Using bi-level programming to analyze the royalty for private–public partnership projects: the operational quantity-based model

Abstract

This paper develops a royalty negotiation model based on the operating quantity of Build, Operate, and Transfer (BOT) projects for both government and the private sector using a bi-level programming (BLP) approach. The royalty negotiation is one of many critical negotiation items of a concession contract. This study develops a royalty negotiation model to simulate the negotiation behavior of two parties, and derives the heuristic algorithm for the BLP problem. A number of factors are incorporated into this algorithm including the concession rate, the time value discount rate, the learning rate, and the number of negotiations. The paper includes a case study of the Taipei Port Container Logistic BOT Project. The results show that the two parties involved completed royalty negotiation at the sixth negotiation stage. The findings show that the government can receive a royalty from the concessionaire, calculated at 0.00386% of the operating quantity of this BOT project. Therefore, the royalty negotiation model developed here could be employed to explain negotiation behavior.     

Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty

The build-operate-transfer (BOT) approach is one of the privatization mechanisms for promoting transportation infrastructure developments by using private funds to construct new infrastructure facilities. In a BOT scheme, it often involves three parties: the government, whose objective is to maximize the benefit defined in terms of social welfare added to the society; the private investors, whose objective is to maximize the profit generated from the investment; and the road users, whose objective is to minimize the inequality of benefit distribution among the road users traveling from different origin–destination pairs. Each of these parties has different objectives that often conflict with each other. In this paper, we develop various optimal road pricing models under demand uncertainty for analyzing the tradeoffs among the three objectives. In addition, a project evaluation framework is developed for assessing the effects of government policy and regulation on the BOT project. Seven cases of the BOT road pricing problem are analyzed: (1) BOT without regulation, (2) BOT with price control regulation, (3) BOT with equity regulation, (4) BOT with construction cost subsidy, (5) BOT with concession period extension, (6) BOT with construction cost subsidy and concession period extension, and (7) BOT with multiple objectives. Numerical results using a real case study of the Ban Pong–Kanchananburi Motorway (BMK) in Thailand are provided to examine the above seven cases.     

The analysis of regulation on private highway investment under a build-operate-transfer scheme

The build-operate-transfer (BOT) approach has become an attractive instrument for public facility provision, especially for a project that faces difficulty with public finance. This study analyzes the regulation alternatives on private highway investment under a BOT scheme and their impacts on traffic flows, travel costs, toll, capacity, and social welfare (total user-benefit in the traffic system including congestion). For comparison, five cases are analyzed: (1) No BOT with maximizing welfare, (2) No BOT with breaking even on finance, (3) BOT without regulation, (4) BOT with a minimum flow constraint (the total users will not be less than those in Case 1), and (5) BOT with a maximum travel cost constraint (the travel cost for users on a non-tolled road will not exceed the maximum tolerance). After each case is modeled and simulated on some functional forms, we find that the case of BOT with regulations performs between the cases of maximizing welfare and that of maximizing profit. From the perspective of the government, regulation has less power in a project with low elastic demand. Furthermore, even when the regulation is strict, a high cost-efficient firm with BOT could result in a higher level of social welfare than that without a BOT scheme.     

On the dual approach to the traffic assignment problem

This paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of its dual problem. It is shown that the dual problem can be formulated as a nonsmooth convex optimization problem of which the objective function values and subgradients are conveniently calculated by solving shortest path problems associated with the transportation network. A subgradient algorithm to solve the dual problem is presented and limited computational experience is reported. The computational results are encouraging enough to demonstrate the effectiveness of the proposed approach.     

Distributed computing approaches for large‐scale probit‐based stochastic user equilibrium problems

Applications of probit‐based stochastic user equilibrium (SUE) principle on large‐scale networks have been largely limited because of the overwhelming computational burden in solving its stochastic network loading problem. A two‐stage Monte Carlo simulation method is recognized to have satisfactory accuracy level when solving this stochastic network loading. This paper thus works on the acceleration of the Monte Carlo simulation method via using distributed computing system. Three distributed computing approaches are then adopted on the workload partition of the Monte Carlo simulation method. Wherein, the first approach allocates each processor in the distributed computing system to solve each trial of the simulation in parallel and in turns, and the second approach assigns all the processors to solve the shortest‐path problems in one trial of the Monte Carlo simulation concurrently. The third approach is a combination of the first two, wherein both different trials of the Monte Carlo simulation as well as the shortest path problems in one trial are solved simultaneously. Performances of the three approaches are comprehensively tested by the Sioux‐Falls network and then a randomly generated network example. It shows that computational time for the probit‐based SUE problem can be largely reduced by any of these three approaches, and the first approach is found out to be superior to the other two. The first approach is then selected to calculate the probit‐based SUE problem on a large‐scale network example. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.     

