Research Article

A New Separable Piecewise Linear Learning Algorithm for the Stochastic Empty Container Repositioning Problem

Table 1

Notations for the ECR problem.

Indices and sets
The index of ports
The set of ports
The service route
The set of service route
The container size
The set of container size
The set of ports on service route
The port corresponding to the stop on service route

Input parameters
The beginning time when service arrives at its stop
The set of beginning time when service arrives at its stop
The ending time when service arrives at its stop
The set of ending time when service arrives at its stop
The transportation time from stop to the next stop on service route
The number of days that the service stays at stop
The capacity of one container size (capacity here means volume and weight)
The quantity of the supply of empty containers of size at port at time
The quantity of the demand of empty containers of size at port at time
The remaining capacity for empty containers on service route when leaving stop at time (laden container excluded)
The cost of unloading one container with size at port at time
The cost of loading one container with size at port at time
Per period cost of storing one container with size at port at time
The penalty cost of one container with size at port at time
The transportation cost from stop to the next stop on service route for one container with size

Decision variables
The number of empty containers of size unloaded at stop on service route at time
The number of empty containers with size loaded at stop on service route at time
The number of empty containers with size stored at port at time
The number of empty containers with size that cannot be satisfied by the empty containers at port at time
The number of empty containers with size transported from stop to the next stop on service route at time