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started before the end of the planning period p +1, are due requests. Additionally,
in order to improve the continuity of the plan, requests whose pickups must be
served soon after the end of the planning period p +1 are also considered as due
requests in our approach.
4.3 Route-Based Request Exchange
In order to solve the DCTPP, the route-based request exchange mechanism
in [31] is adapted and used to solve the static problem periodically within the
rolling horizon framework. Figure 2 shows an overview of the route-based request
exchange mechanism.
Propose requests for exchange in request pool
Preprocessing
Specify transfer price for proposed requests
Initial Route
Generation
Initial route generation
Temporary winner determination
Iterative Route
Generation
Yes
Stop criterion
satisfied?
No
Iterative route generation
Final Winner
Determination
Final winner determination and solution repair
(if necessary)
Fig. 2. Overview of the route-based request exchange mechanism [31]
In preprocessing , all partners propose all their requests for exchange, i.e., R p,d
i
in case of MY, and R p, i in case of FL, into a common request pool for exchange.
After the requests have been proposed, each carrier i solves for himself a routing
problem using his own fleet only for their own requests. Through introducing
aweight w r for each request r
R p, i , the objective function of this routing
problem can be formulated as:
min
k∈K i
β k d uv x uvk +
r∈R p,a
i
γ r w r z r
(1)
( u,v ) ∈A i
K i
K i is the vehicle set available in the current planning. A i is the set of
arcs defined by carrier i 's own requests and vehicles and d uv is the distance of
the arc ( u,v ). The decision variable x uvk ∈{
indicates if an arc ( u,v )is
used in vehicle k 's route and the other binary variable z r indicates if a request is
outsourced to a common carrier. In case of MY, all requests in R p, i have w r =0
and all due requests have a weight of 1. In case of FL, all due requests also have
0 , 1
}
 
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