Modeling and solving the multimodal car- and ride-sharing problem

We introduce the multimodal car- and ride-sharing problem (MMCRP), in which a pool of cars is used to cover a set of ride requests, while uncovered requests are assigned to other modes of transport (MOT). A car's route consists of one or more trips. Each trip must have a specific but non-predetermined driver, start in a depot and finish in a (possibly different) depot. Ride-sharing between users is allowed, even when two rides do not have the same origin and/or destination. A user has always the option of using other modes of transport according to an individual list of preferences. The problem can be formulated as a vehicle scheduling problem. In order to solve the problem, an auxiliary graph is constructed in which each trip starting and ending in a depot, and covering possible ride-shares, is modeled as an edge in a time-space graph. We propose a two-layer decomposition algorithm based on column generation, where the master problem ensures that each request can only be covered at most once, and the pricing problem generates new promising routes by solving a kind of shortest path problem in a time-space network. Computational experiments based on realistic instances are reported. The benchmark instances are based on demographic, spatial, and economic data of Vienna, Austria. We solve large instances with the column generation based approach to near optimality in reasonable time, and we further investigate various exact and heuristic pricing schemes

Sustainable Passenger Transportation: Dynamic Ride-Sharing

Ride-share systems, which aim to bring together travelers with similar itineraries and time schedules, may provide significant societal and environmental benefits by reducing the number of cars used for personal travel and improving the utilization of available seat capacity. Effective and efficient optimization technology that matches drivers and riders in real-time is one of the necessary components for a successful ride-share system. We formally define dynamic ride-sharing and outline the optimization challenges that arise when developing technology to support ride-sharing. We hope that this paper will encourage more research by the transportation science and logistics community in this exciting, emerging area of public transportation

Response Time Reduction and Service Level Differentiation in Supply Chain Design: Models and Solution Approaches

Make-to-order (MTO) and assemble-to-order (ATO) systems are emerging business strategies in managing responsive supply chains, characterized by high product variety, highly variable customer demand, and short product life cycle. Motivated by the strategic importance of response time in today’s global business environment, this thesis presents models and solution approaches for response time reduction and service-level differentiation in designing MTO and ATO supply chains. In the first part, we consider the problem of response time reduction in the design of MTO supply chains. More specifically, we consider an MTO supply chain design model that seeks to simultaneously determine the optimal location and the capacity of distribution centers (DCs) and allocate stochastic customer demand to DCs, so as to minimize the response time in addition to the fixed cost of opening DCs and equipping them with sufficient assembly capacity and the variable cost of serving customers. The DCs are modelled as M/G/1 queues and response times are computed using steady-state waiting time results from queueing theory. The problem is set up as a network of spatially distributed M/G/1 queues and modelled as a nonlinear mixed-integer program. We linearize the model using a simple transformation and a piece-wise linear and concave approximation. We present two solution procedures: an exact solution approach based on cutting plane method and a Lagrangean heuristic for solving large instances of the problem. While the cutting plane approach provides the optimal solution for moderate instances in few iterations, the Lagrangean heuristic succeeds in finding feasible solutions for large instances that are within 5% from the optimal solution in reasonable computation times. We show that the solution procedure can be extended to systems with multiple customer classes. Using a computational study, we also show that substantial reduction in response times can be achieved with minimal increase in total costs in the design of responsive supply chains. Furthermore, we find the supply chain configuration (DC location, capacity, and demand allocation) that considers congestion and its effect on response time can be very different from the traditional configuration that ignores congestion. The second part considers the problem of response time reduction in the design of a two-echelon ATO supply chain, where a set of plants and DCs are to be established to distribute a set of finished products with non-trivial bill-of-materials to a set of customers with stochastic demand. The model is formulated as a nonlinear mixed integer programming problem. Lagrangean relaxation exploits the echelon structure of the problem to decompose into two subproblems - one for the make-tostock echelon and the other for the MTO echelon. We use the cutting plane based approach proposed above to solve the MTO echelon subproblem. While Lagrangean relaxation provides a lower bound, we present a heuristic that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the heuristic solution is on average within 6% from its optimal. In the final part of the thesis, we consider the problem of demand allocation and capacity selection in the design of MTO supply chains for segmented markets with service-level differentiated customers. Demands from each customer class arrives according to an independent Poisson process and the customers are served from shared DCs with finite capacity and generally distributed service times. Service-levels of various customer classes are expressed as the fraction of their demand served within a specified response (sojourn) time. Our objective is to determine the optimal location and the capacity of DCs and the demand allocation so as to minimize the sum of the fixed cost of opening DCs and equipping them with sufficient capacity and the variable cost of serving customers subject to service-level constraints for multiple customer classes. The problem is set up as a network of spatially distributed M/M/1 priority queues and modelled as a nonlinear mixed integer program. Due to the lack of closed form solution for service-level constraints for multiple classes, we present an iterative simulation-based cutting plane approach that relies on discrete-event simulation for the estimation of the service-level function and its subgradients. The subgradients obtained from the simulation are used to generate cuts that are appended to the mixed integer programming model. We also present a near-exact matrix analytic procedure to validate the estimates of the service-level function and its subgradients from the simulation. Our computational study shows that the method is robust and provides an optimal solution in most of the cases in reasonable computation time. Furthermore, using computational study, we examine the impact of different parameters on the design of supply chains for segmented markets and provide some managerial insights

