Dynamic cruise ship revenue management

Recently, it has been recognized that revenue management of cruise ships is different from that of airlines or hotels. Among the main differences is the presence of multiple capacity constraints in cruise ships, i.e., the number of cabins in different categories and the number of lifeboat seats, versus a single constraint in airlines and hotels (i.e., number of seats or rooms). We develop a discrete-time dynamic capacity control model for a cruise ship characterized by multiple constraints on cabin and lifeboat capacities. Customers (families) arrive sequentially according to a stochastic process and request one cabin of a certain category and one or more lifeboat seats. The cruise ship revenue manager decides which requests to accept based on the remaining cabin and lifeboat capacities at the time of an arrival as well as the type of the arrival. We show that the opportunity cost of accepting a customer is not always monotone in the reservation levels or time. This non-monotone behavior implies that “conventional” booking limits or critical time periods capacity control policies are not optimal. We provide analysis and insights justifying the non-monotone behavior in our cruise ship context. In the absence of monotonicity, and with the optimal solution requiring heavy storage for “large” (industry-size) problems, we develop several heuristics and thoroughly test their performance, via simulation, against the optimal solution, well-crafted upper bounds, and a first-come first-served lower bound. Our heuristics are based on rolling-up the multi-dimensional state space into one or two dimensions and solving the resulting dynamic program (DP). This is a strength of our approach since our DP-based heuristics are easy to understand, solve and analyze. We find that single-dimensional heuristics based on decoupling the cabins and lifeboat problems perform quite well in most cases.     

Network capacity management under competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to address the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single-leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.     

A Markov model for single-leg air cargo revenue management under a bid-price policy

In this paper, we consider the capacity allocation problem in single-leg air cargo revenue management. We assume that each cargo booking request is endowed with a random weight, volume and profit rate and propose a Markovian model for the booking request/acceptance/rejection process. The decision on whether to accept the booking request or to reserve the capacity for future bookings follows a bid-price control policy. In particular, a cargo will be accepted only when the revenue from accepting it exceeds the opportunity cost, which is calculated based on bid prices. Optimal solutions are derived by maximizing a reward function of a Markov chain. Numerical comparisons between the proposed approach and two existing static single-leg air cargo capacity allocation policies are presented.     

Strategic and operational decisions in restaurant revenue management

The paper addresses restaurant revenue management from both a strategic and an operational point of view. Strategic decisions in restaurants are mainly related to defining the most profitable combination of tables that will constitute the restaurant. We propose new formulations of the so-called “Tables Mix Problem” by taking into account several features of the real setting. We compare the proposed models in a computational study showing that restaurants, with the capacity of managing tables as renewable resources and of combining different-sized tables, can improve expected revenue performances. Operational decisions are mainly concerned with the more profitable assignment of tables to customers. Indeed, the “Parties Mix Problem” consists of deciding on accepting or denying a booking request from different groups of customers, with the aim of maximizing the total expected revenue. A dynamic formulation of the “Parties Mix Problem” is presented together with a linear programming approximation, whose solutions can be used to define capacity control policies based on booking limits and bid prices. Computational results compare the proposed policies and show that they lead to higher revenues than the traditional strategies used to support decision makers.     

Airline pricing and fare product differentiation: A new theoretical framework

A basic premise in the development of yield management has been that the differentiated fare products offered by airlines are targeted to distinct segments of the total demand for air travel in a market, each of which compete for space on a fixed capacity aircraft. Such representations of differential pricing assume that the airline can segment its demand perfectly and without cost to consumers, and further, ignore the dependence of the demand for a given fare product on the price levels and characteristics of the other available fare products. In this paper, we introduce a new ‘generalised cost’ model of fare product differentiation that incorporates the relationships between available airline fare products as well as the cost incurred by consumers of accepting more restrictions. We extend the model to incorporate the diversion of passengers to lower-priced fare products as a result of their ability to meet the additional restrictions imposed by airlines, and then demonstrate how seat inventory control can be used to induce diverting passengers to ‘sell up’ to higher-priced fare products by applying booking limits. An example of how the model can be used for joint fare product price level optimisation is presented, along with a numerical example that illustrates the extent to which the conventional model of price discrimination over-estimates passenger demand and, in turn, total airline revenues.     

