Originally posted by: TillGoe

Hi together,

I am currently trying to construct an transportation model in CPLEX (12.8.0.0) in OPL. As I am new to CPLEX I need some help understanding the way to put the problem into CPLEX.

It is a model constructed by Ma et al (2017) in "Designing optimal vehicle autonomous vehicle sharing and reservation systems: A linear programming approach".

The problem is basically a network problem which is assigning trip chains to a number of vehicles to serve a specific set of personnel trip demands.

The input would be a set of trip demands from point i- to point i+ , each at a given pickup time ti- and a delivery time ti+.

Since only following demands j with a pickup time tj- later than the delivery time of ti+ can be reached after trip i was served, I guess I need a matrix which displays reachable trips.

But do I know need a travel time from every pickup and delivery location to every other location? And how do I handle trip demands that can not be reached?

I attached the optimization problem.

Can somebody give me a hint on how to start? I was trying to get an idea to insert the problem in CLPEX forever but I simply don't know where to start :(

Every help is much appreciated!!

Did you have a look at the many examples that ship with CPLEX and the user manual here?

If you have a formulation as in your AVSR_Opt_Problem.jpeg image then translating this into OPL is usually pretty simple since it is almost a verbatim translation. For example, the first two constraints would be as simple as

forall (<i,j> in A) x[<i,j>] <= m[<i,j>];
forall (i in I : i != o and i != d) sum (j in I) x[<i,j>] = sum (j in I) x[<j,i>];

Originally posted by: TillGoe

Thanks a lot for your reply!
I had a look at the examples and I think I should be able to transform the general optimization problem into OPL.

As long as I have a small demand set (e.g. <10 trips) it is pretty easy to solve the problem using a matrix with all the trips (origin-destination costs) and all the possible connections from destination i to origin j.

But I have no idea how to efficiently import the data when I have some demand set with >100 trips. Do I really need a matrix with all possible network links? 
Looking at AVSR Model.jpeg, there is no connection between 2+ and 1- because the starting time of 1- is earlier than the arrival time of 2+.
Is there any way of implementing at larger data set without having to create a 100x100 matrix with extreme high costs (e.g. M) where there is no possible link?

I guess what you are looking for to avoid large data sets is tuples. Instead of specifying a matrix with lots of holes or dummy entries, specify a list of tuples that contains only the things that exist.

Originally posted by: TillGoe

when I use:

forall (i in I : i != o and i != d)

I get a syntax error. Are you sure it is the right way to express: forall i in I, but not o and not d.

Is there any other way to exclude o and d for the constraint?

Try '&&' instead of 'and'