On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.revenue management, bid-prices, relaxations, bounds

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.

Discrete dynamic pricing and application of network revenue management for FlixBus

We consider a real discrete pricing problem in network revenue management for FlixBus. We improve the company's current pricing policy by an intermediate optimization step using booking limits from standard deterministic linear programs. We pay special attention to computational efficiency. FlixBus' strategic decision to allow for low-cost refunds might encourage large group bookings early in the booking process. In this context, we discuss counter-intuitive findings comparing booking limits with static bid price policies. We investigate the theoretical question whether the standard deterministic linear program for network revenue management does provide an upper bound on the optimal expected revenue if customer's willingness to pay varies over time

airline revenue management

With the increasing interest in decision support systems and the continuous advance of computer science, revenue management is a discipline which has received a great deal of interest in recent years. Although revenue management has seen many new applications throughout the years, the main focus of research continues to be the airline industry. Ever since Littlewood (1972) first proposed a solution method for the airline revenue management problem, a variety of solution methods have been introduced. In this paper we will give an overview of the solution methods presented throughout the literature.revenue management;seat inventory control;OR techniques;mathematical programming

Efficient compact linear programs for network revenue management

We are concerned with computing bid prices in network revenue management using approximate linear programming. It is well-known that affine value function approximations yield bid prices which are not sensitive to remaining capacity. The analytic reduction to compact linear programs allows the efficient computation of such bid prices. On the other hand, capacity-dependent bid prices can be obtained using separable piecewise linear value function approximations. Even though compact linear programs have been derived for this case also, they are still computationally much more expensive compared to using affine functions. We propose compact linear programs requiring substantially smaller computing times while, simultaneously, significantly improving the performance of capacity-independent bid prices. This simplification is achieved by taking into account remaining capacity only if it becomes scarce. Although our proposed linear programs are relaxations of the unreduced approximate linear programs, we conjecture equivalence and provide according numerical support. We measure the quality of an approximation by the difference between the expected performance of an induced policy and the corresponding theoretical upper bound. Using this paradigm in numerical experiments, we demonstrate the competitiveness of our proposed linear programs