Mathematical programming for network revenue management revisited

Mathematical programming models for airline seat inventory control provide booking limits and bid-prices for all itineraries and fare classes. E.L. Williamson [Airline network seat inventory control: methodologies and revenue impacts, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992] finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics. We argue that this phenomenon is due to a booking process that includes nesting of the fare classes, which is ignored in the modeling phase. The differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case. Our study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.     

基于遗传算法的座位优化控制模型

座位优化控制是航空运输界增加利润的有效方法 .基于旅客的需求预测 ,可以利用数学规划模型为不同的航段和票价组合计算座位销售上限或者销售竞价 ,从而达到单个航班收入最大化的目的 .常用的方法可分为确定模型和概率模型 ,但对多航段多舱位的优化问题 ,由于出现了复杂的组合和约束 ,这些模型必须简化 .提出了基于遗传算法的座位优化控制模型 ,并和常用的优化方法进行了仿真对比 .研究结果表明 ,遗传算法应用于座位优化 ,可得到满意的解 ,同时 ,遗传算法简化了复杂的约束关系 ,易于实现 ,具有明显的优势 .     

Approximate dynamic programming for capacity allocation in the service industry

We consider a problem where different classes of customers can book different types of service in advance and the service company has to respond immediately to the booking request confirming or rejecting it. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as cost of overtime. For the calculation of the latter, information on the underlying appointment schedule is required. In contrast to most models in the literature we assume that the service time of clients is stochastic and that clients might be unpunctual. Throughout the paper we will relate the problem to capacity allocation in radiology services. The problem is modeled as a continuous-time Markov decision process and solved using simulation-based approximate dynamic programming (ADP) combined with a discrete event simulation of the service period. We employ an adapted heuristic ADP algorithm from the literature and investigate on the benefits of applying ADP to this type of problem. First, we study a simplified problem with deterministic service times and punctual arrival of clients and compare the solution from the ADP algorithm to the optimal solution. We find that the heuristic ADP algorithm performs very well in terms of objective function value, solution time, and memory requirements. Second, we study the problem with stochastic service times and unpunctuality. It is then shown that the resulting policy constitutes a large improvement over an “optimal” policy that is deduced using restrictive, simplifying assumptions.     

Integrated supply chain planning under uncertainty using an improved stochastic approach

This paper proposes an integrated model and a modified solution method for solving supply chain network design problems under uncertainty. The stochastic supply chain network design model is provided as a two-stage stochastic program where the two stages in the decision-making process correspond to the strategic and tactical decisions. The uncertainties are mostly found in the tactical stage because most tactical parameters are not fully known when the strategic decisions have to be made. The main uncertain parameters are the operational costs, the customer demand and capacity of the facilities. In the improved solution method, the sample average approximation technique is integrated with the accelerated Benders’ decomposition approach to improvement of the mixed integer linear programming solution phase. The surrogate constraints method will be utilized to acceleration of the decomposition algorithm. A computational study on randomly generated data sets is presented to highlight the efficiency of the proposed solution method. The computational results show that the modified sample average approximation method effectively expedites the computational procedure in comparison with the original approach.     

Wait or buy? The strategic consumer: Pricing and profit implications

Using tools from operations research, airlines have, for many years, taken a strategic approach to pricing the seats available on a particular flight based on demand forecasts and information. The result of this approach is that the same seat on the same flight is often offered at different fares at different times. Setting of these prices using yield-management approaches is a major activity for many airlines and is well studied in the literature. However, consumers are becoming increasingly aware of the existence of pricing strategies used by airlines. In addition, the availability of airline travel pricing on the Internet affords consumers the opportunity to behave more strategically when making purchase decisions. The onset of the information age makes it possible for an informed consumer or a third party, such as a travel agent, to obtain demand information similar to that used by the airlines. In particular, it is possible for consumers or travel agents to purchase historical data or to obtain it by monitoring the seats that are available at various prices for a given flight. If a consumer understands the pricing strategy and has access to demand information, he/she may decide to defer purchase of a ticket because they believe that a cheaper seat may yet become available. If consumers were to make use of this information to make such strategic purchasing decisions, what would be the impact on airline revenues? The purpose of this paper is to investigate these impacts. This work indicates that use of standard yield management approaches to pricing by airlines can result in significantly reduced revenues when buyers are using an informed and strategic approach to purchasing. Therefore, when airlines are setting or presenting prices, they should investigate the effect of strategic purchasing on their decisions.     

