Optimal booking control in revenue management with two substitutable resources

Abstract

This paper studies optimal booking policies for capacity control models in revenue management with two substitutable resources. Our model covers a broader class of problems than previous works including (i) flexible demand and opaque selling for (ii) both dynamic and static demand settings. We provide a unifying characterization of the structure of optimal booking control by exploiting concavity, submodularity, and subconcavity of the value function. Our characterization is based on the notion of optimal "booking paths" formalizing the idea that an optimal allocation of a demand batch decomposes into a sequence of optimal single-request allocations. In addition, we examine the relationship between our booking path-based and a switching curvebased policy, which has been known previously for the case with dynamic demand. We show that both these characterizations describe an optimal policy. Computationally, there is no advantage of implementing either switching curves or booking paths in the dynamic setting. In the static setting, however, one can resort to the simple criteria which we propose in order to construct the optimal booking paths, thereby accelerating the evaluation of the value function.

How much to tell your customer? – A survey of three perspectives on selling strategies with incompletely specified products

“…Given, fixed assignment probabilitiesas used in the context of probabilistic products, but unknown to customersdecrease revenue. Sayah and Irnich (2018) revisit the setting considered by Chen et al (2010) and provide alternative proofs for the structural results obtained there. In addition, they develop a booking path approach that simplifies control in a static setting with batch arrivals, which can partially be accepted.…”

Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers

“…Chen et al (2010) considered a seat capacity control problem with two types of flights and three types of customers in which flights are substitutable for type-three customers. Sayah and Irnich (2019) further investigated a case with batch demands. These two papers explored the structure of the optimal policy.…”

“…Our study differs from them in the following respects: (a) Our model has an extra return process. We take the return rate of containers into consideration when discussing rationing decisions for customers; (b) The optimal policies in Chen et al (2010) and Sayah and Irnich (2019) were characterised by several switching curves, while our optimal policy is characterised by certain thresholds. We further explore the conditions under which the thresholds are independent of the system state; (c) We consider not only contract customers but also walk-in ones, which complicates the analyses, especially when the rental prices for walk-in customers are endogenous; (d) They explored a finite-period problem and modelled it as a time-based MDP, in which the stage changes as time moves.…”

Capacity management for a leasing system with different equipment and batch demands

“…The inventory level for each item was optimized to maximize the total revenue. Sayah and Irnich (2019) studied a capacity control problem with two types of resources. They presented a method to obtain the optimal policy for both single‐unit and multiunit demands.…”