# SCIP

Solving Constraint Integer Programs

main_vrp.cpp File Reference

## Detailed Description

main file for VRP pricer example

We want to solve the vehicle routing problem on a graph $$G = (V,E)$$ with $$V = J \cup \{d\}$$, where d is the depot and the distances are given by the length function $$l_e: E \rightarrow R_{\geq 0}$$.

Consider the MIP formulation

$\begin{array}[t]{rll} \min & \displaystyle \sum_{e \in E} l_e y_e \\ & & \\ s.t. & -y_e + \sum_{t \in T_k} a^t_e x_t \leq 0, & \forall e \in E\\ & \displaystyle \sum_{t \in T_k} a^t_j x_t = 1, & \forall j \in J \\ & y(\delta(j)) = 2, & \forall j \in J \\ & y_e \in \{0,1,2\}, & \forall e \in E \\ & x_t \in [0,1], & \forall t \in T_k \end{array}$

where $$T_k$$ is the set of tours visiting at most k customers with repetitions of customers allowed and $$a^t_e$$ ( $$a^t_j$$) counts how often edge e (node j) is traversed in $$t \in T_k$$.

Examples and the file format are given at https://neo.lcc.uma.es/vrp/vrp-instances/capacitated-vrp-instances/.

Definition in file main_vrp.cpp.

#include <stdio.h>
#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include "objscip/objscip.h"
#include "objscip/objscipdefplugins.h"
#include "pricer_vrp.h"

Go to the source code of this file.

## Functions

static int read_problem (const char *filename, int &num_nodes, int &capacity, vector< int > &demand, vector< vector< int > > &dist)

static SCIP_RETCODE execmain (int argc, char **argv)

int main (int argc, char **argv)

## Function Documentation

 static int read_problem ( const char * filename, int & num_nodes, int & capacity, vector< int > & demand, vector< vector< int > > & dist )
static

Parameters
 filename filename num_nodes number of nodes in instance capacity capacity in instance demand array of demands of instance dist distances between nodes

Definition at line 77 of file main_vrp.cpp.

References x, and y.

Referenced by execmain().

## ◆ execmain()

 static SCIP_RETCODE execmain ( int argc, char ** argv )
static

## ◆ main()

 int main ( int argc, char ** argv )

Definition at line 493 of file main_vrp.cpp.

References execmain(), and SCIP_OKAY.