Performance analysis of distributed solution approaches in simulation-based optimization

Applying computationally expensive simulations in design or process optimization results in long-running solution processes even when using a state-of-the-art distributed algorithm and hardware. Within these simulation-based optimization problems the optimizer has to treat the simulation systems as black-boxes. The distributed solution of this kind of optimization problem demands efficient utilization of resources (i.e. processors) and evaluation of the solution quality. Analyzing the parallel performance is therefore an important task in the development of adequate distributed approaches taking into account the numerical algorithm, its implementation, and the used hardware architecture. In this paper, simulation-based optimization problems are characterized and a distributed solution algorithm is presented. Different performance analysis techniques (e.g. scalability analysis, computational complexity) are discussed and a new approach integrating parallel performance and solution quality is developed. This approach combines a priori and a posteriori techniques and can be applied in early stages of the solution process. The feasibility of the approach is demonstrated by applying it to three different classes of simulation-based optimization problems from groundwater management.     

Embedding evolutionary strategy in ordinal optimization for hard optimization problems

This work proposes a method for embedding evolutionary strategy (ES) in ordinal optimization (OO), abbreviated as ESOO, for solving real-time hard optimization problems with time-consuming evaluation of the objective function and a huge discrete solution space. Firstly, an approximate model that is based on a radial basis function (RBF) network is utilized to evaluate approximately the objective value of a solution. Secondly, ES associated with the approximate model is applied to generate a representative subset from a huge discrete solution space. Finally, the optimal computing budget allocation (OCBA) technique is adopted to select the best solution in the representative subset as the obtained “good enough” solution. The proposed method is applied to a hotel booking limits (HBL) problem, which is formulated as a stochastic combinatorial optimization problem with a huge discrete solution space. The good enough booking limits, obtained by the proposed method, have promising solution quality, and the computational efficiency of the method makes it suitable for real-time applications. To demonstrate the computational efficiency of the proposed method and the quality of the obtained solution, it is compared with two competing methods – the canonical ES and the genetic algorithm (GA). Test results demonstrate that the proposed approach greatly outperforms the canonical ES and GA.     

Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

An efficient computational approach for railway booking problems

This paper deals with the determination of seat allocations for a rail booking system. It is assumed that demand for each trip in the network can be divided into two segments, namely a full fare segment and a discounted fare segment. A constrained nonlinear integer programming model is formulated to deal with this problem. The purpose of this paper is to develop an efficient heuristic approach to develop the booking limits for all ticket types in the railway network. The solutions obtained by the heuristic approach are compared with those found by the Lingo software and the DICOPT solver. Numerical results show that the proposed heuristic approach only require a small number of CPU time to obtain superior solutions.     

Supply capacity acquisition and allocation with uncertain customer demands

We study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts. In this setting, a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets. Our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility. We propose a branch-and-price solution approach for this new class of stochastic assignment and capacity planning problems. For problem instances in which capacity levels must fall between some pre-specified limits, we offer a tailored solution approach that reduces solution time by nearly 80% over an alternative approach using a combination of commercial nonlinear optimization solvers. We have also developed a heuristic solution approach that consistently provides optimal or near-optimal solutions, where solutions within 0.01% of optimality are found on average without requiring a nonlinear optimization solver.     

