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 .     

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.     

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.     

A Lagrangian relaxation approach for network inventory control of stochastic revenue management with perishable commodities

Airline seat inventory control is the allocation of seats in the same cabin to different fare classes such that the total revenue is maximized. Seat allocation can be modelled as dynamic stochastic programs, which are computationally intractable in network settings. Deterministic and probabilistic mathematical programming models are therefore used to approximate dynamic stochastic programs. The probabilistic model, which is the focus of this paper, has a nonlinear objective function, which makes the solution of large-scale practical instances with off-the-shelf solvers prohibitively time consuming. In this paper, we propose a Lagrangian relaxation (LR) method for solving the probabilistic model by exploring the fact that LR problems are decomposable. We show that the solutions of the LR problems admit a simple analytical expression which can be resolved directly. Both the booking limit policy and the bid-price policy can be implemented using this method. Numerical simulations demonstrate the effectiveness of the proposed method.     

Revenue impacts of fare input and demand forecast accuracy in airline yield management

Most airline yield management seat allocation models require inputs of the expected demand by fare class, the variance of this demand, and a revenue value associated with the bookings expected in each class. In this paper, we examine the impacts of errors in the demand forecasts and fare estimates on the revenue performance of some commonly used seat allocation heuristic decision rules. Through simulation analysis of scenarios in which the fare or demand inputs used by the models differ from the ‘actual’ values simulated in the flight booking process, we examine the effects of unexpected variability in the actual fare values, misestimation of the mean fare values of the different booking classes, and forecasting errors in the expected demand for each class. Our findings confirm previous studies that found the accuracy of the demand forecasts to be of greatest importance, but we also uncover some instances where misestimation of the mean demands and/or mean fare values used as inputs to the decision models can actually be beneficial. At the same time, we conclude that the variability of actual fare values around the mean fare values used as inputs does not have a significant impact, given the mathematical characteristics of existing EMSR seat allocation methods.     

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.     

基于旅客选择的高速铁路客运收益管理研究

本文旨在探讨收益管理在高速铁路客运中的应用,给出了存在多级票价时,考虑旅客选择行为的铁路客运收益管理模型,优化结果能够同时给出发车指令和座位出售限制.利用模拟数据对模型进行了数值试验,表明在不同路段长度下,考虑旅客选择行为的总收益较需求独立模型均有所提高,且随着票价等级增多而增长.     

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.     

基于航段需求计算网络竞价的近似动态规划方法

竞价控制是收益管理中广泛应用的一种存量控制方法.将网络存量控制问题描述为一个动态规划模型,通过状态向量的一个仿射函数近似动态规划的最优值函数,并且在航段水平上考虑随机需求,最终得到一个计算网络竞价所需的确定性线性规划(DLP),相对于标准的DLP,这个DLP得到了更接近于动态规划最优值的上界.给出了一个列生成算法用于求解这个DLP,并提供了模拟算例,计算结果表明可获得比标准的DLP方法更好的收益.     

Inventory rationing in an (<Emphasis Type="Italic">s,Q</Emphasis>) inventory model with lost sales and two demand classes

Whenever demand for a single item can be categorised into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s, Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low-priority demand is rejected in anticipation of future high-priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimisation procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained.     

Dynamic simultaneous fare proration for large-scale network revenue management

Network revenue management is concerned with managing demand for products that require inventory from one or several resources by controlling product availability and/or prices in order to maximize expected revenues subject to the available resource capacities. One can tackle this problem by decomposing it into resource-level subproblems that can be solved efficiently, for example by dynamic programming. We propose a new dynamic fare proration method specifically having large-scale applications in mind. It decomposes the network problem by fare proration and solves the resource-level dynamic programs simultaneously using simple, endogenously obtained dynamic marginal capacity value estimates to update fare prorations over time. An extensive numerical simulation study demonstrates that the method results in tightened upper bounds on the optimal expected revenue, and that the obtained policies are very effective with regard to achieved revenues and required runtime.     

