A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion
Table 2
Notations.
Indices
Representations
,,
Indices of the nodes, ,, and .
,
Indices of the transportation services, and .
Directed arc from node to node , and .
Directed arc from node to node , and .
Sets
Representations
Set of the rail services on arc .
Set of the road services on arc .
Set of the transportation services on arc ,, and .
Set of the predecessor nodes to node , and .
Set of the successor nodes to node , and .
Variables
Representations
Charged inventory time for transportation order at node before its containers are moved on arc by service , unit: h.
A binary variable. if service on arc is used for transportation order ; otherwise.
Arrival time of the containers of transportation order at node .
Planned departure time of the containers of transportation order from node .
A nonnegative integer variable that indicates how many periods (24 hours) exceed.
Travel time of road service on arc when used for transportation order , unit: h. where is the piecewise linear function of the travel time with respect to the corresponding planned departure time. Note that in this function, the input departure time should fall within range [0, 24]. Otherwise, it should be first normalized into such range before being input into the function.
Parameters
Representations
Loading/unloading operation start time of rail service at node .
Loading/unloading operation cutoff time of rail service at node .
Fuzzy available capacity of rail service on arc and where , unit: TEU.
Travel distance of service on arc , unit: km.
Unit transportation cost when service is used to move containers on arc , unit: ¥/TEU.
Unit loading/unloading operation costs of service , unit: ¥/TEU.
Unit inventory costs of transportation service at node , unit: ¥/TEU-h.
Unit destination inventory costs for transportation order , unit: ¥/TEU-h.
Unit penalty costs for transportation order caused by delayed delivery at its destination, unit: ¥/h.
Unit CO2 emission costs, unit: ¥/g.
CO2 emission factor for service , unit: g/TEU-km.
Free-of-charge inventory period of service at node , unit: h.