Interactive multiobjective programming in airline network design for international airline code-share alliance

This study presents an interactive airline network design procedure to facilitate bargaining interactions necessitated by international code-share alliance agreements. Code sharing involves partner airlines individually maximizing their own profits, while mutually considering overall profitability, traffic gains, and quality benefits for the markets in which they cooperate with their partners. This study uses a reference point method to solve the interactive multiobjective programming model, to support the bargaining interactions between two partner-airlines in an alliance negotiation. The impact of the code-share alliance network on market demand, alliance partners’ costs and profits, and levels of service are also discussed. A case study demonstrates the feasibility of applying the proposed models and elucidates how interactive multiobjective programming models may be applied to determine flight frequencies for airline code-share alliance networks. The results of this study provide ways by which alliance airlines can evaluate iteratively the output and profits of the alliance members under code-share alliance agreements.     

The combinatorial bandwidth packing problem

In managing a telecommunications network, decisions need to be made concerning the admission of requests submitted by customers to use the network bandwidth. The classical bandwidth packing problem requires that each request submitted by a customer use network resources to establish a one-to-one connection involving one single pair of nodes. We extend the problem to the more practical case where each request submitted by a customer to use the network resources includes a set or combination of calls. This extension suggests that each request requires one-to-many or many-to-many connections to be established between many communicating node pairs. The extension has applications in many important areas such video conferencing and collaborative computing. The combinatorial nature of the requests makes the admission decision more complex because of bandwidth capacity limitations and call routing difficulties. We develop an integer programming formulation of the problem and propose a procedure that can produce verifiably good feasible solutions to the problem. The results of extensive computational experiments over a wide range of problem structures indicate that the procedure provides verifiably good feasible solutions to the problem within reasonable computational times.     

Airline network revenue management by multistage stochastic programming

A multistage stochastic programming approach to airline network revenue management is presented. The objective is to determine seat protection levels for all itineraries, fare classes, points of sale of the airline network and all dcps of the booking horizon such that the expected revenue is maximized. While the passenger demand and cancelation rate processes are the stochastic inputs of the model, the stochastic protection level process represents its output and allows to control the booking process. The stochastic passenger demand and cancelation rate processes are approximated by a finite number of tree structured scenarios. The scenario tree is generated from historical data using a stability-based recursive scenario reduction scheme. Numerical results for a small hub-and-spoke network are reported. This research is supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.     

PBN下多跑道机场航班起降运行排队方式研究

分析多跑道机场终端区的空域结构、飞行、管制状况,利用随机服务系统理论建立运行模型,对航班起降运行排队方式进行讨论.阐明两种排队方式①联合协作(相互支援);②分列独立(互不支援)的运行特点,并建立数学模型,能根据相关参数得到相应排队方式下航班滞留时间、队长和空闲跑道数等有用指标.在相同条件下,定量比较两种运行方式的航班队列服务质量和系统工作特性参数.结果表明:①比②能够支持更多的航班起降请求并提供更高的服务质量,提供利用现有条件扩充跑道容量和缓解航班延误的方法,能满足航空公司和旅客的需求.有较大的理论意义和参考应用价值,实践中得到应用,值得推广.     

Capacity allocation for demand of different customer-product-combinations with cancellations, no-shows, and overbooking when there is a sequential delivery of service

We consider a problem where different classes of customers can book different types of services in advance and the service company has to respond immediately to the booking request confirming or rejecting it. Due to the possibility of cancellations before the day of service, or no-shows at the day of service, overbooking the given capacity is a viable decision. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as the cost of overtime. For the calculation of the latter, information of the underlying appointment schedule is required. Throughout the paper we will relate the problem to capacity allocation in radiology services. Drawing upon ideas from revenue management, overbooking, and appointment scheduling we model the problem as a Markov decision process in discrete time which due to proper aggregation can be optimally solved with an iterative stochastic dynamic programming approach. In an experimental study we successfully apply the approach to a real world problem with data from the radiology department of a hospital. Furthermore, we compare the optimal policy to four heuristic policies, of whom one is currently in use. We can show that the optimal policy significantly improves the currently used policy and that a nested booking limit type policy closely approximates the optimal policy and is thus recommended for use in practice.