This paper introduces a decomposition approach for revenue management within a network context. Our method focuses on dynamically pricing bundles for a network of flights, while optimizing revenue and considering customer choice behavior.
The novelty of our work lies in its complexity. We aim to offer the optimal assortment, selecting bundles from an exponential large set of potential combinations of additional products. Furthermore, we must determine the optimal price for each time within our selling horizon. When combined with the network aspect, we end up with a problem that is very changeling to solve. We address the problem by using dynamic programming decomposition, by breaking down itineraries into individual legs, and solving them one at a time. The non-feasible solution is then reconstructed with a Lagrangian heuristic.
Benchmarks in computational experiments demonstrates that our method yields improvements in both upper bound and expected revenue. This highlights the effectiveness of our approach in network revenue management.

For selling bundles of many goods with independent and identically distributed (i.i.d.) valuations, we develop
a distributionally robust framework, consisting of a two-player game between seller and nature. The seller
has only limited knowledge about the value distribution. Nature chooses a revenue-minimizing distribution
from all distributions that comply with the limited knowledge, upon which the seller selects a revenue-
maximizing mechanism that counters nature’s worst-case choice. When the seller knows the mean and
variance of valuations, bundling is known to be an asymptotically optimal deterministic mechanism, achieving
a normalized revenue close to the mean. Moving beyond this variance assumption, we assume knowledge
of the mean absolute deviation (MAD), accommodating more dispersion and heavy-tailed valuations with
infinite variance. We show for a large range of MAD values that bundling remains optimal, but the seller can
only guarantee a revenue strictly smaller than the mean. Another noteworthy finding is indifference to the
order of play, as both the max-min and min-max versions of the problem yield identical values. This contrasts
with deterministic mechanisms and the separate sale of goods, where the order of play significantly impacts
outcomes. We further underscore the universality of the optimal bundling price by demonstrating its efficacy
in optimizing not only absolute revenue but also the absolute regret and ratio objective among all bundling
prices

Real-world decision-making problems involve Type 1 decision-dependent uncertainty, where the probability distribution of the stochastic process depends on the model decisions. However, few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We thus propose herein a general method for solving a class of these programs based on the transformation of random variables, a technique widely employed in probability and statistics. The proposed method is tailored to large-scale problems with discrete or continuous endogenous random variables. The random variable transformation allows the use of the sample average approximation (SAA) method, which provides optimality convergence guarantees under certain conditions. We show that, for some classical distributions, the proposed method reduces to solving mixed-integer linear or convex programs. Finally, we validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. Whereas most distributions result in a nonlinear nonconvex deterministic equivalent program, the proposed method solves mixed-integer linear programs in all cases. In addition, it produces attractive performance estimators for the SAA method in a reasonable computational time and outperforms the case in which the endogenous distribution defines a mixed-integer deterministic equivalent.

We consider a capacitated location-allocation-pricing problem in a single-commodity supply chain with stochastic price-sensitive demands, where the location, allocation and pricing decisions are made simultaneously. Under a general risk measure representing an arbitrary risk tolerance policy, the problem is modeled as a two-stage stochastic integer program (2SIP). To solve the problem, we adapt an integer L-shaped method for 2SIPs with a translation invariant monotone risk measure and demonstrate its applicability on three common risk measures for moderate, cautious and pessimistic policies. We also introduce two family of problem-specific cuts to enhance the performance of the algorithm. Our computational experiments are conducted to study the effectiveness of the algorithm, along with a comparison between the impact of different policies on the solution of the problem. Our approach for incorporating the risk and the proposed solution framework is general and can be used for other similar discrete optimization problems that make use of risk measures.