Infeasible vehicle routing problem (VRP) with MILP and continuous DV
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Hi,
I am having troubles getting my program to be feasible. I am modelling a VRP with one binary x[ac,tb,n,m,k] and one continuous decision variable T[ac,tb,k].
I have taken this problem from the following source:
Evertse, C., and Visser, H. Realtime airport surface movement planning: Minimizing aircraft emissions. Transportation Research Part C 79(2017), 224–241
(I don't know how to attach documents to this question, so I have added a link to the doc: https://tinyurl.com/2h63n32z)
Here, ac=aircraft (1st vehicle type, from 0 to 1000 in which 0 means no ac is attached in the ac-vehicle combination),
tb=robot(2nd vehicle type, from 0 to 50, in which 0 means no robot is attached to the ac-vehicle combination),
n and m are nodes in the nodal network and k is the stage (representing time in some sense, from 0 to a predefined number, eg 100).
so x = 1 if aircraft ac is attached to robot tb and travelling from node n to node m at stage k.
T represents the time at which aircraft ac is attached to robot tb at stage k.
In the given source, only one type of vehicle is used (ac), however I have extended the problem to two types of vehicles (ac and tb, in which the combinations 1-0, 0-1 and 1-1 are possible, but 0-0 isn't). Only certified aircraft can be attached to robot tb
I have extended the set of constraints given in the paper, however constraints numbered C3 and C7 make the problem infeasible. After I remove constraints C7, constraints C1, C3 and C5 appear to be infeasible. Hence I conclude from this that some interconnectivity within the constraints is causing a problem.
The attached image (taken from pg. 229 from the above source) visually represents the flow of the problem and its associated decision variables.
The following link provides the increased problem worked out, i.e. sets, decision variables, objective function and abovementioned constraints: https://tinyurl.com/jfvjp65w
It would be great to find out how to solve this problem.
It is quite an extensive problem and so question, so if I forgot to mention or provide something, please do tell me. I am new to this forum, so I might have forgotten something.
Thanks in advance!
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Hi Bas,
Welcome to the Gurobi Community Forum!
It is pretty hard to help you with this very in-depth question. You should write out an LP file of your model and then compare the constraints in this file to those of your mathematical model to find out where the infeasible or inconsistency comes from.
Best regards,
Matthias0 -
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