A Path-Based Solution Algorithm for Dynamic Traffic Assignment

The approximation of the traversal cost is a critical component of dynamic traffic assignment model. In link based traffic assignment, it assumes that the constraints sets are linear or convex and it is not realistic in general traffic networks. Comparing with the link based model, the path cost in the objective function of the path based traffic assignment model is implicitly nonlinear or non-convex, which is difficult to solve. In this paper, a path based traffic assignment model combining the generalized expansion method in M/G/c/c model with the point queue model is proposed to extend the link traversal cost to the travel cost along the path. Comparing with the link based model without considering intersection effects, this proposed path based model can take into account queuing delays between intersections and it is easy to implement. In order to validate the proposed path based model, a comparative experiment is implemented by comparing with the traditional travel cost models in Sydney traffic networks. Taking into account travel flow changes and blocking time, the proposed path based model is more effective for travellers from the uncongested traffic to congested traffic networks. In addition, the results from traffic assignment model show that the proposed model can achieve feasible results.     

Storage assignment problem with travel distance and blocking considerations for a picker-to-part order picking system

Order picking is a key operation in managing a warehouse efficiently. Most previous studies on picking only considered single-picker operation; however, many pickers frequently work concurrently in the same region. Since congestion may occur in such a multi-picker system, waiting time must be taken into account together with travel time and distance when evaluating the efficiency of picking operations. The picking model under investigation can be formulated as a queueing network, and a heuristic storage assignment policy that considers both the travel time and the waiting time simultaneously by minimizing the average order fulfillment time is developed in the paper. An approximation method and a simulation model using eM-plant software are presented to implement the proposed heuristic algorithm and to compare the mean travel time for different storage assignment polices as well. The results indicate that the proposed heuristic policy outperforms existing storage assignment policies in a multi-picker warehouse environment.     

Figure-ground discrimination: a combinatorial optimization approach

The figure-ground discrimination problem is considered from a combinatorial optimization perspective. A mathematical model encoding the figure-ground discrimination problem that makes explicit a definition of shape based on cocircularity, smoothness, proximity, and contrast is presented. This model consists of building a cost function on the basis of image element interactions. This cost function fits the constraints of an interacting spin system that, in turn, is a well suited physical model that solves hard combinatorial optimization problems. Two combinatorial optimization methods for solving the figure-ground problem, namely mean field annealing, which combines mean field approximation theory and annealing, and microcanonical annealing, are discussed. Mean field annealing may be viewed as a deterministic approximation of stochastic methods such as simulated annealing. The theoretical bases of these methods are described, and the computational models are derived. The efficiencies of mean field annealing, simulated annealing, and microcanonical annealing algorithms are compared. Within the framework of such a comparison, the figure-ground problem may be viewed as a benchmark     

Modeling Business Land Use Equilibrium for Small Firms’ Relocation and Consumers’ Trip in a Transportation Network

This paper studies the integrated models for small and medium-sized enterprises’ distribution and consumers’ trip in an urban network based on the simultaneous equilibrium approach. In this paper, each firm aims at finding some business centers to set up shops to maximize his net profit while each consumer is a traveler who chooses his destination (business center) and travel route according to the minimization of individual net social cost, which is equal to the cost of travel time minus the destination attraction measure. The contribution of this paper can be divided into three parts. Firstly, a new deterministic equilibrium model is developed to capture consumers’ travel choice and firms’ location choice. The relocation cost between any two business centers is explicitly considered. Furthermore, the business center passenger/firm flow capacity constraint is incorporated into the previous model. Mathematically, we prove that this extension will derive the endogenous location transfer market in a business center for firms if the maximum firm flow capacity is reached at equilibrium. Finally, we extend the preceding deterministic models to the stochastic case.     

机票定价与舱位控制两阶段决策方法

针对航空收益管理中定价与舱位控制联合决策问题,提出一种两阶段决策方法.以最大化总收益为目标,建立和分析相应的联合决策模型,包括非嵌套模型(确定性模型和随机模型)和嵌套模型.通过对模型的求解和仿真得到:在价格方面,随机模型定价最高,其次是嵌套模型,确定性模型定价最低;在对低票价等级的订座限制方面,随机模型限制最严,其次是确定性模型,嵌套模型限制最宽松;最终总收益方面,嵌套模型的总收益最高,而随机模型与确定性模型总收益的高低视情况而定.为应对求解大规模嵌套模型算例时的复杂性,分别将非嵌套模型计算所得的定价结果作为嵌套模型的输入价格,求得对应的座位分配结果.对所得到的两阶段策略进行仿真得到,随机模型与嵌套模型相结合所得到的两阶段策略表现更好,能够使总收益接近最优水平.     

