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# specific constraints

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Hello guys,

currently im doing a Project at my University. I have to do a Simulation Pretty simular to the tutorial for begginers.
But i have some more constraits which i have to imply but have no clue how to.code theese.

In General: I have to get my products to the different customers. but i just have one “car” with a set storage. the case is, that the car definetly Needs to drive sometimes back to the warehouse, but i want to optimize the Situation.
for example: i can fit product a for customer a in the car. and the half of product b for customer b. so i want to know whether it is more worth driving back and then Picking up the whole product for customer b. or is it more worth to immediately drive to customer b and in the 2nd route i allready can pick up e.g. product c for customer c.
In Addition to this: i also want to imply, that there is a amount of time needed to put the products in and out of the Vehicle.

My native language is not english, but i hope you could understand that “Problem”
im going to do the professional tutotial. Maybe i will find some Solutions there.

best regards,

Bernd Götz

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Best answer by mohansx 30 July 2020, 00:34

@sineplexus , I agree with what Mateus that this would likely be captured in vehicle routing problems. The tutorial for professionals will not be of much help (modelling wise, still a great resource to get familiar with AIMMS) as it does not discuss a routing problem

Here are two of our examples which would be most relevant for you,

https://www.aimms.com/english/developers/resources/examples/practical-examples/vehicle-routing-vrptw

https://www.aimms.com/english/developers/resources/examples/practical-examples/vehicle-routing-cvrp

You wrote:

for example: i can fit product a for customer a in the car. and the half of product b for customer b. so i want to know whether it is more worth driving back and then Picking up the whole product for customer b.

or is it more worth to immediately drive to customer b and in the 2nd route i allready can pick up e.g. product c for customer c.

The key difference in these two cases is that the car can visit a customer only once in case 1 (visit customer x only if car is carrying all the demand of customer x) vs the car can visit any customer multiple times.

The first case is typical and you can find it in the standard VRPs, in the examples as well. To compare case 1 with case 2, you will need to relax the “visit each customer only once” constraint and will likely need additional variables/constraints to balance all the flows. A complication you could add to case 1 is if there is a customer with demand greater than the car capacity. In that case the car will need to visit the customer multiple times.

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Userlevel 5

Hi, @sineplexus. Maybe you could search for Pickup and Delivery Problem on operations research hubs. Or maybe under vehicle routing problems.

Imo, tutorial for professionals will help you to understand and use AIMMS properly but won’t provide the modeling of this specific problem.

Userlevel 4

@sineplexus , I agree with what Mateus that this would likely be captured in vehicle routing problems. The tutorial for professionals will not be of much help (modelling wise, still a great resource to get familiar with AIMMS) as it does not discuss a routing problem

Here are two of our examples which would be most relevant for you,

https://www.aimms.com/english/developers/resources/examples/practical-examples/vehicle-routing-vrptw

https://www.aimms.com/english/developers/resources/examples/practical-examples/vehicle-routing-cvrp

You wrote:

for example: i can fit product a for customer a in the car. and the half of product b for customer b. so i want to know whether it is more worth driving back and then Picking up the whole product for customer b.

or is it more worth to immediately drive to customer b and in the 2nd route i allready can pick up e.g. product c for customer c.

The key difference in these two cases is that the car can visit a customer only once in case 1 (visit customer x only if car is carrying all the demand of customer x) vs the car can visit any customer multiple times.

The first case is typical and you can find it in the standard VRPs, in the examples as well. To compare case 1 with case 2, you will need to relax the “visit each customer only once” constraint and will likely need additional variables/constraints to balance all the flows. A complication you could add to case 1 is if there is a customer with demand greater than the car capacity. In that case the car will need to visit the customer multiple times.