弹性需求下城市公交网络服务的优化

对具有弹性需求的城市公交网络系统进行了票价结构与发车频率组合的优化。考虑到公交定价和发车频率会影响乘客需求以及乘客对路径的选择行为,将这一问题描述为一个双层规划问题,上层是寻求社会福利最大的优化问题;下层考虑了乘客的出行选择行为,为弹性需求下乘客在城市公交网络上流量分布的随机用户平衡分配模型。鉴于双层规划问题的非凸性,运用模拟退火算法对模型进行求解,并给出一个仿真算例说明提出的模型和算法的合理性。     

Optimum inventory policies with discrete time proportional demand,discrete replenishment opportunities and different optimizing criteria

This paper extends the deterministic, single product, dynamic E0Q model to the case where demand increases linearly with time but at discrete time points and where the number of replenishments is also discrete. The problem is to find the number of orders and the replenishment schedule that will either maximize the return on the investment on inventory or minimize inventory costs. The proposed solution to either problem requires to first find the replenishment schedule that will minimize the total inventory throughout the planning horizon, for a given number of orders and then find the optimal number of replenishment points. The solution algorithms exploit the discrete nature of the demand and do not require the decomposability property of dynamic programming. This is particularly important in the return on investment case, where decomposability cannot be achieved.     

Analysis of seat allocation and overbooking decisions with hybrid information

We investigate a single-leg airline revenue management problem where an airline has limited demand information and uncensored no-show information. To use such hybrid information for simultaneous overbooking and booking control decisions, we combine expected overbooking cost with revenue. Then we take a robust optimization approach with a regret-based criterion. While the criterion is defined on a myriad of possible demand scenarios, we show that only a small number of them are necessary to compute the objective. We also prove that nested booking control policies are optimal among all deterministic ones. We further develop an effective computational method to find the optimal policy and compare our policy to others proposed in the literature.     

The Classical Economic Order Quantity Formula

Most continuous time inventory models which allow for the stochastic nature of demands usually include a delivery lag. This disguises a close link between deterministic and stochastic formulations of the inventory problem. By assuming that there is no delivery lag a stochastic version of the classical economic lot size model is developed. It yields the traditional square root formula where the constant demand term is replaced by mean demand.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

考虑乘客取消订单的网约车平台定价策略

针对乘运市场供需不匹配的情况,考虑乘客在网约车平台预约订单后的取消行为,以平台利润最大化为目标,首先建立乘客选择模型计算乘客取消订单概率,再分别构建市场供过于求和供不应求状态下的利润模型,求解平台最优定价。研究表明:制定适当的违约规则可以有效减少乘客取消订单的概率,提高平台利润;最优定价随着服务质量的提高而增加,在打车非高峰期,平台可以通过提高服务质量来增加平台利润;非高峰期平台最优定价随着出租车费用的增加而减少,而高峰期定价策略受出租车费用影响较小。     

A scenario‐based stochastic programming model for the control or dummy wafers downgrading problem

The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two‐stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real‐world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. Copyright © 2008 John Wiley & Sons, Ltd.     

A newsvendor model with fuzzy price-dependent demand

Price-dependence is an important characteristic for some inventory problems. This paper proposes a newsvendor model with fuzzy price-dependent demand, and discusses the conditions to determine the optimal pricing and inventory decisions jointly so that the expected profit could be maximized. Then an algorithm combining the method of ranking fuzzy numbers is developed to tackle the problem. Furthermore, comparison is made between the fuzzy model and the deterministic model to study the effect of the uncertain price-dependent demand, and the sensitivity properties of the joint optimal decisions are illustrated through numerical examples.     

A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders

In this paper, we present a robust optimization formulation for dealing with demand uncertainty in a dynamic pricing and inventory control problem for a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting. We introduce a demand-based fluid model where the demand is a linear function of the price, the inventory cost is linear, the production cost is an increasing strictly convex function of the production rate and all coefficients are time-dependent. A key part of the model is that no backorders are allowed. We show that the robust formulation is of the same order of complexity as the nominal problem and demonstrate how to adapt the nominal (deterministic) solution algorithm to the robust problem.