Application of hierarchical matrices for computing the Karhunen–Loève expansion

Realistic mathematical models of physical processes contain uncertainties. These models are often described by stochastic differential equations (SDEs) or stochastic partial differential equations (SPDEs) with multiplicative noise. The uncertainties in the right-hand side or the coefficients are represented as random fields. To solve a given SPDE numerically one has to discretise the deterministic operator as well as the stochastic fields. The total dimension of the SPDE is the product of the dimensions of the deterministic part and the stochastic part. To approximate random fields with as few random variables as possible, but still retaining the essential information, the Karhunen–Loève expansion (KLE) becomes important. The KLE of a random field requires the solution of a large eigenvalue problem. Usually it is solved by a Krylov subspace method with a sparse matrix approximation. We demonstrate the use of sparse hierarchical matrix techniques for this. A log-linear computational cost of the matrix-vector product and a log-linear storage requirement yield an efficient and fast discretisation of the random fields presented.     

Uplink scheduling for joint wireless orthogonal frequency and time division multiple access networks

In this paper, we present a deterministic resource allocation model for a hybrid uplink wireless orthogonal frequency and time division multiple access network. Since the input data of the model may be affected by uncertainty, we further consider a stochastic formulation of the problem which we transform into an equivalent deterministic binary second-order conic program (SOCP). Subsequently, we use this binary SOCP to derive an equivalent integer linear programming formulation. The proposed models are aimed at maximizing the total bandwidth channel capacity subject to user power and sub-carrier assignment constraints while simultaneously scheduling users in time. As such, the models are best suited for non-real-time applications where sub-channel multiuser diversity can be further exploited simultaneously in frequency and time domains. Finally, in view of the large execution times required by CPLEX to solve the proposed models, we propose a variable neighborhood search metaheuristic procedure. Our numerical results show tight bounds and near optimal solutions for most of the instances when compared to the optimal solution of the problem. Moreover, we obtain better feasible solutions than CPLEX in the stochastic case. Finally, these bounds are obtained at a very low computational cost.     

A Stochastic Process Approach for Frequency-based Transit Assignment with Strict Capacity Constraints

Transit assignment models represent the stochastic nature of waiting times, but usually adopt a deterministic representation route flows and costs. Especially in cities where transit vehicles are small and not operating to timetables, there is a need to represent the variability in flows and costs to enable planners make more informed decisions. Stochastic process (SP) models consider the day-to-day dynamics of the transit demand-supply system, explicitly modelling passengers’ information acquisition and decision processes. A Monte Carlo simulation based SP model that includes strict capacity constraints is presented in this paper. It uses micro-simulation to constrain passenger flows to capacities and obtain realistic cost estimates. Applications of the model and its comparison with the De Cea and Fernandez (Transp Sci, 27:133–147, 1993) model are presented using a small network.     

Pre-positioning disaster response facilities at safe locations: An evaluation of deterministic and stochastic modeling approaches

Choosing the locations of disaster response facilities for the storage of emergency supplies is critical to the quality of service provided post-occurrence of a large scale emergency like an earthquake. In this paper, we provide two location models that explicitly take into consideration the impact a disaster can have on the disaster response facilities and the population centers in surrounding areas. The first model is a deterministic model that incorporates distance-dependent damages to disaster response facilities and population centers. The second model is a stochastic programming model that extends the first by directly considering the damage intensity as a random variable. For this second model we also develop a novel solution method based on Benders Decomposition that is generalizable to other 2-stage stochastic programming problems. We provide a detailed case study using large-scale emergencies caused by an earthquake in California to demonstrate the performance of these new models. We find that the locations suggested by the stochastic model in this paper significantly reduce the expected cost of providing supplies when one considers the damage a disaster causes to the disaster response facilities and areas near it. We also demonstrate that the cost advantage of the stochastic model over the deterministic model is especially large when only a few facilities can be placed. Thus, the value of the stochastic model is particularly great in realistic, budget-constrained situations.     

Logistical support scheduling under stochastic travel times given an emergency repair work schedule

Stochastic factors during the operational stage could have a significant influence on the planning results of logistical support scheduling for emergency roadway repair work. An optimal plan might therefore lose its optimality when applied in real world operations where stochastic disturbances occur. In this study we employ network flow techniques to construct a logistical support scheduling model under stochastic travel times. The concept of time inconsistency is also proposed for precisely estimating the impact of stochastic disturbances arising from variations in vehicle trip travel times during the planning stage. The objective of the model is to minimize the total operating cost with an unanticipated penalty cost for logistical support under stochastic traveling times in short term operations, based on an emergency repair work schedule, subject to related operating constraints. This model is formulated as a mixed-integer multiple-commodity network flow problem and is characterized as NP-hard. To solve the problem efficiently, a heuristic algorithm, based on problem decomposition and variable fixing techniques, is proposed. A simulation-based evaluation method is also presented to evaluate the schedules obtained using the manual method, the deterministic model and the stochastic model in the operation stage. Computational tests are performed using data from Taiwan’s 1999 Chi-Chi earthquake. The preliminary test results demonstrate the potential usefulness of the proposed stochastic model and solution algorithm in actual practice.