1. This repository is a fork of laseryuan/mutual-bly, which is the code for the paper Bensoussan, Yuan, and Liu (2023). The purpose of this fork is not to comment on its efficiency or to conduct further numerical experiments. Instead, it is to keep a copy of the version (commit 95c935b997576445fb6d3f9b12f2e1af4bd5494f) for easy future reference and to document the building and running environment of the code for reproducibility purposes.
2. Bensoussan, Yuan, and Liu (2023) is a paper published in Operations Research, a top journal in the field of operations research and management science. It studies the two-band impulse control of Brownian motion with the two-piece linear inventory cost structure ($f(x)=hx^++px^-$), which is a special case of the problem with a general convex $f(x)$ studied by Feng and Muthuraman (2010). Bensoussan, Yuan, and Liu (2023) develop a new method called the splitting method and benchmark their method against the one proposed by Feng and Muthuraman (2010). The authors of Bensoussan, Yuan, and Liu (2023) implement the splitting method and the benchmarking experiments in this codebase.
3. The source codes are the same as those in the original repo (commit 95c935b997576445fb6d3f9b12f2e1af4bd5494f)
   • Only the README.md is modified to better document the steps to build and run the code.
   • A .gitignore file is added to ignore the built executable file bin/Mutual-BLY.
   • A cpp_build.yml file for Github Actions is added. Its path is .github/workflows/cpp_build.yml. This is added to attemp to run the code using Github Actions.

• It has been tested on WSL 2 (Windows Subsystem Linux Version 2) with the Ubuntu 22.04 installed.
• It should also work in other Unix-like systems

1. The compiler: clang
2. The GSL development libraries (libgsl-dev)

• If any of them is missing, it is straightforwad to install the missing one.
• For example, in a Debian-based system (e.g., Ubuntu), we can install libgsl-dev by:

sudo apt install libgsl-dev

• Note that Tthe Eigen library is also needed, but the files are already in 'include/eigen' of this repo.

• Assuming
  1. The headers of the 'gsl' library is in the directory '/usr/include/gsl'
  2. The shared libraries 'libgsl.so' and 'libgslcblas.so' for the GSL library can be found in the directory '/usr/lib/x86_64-linux-gnu/'
     • If this is not the case, one can find them using the following two commands, repectively,

     sudo find /usr/lib/ /usr/local/lib/ /lib/ -name libgsl.so 2>/dev/null
     sudo find /usr/lib/ /usr/local/lib/ /lib/ -name libgslcblas.so 2>/dev/null
     

• Step 1. git clone the repo and change directory to the local folder using

git clone https://github.com/fenghaolin/mutual-bly.git mutual-bly-OR2023 && cd mutual-bly-OR2023

• Step 2. Buildi the executable file Mutual-BLY and put it into bin:

clang++ -I ./include/eigen -I /usr/include/gsl -std=c++11 Main.cpp -o bin/Mutual-BLY /usr/lib/x86_64-linux-gnu/libgsl.so /usr/lib/x86_64-linux-gnu/libgslcblas.so

• The code is written in C++ by the authors of Bensoussan, Yuan, and Liu (2023). Without any modification of the source files, the project can be built successfully using the above clang command with warning message about with the style not following the requirements of ISO C++. However, if one wants to replace the clang compiler with the g++ one, it will fail with errors, some of which are easily fixable while others may not be. This note is a reminder for anyone interested in building and running the code.

[1] Bensoussan, A., Liu, J. J., & Yuan, J. (2023). A Splitting Method for Band Control of Brownian Motion: With Application to Mutual Reserve Optimization. Operations Research.

[2] Feng, H., & Muthuraman, K. (2010). A computational method for stochastic impulse control problems. Mathematics of Operations Research, 35(4), 830-850.

git clone https://github.com/laseryuan/mutual-bly && cd mutual-bly  
docker run -it -v $PWD:/home/app/app lasery/cling bash

It took about 3 minutes to finish all the test cases on Intel Core i7-2600 @ 3.40GHz.

The performance comparison between our method and the benchmark is recorded in the benchmark.txt file.

LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib bin/Mutual-BLY
cat output/benchmark.txt

clang++ -I /home/app/app/include/eigen -I /usr/local/include/gsl -std=c++11 Main.cpp -o bin/Mutual-BLY /usr/local/lib/libgsl.so /usr/local/lib/libgslcblas.so