## Invited Session Fri.2.H 0106

#### Friday, 13:15 - 14:45 h, Room: H 0106

**Cluster 13: Logistics, traffic, and transportation** [...]

### Revenue management applications

**Chair: Paat Rusmevichientong**

**Friday, 13:15 - 13:40 h, Room: H 0106, Talk 1**

**Srikanth Jagabathula**

Assortment optimization under general choice

**Coauthors: Vivek Farias, Devavrat Shah**

**Abstract:**

We consider the problem of static assortment optimization, where the goal is to find the assortment of size at most *C* that maximizes revenues. This is a fundamental decision problem in the area of Operations Management. It has been shown that this problem is provably hard for most of the important families of parametric of choice models, except the multinomial logit (MNL) model. In addition, most of the approximation schemes proposed in the literature are tailored to a specific parametric structure. We deviate from this and propose a general algorithm to find the optimal assortment assuming access to only a subroutine that gives revenue predictions; this means that the algorithm can be applied with any choice model. We prove that when the underlying choice model is the MNL model, our algorithm can find the optimal assortment efficiently. We also perform an extensive numerical studies to establish the accuracy of the algorithm under more complex choice models like the mixture of MNL models.

**Friday, 13:45 - 14:10 h, Room: H 0106, Talk 2**

**Arnoud den Boer**

Simultaneously learning and optimizing in dynamic pricing and revenue management

**Coauthor: Bert Zwart**

**Abstract:**

`Dynamic pricing' refers to practices where the selling price of a product is not a fixed quantity, but can easily be adjusted over time and adapted to changing circumstances. In an online sales channel, the availability of digital sales data enables firms to continuously learn about consumer behavior, and optimize pricing decisions accordingly. As a result, estimation and optimization can be considered simultaneously; the problem then is not only to optimize profit, but also to optimize the `learning process'. A key question in these problems is whether a learning-by-doing approach - always choosing the optimal price w.r.t. current estimates - has a good performance, or whether the decision maker should actively experiment in order to improve his/her knowledge on consumer behavior.

We show that when finite inventory is sold during finite selling seasons, learning-by-doing performs well, and give a bound on the regret (which quantifies the costs for learning). In contrast, in a setting with no inventory restrictions, active experimentation is necessary for optimal learning. We offer an explanation why in these two models, the cost-for-learning behaves differently.

**Friday, 14:15 - 14:40 h, Room: H 0106, Talk 3**

**James Davis**

Assortment optimization under variants of the nested logit model

**Coauthors: Guillermo Gallego, Huseyin Topaloglu**

**Abstract:**

We study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model. There is a fixed revenue associated with each product. The objective is to find an assortment of products to offer that maximizes the expected revenue per customer. There are several variants of the nested logit model and the tractability of the optimization problem depends on which variant is used. The problem is solvable when the range of the nest dissimilarity parameters are between zero and one, and nests do not contain a no purchase option. By removing either of these restrictions the problem becomes NP-hard. However, in these other variants we are able to develop algorithms with desirable worst-case performance guarantees. Of particular note is a data independent approximation algorithm when the nest dissimilarity parameters are restricted to be between zero and one. The algorithms we propose across all variants perform well in computational experiments, generating solutions within a fraction of a percent of optimal.