Data-driven algorithms for operational problems

Abstract

In this thesis, we propose algorithms for solving revenue maximization and inventory control problems in data-driven settings. First, we study the choice-based network revenue management problem. We propose the Approximate Column Generation heuristic (ACG) and Potential Based algorithm (PB) for solving the Choice-based Deterministic Linear Program, an LP relaxation to the problem, to near-optimality. Both algorithms only assume the ability to approximate the underlying single period problem. ACG inherits the empirical efficiency from the Column Generation heuristic, while PB enjoys provable efficiency guarantee. Building on these tractability results, we design an earning-while-learning policy for the online problem under a Multinomial Logit choice model with unknown parameters. The policy is efficient, and achieves a regret sublinear in the length of the sales horizon. Next, we consider the online dynamic pricing problem, where the underlying demand function is not known to the monopolist. The monopolist is only allowed to make a limited number of price changes during the sales horizon, due to administrative constraints. For any integer m, we provide an information theoretic lower bound on the regret incurred by any pricing policy with at most m price changes. The bound is the best possible, as it matches the regret upper bound incurred by our proposed policy, up to a constant factor. Finally, we study the data-driven capacitated stochastic inventory control problem, where the demand distributions can only be accessed through sampling from offline data. We apply the Sample Average Approximation (SAA) method, and establish a polynomial size upper bound on the number of samples needed to achieve a near-optimal expected cost. Nevertheless, the underlying SAA problem is shown to be #P hard. Motivated by the SAA analysis, we propose a randomized polynomial time approximation scheme which also uses polynomially many samples. To complement our results, we establish an information theoretic lower bound on the number of samples needed to achieve near optimality.