A semi-analytical approach for solving the bottleneck model with general user heterogeneity

This paper proposes a novel semi-analytical approach for solving the dynamic user equilibrium (DUE) of a bottleneck model with general heterogeneous users. The proposed approach makes use of the analytical solutions from the bottleneck analysis to create an equivalent assignment problem that admits closed-form commute cost functions. The equivalent problem is a static and asymmetric traffic assignment problem, which can be formulated as a variational inequality problem (VIP). This approach provides a new tool to analyze the properties of the bottleneck model with general heterogeneity, and to design efficient solution methods. In particular, the existence and uniqueness of the DUE solution can be established using the P-property of the Jacobian matrix. Our numerical experiments show that a simple decomposition algorithm is able to quickly solve the equivalent VIP to high precision. The proposed VIP formation is also extended to address simultaneous departure time and route choice in a single O–D origin-destination network with multiple parallel routes.     

BOT方式投资建设高速公路的风险及其规避措施

BOT是＂build-operate-transfer＂的缩写,意为＂建设-经营-转让＂,是私营企业参与基础设施建设,向社会提供公共服务的一种方式。文章阐述了高速公路项目采用BOT投资方式的优势,并应用具体实例分析了高速公路BOT项目的建设期风险、经营期风险和市场风险,探讨了BOT投资方式项目经营者的风险规避措施和方法。     

A hybrid Genetic Algorithm approach to minimize the total joint cost of a single-vendor multi-customer integrated scheduling problem

This paper addresses the scheduling of supply chains with interrelated factories consisting of a single vendor and multiple customers. In this research, one transporter is available to deliver jobs from vendor to customers, and the jobs can be processed by batch. The problem studied in this paper focuses on a real-case scheduling problem of a multi-location hospital supplied with a central pharmacy. The objective of this work is to minimize the total cost, while satisfying the customer’s due dates constraints. A mathematical formulation of the problem is given as a Mixed Integer Programming model. Then, a Branch-and-Bound algorithm is proposed as an exact method for solving this problem, a greedy local search is developed as a heuristic approach, and a hybrid Genetic Algorithm is presented as a meta-heuristic. Computation experiments are conducted to highlight the performance of the proposed methods.     

An algorithm for the combined distribution and assignment problem

Much interest has recently been shown in the combination of the distribution and assignment models. In this paper we adopt a generalized Benders' decomposition to solve this combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows. The master problem which is generated is used to show that the combined problem can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function. An algorithm for solving the master problem is discussed, and some computational results presented.     

Routing and charging locations for electric vehicles for intercity trips

This study addresses two problems in the context of battery electric vehicles (EVs) for intercity trips: the EV routing problem and the EV optimal charging station location problem (CSLP). The paper shows that EV routing on the shortest path subject to range feasibility for one origin–destination (O–D) pair, called the shortest walk problem (SWP), as well as a stronger version of the problem – the p-stop limited SWP – can be reduced to solving the shortest path problem on an auxiliary network. The paper then addresses optimal CSLPs in which EVs are range feasible with and without p-stops. We formulate the models as mixed-integer multi-commodity flow problems on the same auxiliary network without path and relay pattern enumeration. Benders decomposition is used to propose an exact solution approach. Numerical experiments are conducted using the Indiana state network.     

System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network

Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure. We first show that the non-convexity of the problem can be circumvented by first solving a relaxed problem and then applying a traffic holding elimination procedure to obtain the solution(s) of the original problem. To efficiently solve the relaxed problem, we explore the relationship between the relaxed problems based on different traffic flow models (PQ, SQ, CTM) and a minimal cost flow (MCF) problem for a special space-expansion network. It is shown that all the four problem formulations produce the same minimal system cost and share one common solution which does not involve inside queues in the network. Efficient solution algorithms such as the network simplex method can be applied to solve the MCF problem and identify such an optimal traffic pattern. Numerical examples are also presented to demonstrate the efficiency of the proposed solution procedure.     

Optimal choice of capacity,toll and government guarantee for build-operate-transfer roads under asymmetric cost information

The private provision of public roads via the build-operate-transfer (BOT) mode has been increasingly used around the world. By viewing a BOT contract as a combination of road capacity, toll and government guarantee, this paper investigates optimal concession contract design under both symmetric and asymmetric information about the marginal maintenance cost of private investors. Under asymmetric information, the government guarantee serves as an instrument to induce a private investor to reveal his true cost information. Compared with the situation under symmetric information, the government will suffer a loss of social welfare; the private investor will charge a higher toll that increases in his reported marginal maintenance cost, and specify a lower capacity that decreases with the reported cost. The results also show that the private investor obtains extra information rent beyond the reservation level of return and the rent decreases with his reported cost. However, the resulting volume-capacity ratios of the BOT road under both information structures are the same.     

