This repository contains the source code and datasets to allow the replication of the results from the paper:
Florio, A. M., Gendreau, M., Hartl, R. F., Minner, S., & Vidal, T. (2023). Recent Advances in Vehicle Routing with Stochastic Demands: Bayesian Learning for Correlated Demands and Elementary Branch-Price-and-Cut. European Journal of Operational Research 306(3), 1081-1093.
The paper is also freely available at https://arxiv.org/abs/2302.02538
The code implements a branch-price-and-cut (BP&C) algorithm for the VRPSD under optimal restocking.
The implementation requires:
- The CPLEX Optimization Studio, which is free for academic use.
- The CVRPSEP library for the separation of capacity cuts. The CVRPSEP sources are included in this repo.
A Makefile is provided for reference only. This should be adapted to match the specific host requirements, including CPLEX header files and libraries. The CVRPSEP library should be compiled separately.
The code compiles into a single executable vrpsd. To facilitate scripting, a numerical code is assigned to each standard VRPSD instance. This mapping is available in the source file Instance.cpp. For example, instance A-n32-k5 (Augerat, 1995) corresponds to the instance number 2001. To solve this instance, simply run:
$ ./vrpsd 0 2001
Basic instance information is displayed before the algorithm starts to execute:
Instance info:
ID: 2001
N: 31
Q: 100
f: 1.000
round to integer: 0
max vehicles: 5
demand distribution: Poisson
expected demand: 410.000
load coeff.: 4.100
*** BRANCH AND PRICE ***
customer 1 demands in [4,39]
customer 2 demands in [5,42]
customer 3 demands in [0,19]
[...]
The app is output intensive, so we recommend redirecting the output to a file for posterior analysis. After a few minutes (even though instance 2001 has only 31 customers, it is a difficult instance as many SRCs need to be separated to close the optimality gap), the algorithm finishes and the optimal solution is printed alongside some statistics:
Solution value: 856.310
1.000 {0,12,1,16,30,0} n=4 l=72 ec=73.507 ap=73.486 rc=-0.273
1.000 {0,21,31,19,17,13,26,0} n=6 l=82 ec=157.816 ap=156.055 rc=-1.958
1.000 {0,20,5,25,10,15,29,27,0} n=7 l=91 ec=203.351 ap=195.048 rc=-4.344
1.000 {0,22,9,11,4,28,8,18,14,0} n=8 l=78 ec=238.666 ap=238.030 rc=-0.506
1.000 {0,7,2,3,23,6,24,0} n=6 l=87 ec=182.969 ap=179.151 rc=-0.335
sum of coefficients: 5.000
Accelerated Column Generation finished: 1
a-priori length of the DE solution: 787.808
Value of the Stochastic Solution (VSS) = 37.328 (4.177%)
BnP solution (value): 856.310
BnP solution (routes):
{0,12,1,16,30,0} n=4 l=72 ec=73.507 ap=73.486 rc=-0.273
{0,21,31,19,17,13,26,0} n=6 l=82 ec=157.816 ap=156.055 rc=-1.958
{0,20,5,25,10,15,29,27,0} n=7 l=91 ec=203.351 ap=195.048 rc=-4.344
{0,22,9,11,4,28,8,18,14,0} n=8 l=78 ec=238.666 ap=238.030 rc=-0.506
{0,7,2,3,23,6,24,0} n=6 l=87 ec=182.969 ap=179.151 rc=-0.335
verifying route expected costs with the SDP algorithm
Route: 73.507 SDP: 73.510 off by: -0.004%
(under Switch policy: 73.508 -0.003%)
Route: 157.816 SDP: 157.826 off by: -0.006%
(under Switch policy: 157.818 -0.005%)
Route: 203.351 SDP: 203.364 off by: -0.006%
(under Switch policy: 203.352 -0.006%)
Route: 238.666 SDP: 238.678 off by: -0.005%
(under Switch policy: 238.667 -0.004%)
Route: 182.969 SDP: 182.978 off by: -0.005%
(under Switch policy: 182.971 -0.004%)
Switch policy (total): -0.005%
TIME PROFILING
adding nodes: 151.003 secs
... dcost: 132.054 secs
MEMORY PROFILING
profiling: peak memory allocated to labels: 0.782G
time elapsed: 577 secs