Stable Matching for Dynamic Ride-sharing Systems

Dynamic ride-sharing systems enable people to share rides and increase the efficiency of urban transportation by connecting riders and drivers on short notice. Automated systems that establish ride-share matches with minimal input from participants provide the most convenience and the most potential for system-wide performance improvement, such as reduction in total vehicle-miles traveled. Indeed, such systems may be designed to match riders and drivers to maximize system performance improvement. However, system-optimal matches may not provide the maximum benefit to each individual participant. In this paper we consider a notion of stability for ride-share matches and present several mathematical programming methods to establish stable or nearly-stable matches, where we note that ride-share matching optimization is performed over time with incomplete information. Our numerical experiments using travel demand data for the metropolitan Atlanta region show that we can significantly increase the stability of ride-share matching solutions at the cost of only a small degradation in system-wide performance

Modelling the Interactions between Information and Communication Technologies and Travel Behaviour

The growing capabilities and widespread proliferation of information and communication technologies (ICT) into virtually every aspect of lifestyle, combined with the continuing challenges faced by transport systems, has ensured ongoing interest in the interactions between ICT and travel behaviour. Yet, despite more than three decades of efforts to understand these relationships, few point of consensus have so far emerged, partly due to the rapidly evolving character of ICT, and partly due to the inherent complexity of such interactions. This thesis seeks to develop novel understandings of such interactions by introducing a number of extensions to the existing modelling frameworks. This is achieved through three interrelated research objectives which seek to explore the topic from macro, micro, and temporal perspectives. The macro perspective takes the form of a structural equation analysis of the relationships between ICT use and travel behaviour across four countries: Canada, the United States, the United Kingdom, and Norway, with the data for the latter three obtained by pooling separate datasets on ICT use and travel behaviour. The micro perspective seeks to develop a microeconomic model of an individual maximising utility through joint choice of activities, including in-travel activities, ICT use, as well as the choice of travel mode, timing and route, with the decisions motivated by contribution towards satisfaction, productivity, and consumption. The model is subsequently tested in the empirical contexts of rail business travel time, business travel time valuation, and conceptualisation of the ICT and travel behaviour interaction scenarios reported elsewhere in the literature. The final, temporal perspective analyses the comparatively least explored topic of evolution in the relationships between ICT use and travel behaviour over time. This is achieved by analysing repeated cross-sectional data using structural equation modelling, and interpreted with reference to the theory of diffusion of innovations. The thesis also discusses a number of potential research, policy and industrial applications of its empirical and theoretical contributions.Open Acces