A case study of Beijing bus crew scheduling: a variable neighborhood‐based approach

Crew scheduling for bus drivers in large bus agencies is known to be a time‐consuming and cumbersome problem in transit operations planning. This paper investigates a new meta‐heuristics approach for solving real‐world bus‐driver scheduling problems. The drivers' work is represented as a series of successive pieces of work with time windows, and a variable neighborhood search (VNS) algorithm is employed to solve the problem of driver scheduling. Examination of the modeling procedure developed is performed by a case study of two depots of the Beijing Public Transport Group, one of the largest transit companies in the world. The results show that a VNS‐based algorithm can reduce total driver costs by up to 18.1%, implying that the VNS algorithm may be regarded as a good optimization technique to solve the bus‐driver scheduling problem. Copyright © 2015 John Wiley & Sons, Ltd.     

A constraint generation algorithm for the construction of periodic railway timetables

This paper addresses the problem of constructing periodic timetables for train operations. We use a mathematical model consisting of periodic time window constraints by means of which arrival and departure times can be related pairwise on a clock, rather than on a linear time axis. Constructing a timetable, then, means solving a set of such constraints. This problem is known to be hard, i.e. it is NP-complete. We describe a new algorithm to solve the problem based on constraint generation and work out a real-life example. It appears that, for problem instances of modest, yet non-trivial, size, the algorithm performs very well, which opens a way to thorough performance analysis of railway systems by studying a large number of possible future timetables.     

Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach

This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature.     

Stochastic optimal path problem with relays

This paper studies the optimal path problem for travelers driving with vehicles of a limited range, such as most battery electric vehicles currently available in the market. The optimal path in this problem often consists of several relay points, where the vehicles can be refueled to extend its range. We propose a stochastic optimal path problem with relays (SOPPR), which aims at minimizing a general expected cost while maintaining a reasonable arrival probability. To account for uncertainty in the road network, the travel speed on a road segment is treated as a discrete random variable, which determines the total energy required to traverse the segment. SOPPR is formulated in two stages in this paper. In the first stage, an optimal routing problem is solved repeatedly to obtain the expected costs and arrival probabilities from any node to all refueling nodes and the destination. With this information, the second stage constructs an auxiliary network, on which the sequence of refueling decisions can be obtained by solving another optimal path problem. Label-correcting algorithms are developed to solve the routing problems in both stages. Numerical experiments are conducted to compare the stochastic and deterministic models, to examine the impact of different parameters on the routing results, and to evaluate the computational performance of the proposed algorithms.     

Truck backhauling on networks with many terminals

Truck backhauling reduces empty truck-miles by having drivers haul loads on trips back to their home terminal. This paper develops a model to help coordinate backhauling between many (more than two) terminals. Two mathematical programming formulations of this backhauling problem are given. One formulates it as a “matching” problem that leads to a heuristic for solving the very large backhauling problems that arise in practice. Using Lagrangian relaxation, the other formulation allows a very tight bound on the optimal solution to be calculated. The quality of the heuristic solution can be determined by comparison with this bound. A large scale example based on actual truck shipments demonstrates how the model might be used in planning truck backhauling. For this example, the heuristic yields a solution within 1% of optimal.     

Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets

Boundedly rational user equilibria (BRUE) represent traffic flow distribution patterns where travellers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost. Those traffic flow patterns satisfying the above condition constitute a set, named the BRUE solution set. It is important to obtain all the BRUE flow patterns, because it can help predict the variation of the link flow pattern in a traffic network under the boundedly rational behavior assumption. However, the methodology of constructing the BRUE set has been lacking in the established literature. This paper fills the gap by constructing the BRUE solution set on traffic networks with fixed demands. After defining ε-BRUE, where ε is the indifference band for the perceived travel cost, we formulate the ε-BRUE problem as a nonlinear complementarity problem (NCP), so that a BRUE solution can be obtained by solving a BRUE–NCP formulation. To obtain the BRUE solution set encompassing all BRUE flow patterns, we propose a methodology of generating acceptable path set which may be utilized under the boundedly rational behavior assumption. We show that with the increase of the indifference band, the acceptable path set that contains boundedly rational equilibrium flows will be augmented, and the critical values of indifference band to augment these path sets can be identified by solving a family of mathematical programs with equilibrium constraints (MPEC) sequentially. The BRUE solution set can then be obtained by assigning all traffic demands to the acceptable path set. Various numerical examples are given to illustrate our findings.     

Globally energy-optimal speed planning for road vehicles on a given route

This paper provides a globally optimal solution to an important problem: given a real-world route, what is the most energy-efficient way to drive a vehicle from the origin to the destination within a certain period of time. Along the route, there may be multiple stop signs, traffic lights, turns and curved segments, roads with different grades and speed limits, and even leading vehicles with pre-known speed profiles. Most of such route information and features are actually constraints to the optimal vehicle speed control problem, but these constraints are described in two different domains. The most important concept in solving this problem is to convert the distance-domain route constraints to some time-domain state and input constraints that can be handled by optimization methods such as dynamic programming (DP). Multiple techniques including cost-to-go function interpolation and parallel computing are used to reduce the computation of DP and make the problem solvable within a reasonable amount of time on a personal computer.