Compartment Access Restriction

Characteristic

Detailed Consideration

Suppose there are two compartments in a vehicle, one of which cannot be reached from the outside. Instead, there is a door in the wall that separates the 'separate' compartment from the 'walk-through' compartment. In practice, the door in the wall may be unreachable when the walk-through compartment is too crammed. If that happens, the separate compartment cannot be accessed anymore and no goods can be picked up or deposited there.

In the following, this feature is explained by means of an example. We start with a very basic setting that evolves in three steps.

1. Two temperature zones

In our example, we have one vehicle with two compartments that differ in their temperature - cool and warm. Correspondingly, we have goods that either need to be transported in the cool or in the warm compartment. For the sake of simplicity, we assume that all goods are packed into containers, and we do not need to consider weight or volume but only the number of cool and warm containers. We store

• the number of cool containers at index 0 and the number of warm containers at index 1 in the quantities of the transport orders,
• the maximum number of cool containers at index 0 and the maximum number of warm containers at index 1 in the quantities of the (only) maximum quantity scenario of the vehicle.

For the definition of the compartment access restriction, we define that the cold and warm compartmens can also be called compartments A and B, respectively, by setting the compartment quantity indices as follows:

• Compartment A is index 0 and
• Compartment B is index 1.

Let us assume the separate compartment is cool and has a capacity of 4 while the walk-through compartment is warm and has a capacity of 8 (containers, respectively). Accordingly, we set the quantities and the compartment setup in the (only) maximum quantity scenario of the vehicle as follows:

• Quantities are (4,8),
• Compartment setup is ACCESS_A_THROUGH_B.

In the following picture, the blue and red cubes represent the cold and red containers, respectively.

Finally, we assume the separate compartment can only be reached when there are no more than 4 containers (=50%) in the walk-through compartment and specify the load threshold for the compartment access restriction of the vehicle as follows:

• Load threshold to access A through B is 50.

Example instance

We have to pickup containers at the customers C1, C2, C3 before we deliver them to the depot.

The load in the vehicle is (1,2) after leaving C1 and (2,4) after leaving C2. Still, the walk-through compartment is not crammed yet as it is filled to exactly 50% and not more. At C3, the compartment access restriction is not violated as the cool containers can be loaded before the warm containers. However, if the load threshold was less than 50, there would have been a CompartmentAccessViolation. At the depot, the compartment access restriction is again not violated as the warm containers can be unloaded before the cool containers.

2. Temperature zones can be swapped

Suppose the temperature in the compartments can be changed and we could as well put the cool containers into the walk-through compartment and the warm containers into the separate compartment. In this setting, we need a second maximum quantity scenario for the vehicle. We set the quantities and the compartment setup in the second maximum quantity scenario of the vehicle as follows:

• Quantities are (8,4),
• Compartment setup is ACCESS_B_THROUGH_A.

In the following picture, the truck has turned such that compartment A is again on the left and compartment B on the right.

In case of swapped temperature zones, we want all cool containers to be unloaded before warm containers are picked up or delivered. Consequently, we define the other load threshold differently:

• Load threshold to access B through A is 0.

Example instance

This time, we pick up containers at the depot and deliver them to the customers C1, C2 and C3.

The load in the vehicle after leaving the depot is (5,3). At this point, it is clear that the first maximum quantity scenario is not feasible capacity-wise while the second scenario still is. At C1, we do not need to access the warm compartment and thus do not need to check the compartment access restriction for the second scenario. At C2, the cool containers are unloaded first such that when the warm containers are unloaded the cool compartment is empty. And it stays empty until the end, so the load threshold of 0 is never exceeded.

3. Separating wall is movable

Suppose the separating wall can split the whole cargo area either at 1/3 or at 2/3. Then we need two more maximum quantity scenarios than the two already defined before. We set the third maximum quantity scenario of the vehicle as follows:

• Quantities are (8,4),
• Compartment setup is ACCESS_A_THROUGH_B.

and the fourth maximum quantity scenario of the vehicle as follows:

• Quantities are (4,8),
• Compartment setup is ACCESS_B_THROUGH_A.

Example instance

Again, we pick up containers at the depot and deliver them to the customers C1, C2 and C3.

In this example, only the third maximum quantity scenario is feasible. The load in the vehicle after leaving the depot is again (5,3). At C1, 1 warm container is delivered first, leaving only 2 (=50%) warm containers in the walk-through compartment. From this point on, the load threshold of 50 is never exceeded.

Good to know

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