Replication package for "Fractile or Expectile? Regret Bounds for a Newsvendor with Misspecified Penalties"

Description

Code, outputs and computer-assisted proofs for the article "Fractile or Expectile? Regret Bounds for a Newsvendor with Misspecified Penalties" by Kemal Güler and Nurten Ulusay (submitted to the European Journal of Operational Research). Under quadratic shortage and excess penalties, the newsvendor's optimal order is an expectile of demand. The article bounds the cost of ordering at the critical fractile instead: - at most twice the optimum for any demand with finite variance; - at most 31.42% (critical ratios 0.1–0.9) and 36.85% (0.005–0.995) of the optimum for log-concave demand; - 60–65% of the optimum for unimodal demand at the certified cost ratios. The package has two parts: 1. *replicate_cost.py* recomputes every number in the article in floating point and checks it against the printed value. It runs 217 checks, all of which pass, and also regenerates Figure 1. 2. *certify/* carries out the computer-assisted proofs of Appendix A in interval (ball) arithmetic with Arb, through python-flint. It writes certification logs, and part 1 checks every certified number in the article against them.

Steps to reproduce

1. Install the requirements: pip install -r requirements.txt. This needs Python 3.10 or later; python-flint is needed for part 2 only. 2. Run part 1: python3 replicate_cost.py. It takes about 10 minutes, and every check should report PASS. 3. Optionally, run part 2: sh certify/run_all.sh. It takes about 5 hours on one core and rewrites certify/logs/.

Institutions

• Nevşehir Hacı Bektaş Veli University

  Nevşehir Province, Nevşehir
• Rauf Denktas University

  Nicosia, Nicosia

Categories

Licence