempo
Fig. 1: Example of time window assignment.

Fig. 1 shows that nearby service points may or may not have overlapping time windows. As a consequence, in order to be able to deliver/pick up each order within its corresponding time window, it is necessary to plan routes whose logistics cost is higher in terms of distance traveled compared to a logistics planning made without considering these time restrictions.

At OGA, through projects carried out for large clients in the logistics sector, we have observed that an inadequate use of time windows can lead to an increase in logistics costs of more than 30%. That is why at OGA we accompany our clients in the study of the configuration of the time windows of their service points and in the detection of those service points that have a greater impact on their costs..

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.

In view of this incompatibility due to the use of time windows, two service points are said to be incompatible with each other due to time windows when:

  • 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).

That is, when:

tAini + tAs + tA-B > tBfinor 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.
Histogram of the number of incompatible service points as a function of distance.
Fig 2: Histogram of the number of incompatible service points as a function of distance.

Another type of useful information that can be extracted is the degree to which the time windows need to be changed to reduce (or eliminate) incompatibilities per time window. For this, we first calculate the minimum change that needs to be applied to the time windows to convert a pair of incompatible service points into compatible service points. Once the above is calculated for any pair of incompatible service points, the histogram in Fig. 3 is generated to determine which are the most frequent changes. From the histogram in Fig. 3 it can be concluded that, in this example, 90% of the incompatibilities require a change less than or equal to 65 minutes in the time windows.

Histogram of the changes to be made in the time windows to avoid incompatibilities.
Fig 3: Histogram of the changes to be made in the time windows to avoid incompatibilities.

Detección de quick-wins operativos

Once we have detected the presence of incompatibilities between service points by using time windows and analyzed the nature of these incompatibilities, what is the best strategy to correct the incompatibilities by time windows? Should we modify the time window of every service point with an incompatibility or can we modify only the time windows of a subset of service points?

In this network, each node is a service point that has one incompatibility per time window and is connected to all service points with which it is incompatible. In addition, each node has been colored according to its degree in order to observe which nodes have the highest number of incompatibilities. In this example, it can be seen that there are nodes with a high concentration of incompatibilities (red orange or even green nodes). Therefore, changing only the time windows of these service points would considerably reduce the number of incompatibilities with a minimum number of changes.

Detection of operational quick-wins.
Fig 4: Detection of operational quick-wins.

Reducing the number of incompatibilities has a clear benefit, namely the reduction of logistics costs. This cost reduction will depend on each particular scenario and how time window modifications have been applied. If your logistics operation is affected by time windows, please contact OGA, our team of experts will be happy to analyze your case in detail and propose improvements to maximize the efficiency of your operation.

Acerca del autor

Víctor Berrocal
Senior Optimization Consultant en oga