Network revenue management with product-specific no-shows

Revenue management practices often include overbooking capacity to account for customers who make reservations but do not show up. In this paper, we consider the network revenue management problem with no-shows and overbooking, where the show-up probabilities are specific to each product. No-show rates differ significantly by product (for instance, each itinerary and fare combination for an airline) as sale restrictions and the demand characteristics vary by product. However, models that consider no-show rates by each individual product are difficult to handle as the state-space in dynamic programming formulations (or the variable space in approximations) increases significantly. In this paper, we propose a randomized linear program to jointly make the capacity control and overbooking decisions with product-specific no-shows. We establish that our formulation gives an upper bound on the optimal expected total profit and our upper bound is tighter than a deterministic linear programming upper bound that appears in the existing literature. Furthermore, we show that our upper bound is asymptotically tight in a regime where the leg capacities and the expected demand is scaled linearly with the same rate. We also describe how the randomized linear program can be used to obtain a bid price control policy. Computational experiments indicate that our approach is quite fast, able to scale to industrial problems and can provide significant improvements over standard benchmarks.Network revenue management, linear programming, simulation, overbooking, no-shows.

Multi-resolution analysis of earthquake losses : from city block to national scale

Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2002.Includes bibliographical references (leaves 147-151).by Sumit Mathew Kunnumkal.S.M.in Transportatio

Approximate Dynamic Programming and Stochastic Approximation Methods for Inventory Control and Revenue Management

In this thesis, we develop approximate dynamic programming and stochastic approximation methods for problems in inventory control and revenue management. A unifying feature of the methods we develop is that they exploit the underlying problem structure. By doing so, we are able to establish certain theoretical properties of our methods, make them more computationally efficient and obtain a faster rate of convergence. In the stochastic approximation framework, we develop an algorithm for the monotone estimation problem that uses a projection operator with respect to the max norm onto the order simplex. We show the almost sure convergence of this algorithm and present applications to the Q-learning algorithm and the newsvendor problem with censored demands. Next, we consider a number of inventory control problems for which the so-called base-stock policies are known to be optimal. We propose stochastic approximation methods to compute the optimal base-stock levels. Existing methods in the literature have only local convergence guarantees. In contrast, we show that the iterates of our methods converge to base-stock levels that are globally optimal. Finally, we consider the revenue management problem of optimally allocating seats on a single flight leg to demands from multiple fare classes that arrive sequentially. We propose a stochastic approximation algorithm to compute the optimal protection levels. The novel aspect of our method is that it works with the nonsmooth version of the problem where capacity can only be allocated in integer quantities. We show that the iterates of our algorithm converge to the globally optimal protection levels. In the approximate dynamic programming framework, we use a Lagrangian relaxation strategy to make the inventory control decisions in a distribution system consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. Our method is based on relaxing the constraints that ensure the nonnegativity of the shipments to the retailers by associating Lagrange multipliers to them. We show that our method naturally provides a lower bound on the optimal objective value. Furthermore, a good set of Lagrange multipliers can be obtained by solving a convex optimization problem

Linear programming based decomposition methods for inventory distribution systems

We consider an inventory distribution system consisting of one warehouse and multiple retailers. The retailers face random demand and are supplied by the warehouse. The warehouse replenishes its stock from an external supplier. The objective is to minimize the total expected replenishment, holding and backlogging cost over a finite planning horizon. The problem can be formulated as a dynamic program, but this dynamic program is difficult to solve due to its high dimensional state variable. It has been observed in the earlier literature that if the warehouse is allowed to ship negative quantities to the retailers, then the problem decomposes by the locations. One way to exploit this observation is to relax the constraints that ensure the nonnegativity of the shipments to the retailers by associating Lagrange multipliers with them, which naturally raises the question of how to choose a good set of Lagrange multipliers. In this paper, we propose efficient methods that choose a good set of Lagrange multipliers by solving linear programming approximations to the inventory distribution problem. Computational experiments indicate that the inventory replenishment policies obtained by our approach can outperform several standard benchmarks by significant margins.Inventory distribution Approximate dynamic programming Inventory control