Liner container assignment model with transit-time-sensitive container shipment demand and its applications

This paper proposes a practical tactical-level liner container assignment model for liner shipping companies, in which the container shipment demand is a non-increasing function of the transit time. Given the transit-time-sensitive demand, the model aims to determine which proportion of the demand to fulfill and how to transport these containers in a liner shipping network to maximize the total profit. Although the proposed model is similar to multi-commodity network-flow (MCNF) with side constraints, unlike the MCNF with time delay constraints or reliability constraints that is NP-hard, we show that the liner container assignment model is polynomially solvable due to its weekly schedule characteristics by developing two link-based linear programing formulations. A number of practical extensions and applications are analyzed and managerial insights are discussed. The polynomially solvable liner container assignment model is then applied to address several important decision problems proposed by a global liner shipping company.     

Liner ship route schedule design with port time windows

This paper examines a practical tactical liner ship route schedule design problem, which is the determination of the arrival and departure time at each port of call on the ship route. When designing the schedule, the availability of each port in a week, i.e., port time window, is incorporated. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear nonconvex optimization model. In view of the problem structure, an efficient holistic solution approach is proposed to obtain global optimal solution. The proposed solution method is applied to a trans-Atlantic ship route. The results demonstrate that the port time windows, port handling efficiency, bunker price and unit inventory cost all affect the total cost of a ship route, the optimal number of ships to deploy, and the optimal schedule.     

Container vessel fleet deployment for liner shipping with stochastic dependencies in shipping demand

The problem of optimal container vessels deployment is one of great significance for the liner shipping industry. Although the pioneering work on this problem dates back to the early 1990s, only until recently have researchers started to acknowledge and account for the significant amount of uncertainty present in shipping demand in real world container shipping. In this paper, new analytical results are presented to further relax the input requirements for this problem. Specifically, only the mean and variance of the maximum shipping demand are required to be known. An optional symmetry assumption is shown to further reduce the feasible region and deployment cost for typical confidence levels. Moreover, unlike previous work that tends to ignore stochastic dependencies between the shipping demands on the various routes (that are known to exist in the real world), our models account for such dependencies in the most general setting to date. A salient feature of our modeling approach is that the exact dependence structure does not need to be specified, something that is hard, if not simply impossible, to determine in practice. A numerical case study is provided to illustrate the proposed models.     

Profit-based maritime container assignment models for liner shipping networks

We propose the problem of profit-based container assignment (P-CA), in which the container shipment demand is dependent on the freight rate, similar to the “elastic demand” in the literature on urban transportation networks. The problem involves determining the optimal freight rates, the number of containers to transport and how to transport the containers in a liner shipping network to maximize the total profit. We first consider a tactical-level P-CA with known demand functions that are estimated based on historical data and formulate it as a nonlinear optimization model. The tactical-level P-CA can be used for evaluating and improving the container liner shipping network. We then address the operational-level P-CA with unknown demand functions, which aims to design a mechanism that adjusts the freight rates to maximize the profit. A theoretically convergent trial-and-error approach, and a practical trial-and-error approach, are developed. A numerical example is reported to illustrate the application of the models and approaches.     

Routing and fleet deployment in liner shipping with spot voyages

The routing, scheduling and fleet deployment is an important integrated planning problem faced by liner shipping companies which also lift load from the spot market. This paper is concerned with coordinating the decisions of the assignment of ships to contractual and spot voyages, and the determination of ship routes and schedules in order to maximize profit. We propose a new model for representing voyages as nodes of a directed graph which is used to build a mixed integer programming formulation. Besides contractual and spot nodes, another type of node is put forward to represent a combination of a contractual voyage with one or more spot voyages. In addition, the concept of dominated nodes is introduced in order to discard them and reduce the effort of the search for an optimal solution. A set of test problems has been generated taking into account real world assumptions. The test problems are solved by an optimization software and computational results are reported. The results show the potential of the approach to solve test problems of moderate size.     

Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.     

Integrating parking behaviour in activity-based travel demand modelling: Investigation of the relationship between parking type choice and activity scheduling process

Traditionally, the parking choice/option is considered to be an important factor in only in the mode choice component of a four-stage travel demand modelling system. However, travel demand modelling has been undergoing a paradigm shift from the traditional trip-based approach to an activity-based approach. The activity-based approach is intended to capture the influences of different policy variables at various stages of activity-travel decision making processes. Parking is a key policy variable that captures land use and transportation interactions in urban areas. It is important that the influences of parking choice on activity scheduling behaviour be identified fully. This paper investigates this issue using a sample data set collected in Montreal, Canada. Parking type choice and activity scheduling decision (start time choice) are modelled jointly in order to identify the effects of parking type choice on activity scheduling behaviour. Empirical investigation gives strong evidence that parking type choice influences activity scheduling process. The empirical findings of this investigation challenge the validity of the traditional conception which considers parking choice as exogenous variable only in the mode choice component of travel demand models.     

A two-stage taxi scheduling strategy at airports with multiple independent runways

Long taxiing times at large airports lead to fuel wastage and dissatisfied passengers. This paper investigates the 4D taxi scheduling problem in airports to minimize the taxiing time. We propose an iterative two-stage scheduling strategy. In the first stage, all aircrafts in a current schedule period are assigned initial 4D routes. In the second stage, landing aircrafts that are unavailable to fulfil their initially assigned routes are rescheduled using a shortest path algorithm based approach. In this paper, the simplified model used in most existing literature, that depicts a runway as having a single entrance and a single exit or even sets only one point to represent both of them has been discarded. Instead, we model the fact that a runway has multiple entrance and exit points and use an emerging concept—Runway Exit Availability (REA)—to measure the probability of clearing a runway from a specific exit during a specific time interval so that the taxiing scheduling model can be much higher approximation to the practical operation. An integer programming (IP) model factoring REA is proposed for assigning 4D taxiing routes in the first stage. The IP model covers most practical constraints faced in airport taxiing procedures, such as the rear-end/head-on conflict constraint, runway-crossing constraint, take-off/landing separation constraint, and taxi-out constraint. Besides, flight holding patterns at intersections are much more realistically modelled. Furthermore, to accelerate the solving process of the IP model, we have refined the formulation using several tricks. Simulation results by proposed scheduling approach for operations at the Beijing Capital International Airport (PEK) for an entire day demonstrate a surprising taxiing time saving against the empirical data and simulation results based on a strategy similar to what being used now days while showing an acceptable running time of our approach, which supports that our approach may help in real operation in the future.     

Capturing correlation with a mixed recursive logit model for activity-travel scheduling

Representing activity-travel scheduling decisions as path choices in a time–space network is an emerging approach in the literature. In this paper, we model choices of activity, location, timing and transport mode using such an approach and seek to estimate utility parameters of recursive logit models. Relaxing the independence from irrelevant alternatives (IIA) property of the logit model in this setting raises a number of challenges. First, overlap in the network may not fully characterize perceptual correlation between paths, due to their interpretation as activity schedules. Second, the large number of states that are needed to represent all possible locations, times and activity combinations imposes major computational challenges to estimate the model. We combine recent methodological developments to build on previous work by Blom Västberg et al. (2016) and allow to model complex and realistic correlation patterns in this type of network. We use sampled choices sets in order to estimate a mixed recursive logit model in reasonable time for large-scale, dense time-space networks. Importantly, the model retains the advantage of fast predictions without sampling choice sets. In addition to estimation results, we present an extensive empirical analysis which highlights the different substitution patterns when the IIA property is relaxed, and a cross-validation study which confirms improved out-of-sample fit.