This directory provides an implementation of the algorithms for dynamic assortment optimization under the Multinomial logit choice model.

Dependencies

The package dependencies of the code are latest versions of the following packages:

• numpy
• pandas
• gurobipy
• scipy
• numba

Functional description

The object constructed with Numerical() instanciates the random generator of the simulation.

• The method refresh_data() samples new inputs,
• The method sample_revenue() uses a sampling-based estimator for the expected revenue,
• Several algorithmic methods are implemented: our constant-factor approximation algorithm(), a discrete greedy heuristic greedy(), a greedy local search method local_search(), a gradient-descent with regards to the Lovasz extension of the expected revenue function lovasz_greedy(), a dynamic programming-based relaxation relaxation_topaloglu(), an MIP-based deterministic relaxation relaxation_deterministic().
• Other functions are auxiliary and need not be referenced in running the code.

The file Numericals.py() can be run as a script to replicate the computational results in the paper Greedy-Like Algorithms for Dynamic Assortment Planning Under Multinomial Logit Preferences, A. Aouad, R. Levi and D. Segev (2018) that appeared in Operations Research.

A work-in-progress implementation of a polynomial-time approximation scheme is provided in the file Ptas.py.