A Hybrid Approach to the Optimization of Multiechelon Systems

Table 2

Summary indices, parameters, and decision variables.

Symbol

Description

Indices

Number of satellites

Number of customers

Deport

Set of satellites

Set of customers

Parameters

Number of the 1st-level vehicles

Number of the 2nd-level vehicles

Capacity of the vehicles for the 1st level

Capacity of the vehicles for the 2nd level

Demand required by customer

Cost of the arc()

Cost of loading/unloading operations of a unit of freight in satellite

Decision variables

An integer variable of the 1st-level routing is equal to the number of 1st-level vehicles using arc()

A binary variable of the 2nd-level routing is equal to 1 if a 2nd-level vehicle makes a route start from satellite and go from node to node and 0 otherwise

The freight flow arc() for the first level

The freight arc() where represents the satellite where the freight is passing through.

A binary variable that is equal to 1 if the freight to be delivered to customer is consolidated in satellite and 0 otherwise