arXiv subjects

Maximilian Schiffer

Publications and source records attributed to Maximilian Schiffer.

At least 55 records · Page 3Linked to original sources

arXiv2023

Driver Routing and Scheduling with Synchronization Constraints

This paper investigates a novel type of driver routing and scheduling problem motivated by a practical application in long-distance bus networks. A key difference from other crew scheduling problems is that drivers can be exchanged between buses at arbitrary intermediate stops en route such that our problem requires additional synchronization constraints. We present a mathematical model for this problem that leverages a time-expanded multi-digraph and derive bounds for the total number of required drivers. Moreover, we develop a destructive-bound-enhanced matheuristic that converges to provably optimal solutions and apply it to a real-world case study for Flixbus, one of Europe's leading coach companies. We demonstrate that our matheuristic outperforms a standalone MIP implementation in terms of solution quality and computational time and reduces the number of required drivers by up to 56% compared to approaches currently used in practice. Our solution approach provides feasible solutions for all instances within seconds and solves instances with up to 390 locations and 70 requests optimally with an average computational time under 210 sec. We further study the impact of driver exchanges on the total driver count and show that allowing for such exchanges leads to average savings of 42.69%.

math.OC↗

arXiv2023

Strategic Workforce Planning in Crowdsourced Delivery with Hybrid Driver Fleets

Nowadays, logistics service providers (LSPs) increasingly consider using a crowdsourced workforce on the last mile to fulfill customers' expectations regarding same-day or on-demand delivery at reduced costs. The crowdsourced workforce's availability is, however, uncertain. Therefore, LSPs often hire additional fixed employees to perform deliveries when the availability of crowdsourced drivers is low. In this context, the reliability versus flexibility trade-off which LSPs face over a longer period, e.g., a year, remains unstudied. Against this background, we jointly study a workforce planning problem that considers fixed drivers (FDs) and the temporal development of the crowdsourced driver (CD) fleet over a long-term time horizon. We consider two types of CDs, gigworkers (GWs) and occasional drivers (ODs). While GWs are not sensitive to the request's destination and typically exhibit high availability, ODs only serve requests whose origin and destination coincide with their own private route's origin and destination. Moreover, to account for time horizon-specific dynamics, we consider stochastic turnover for both FDs and CDs as well as stochastic CD fleet growth. We formulate the resulting workforce planning problem as a Markov decision process (MDP) whose reward function reflects total costs, i.e., wages and operational costs arising from serving demand with FDs and CDs, and solve it via approximate dynamic programming (ADP). Applying our approach to an environment based on real-world demand data from GrubHub, we find that in fleets consisting of FDs and CDs, ADP-based hiring policies can outperform myopic hiring policies by up to 19% in total costs. In the studied setting, we observed that GWs reduce the LSP's total costs more than ODs. When we account for CDs' increased resignation probability when not being matched with enough requests, the amount of required FDs increases.

eess.SY↗

arXiv2023

Branch-and-Price for the Stochastic TSP with Generalized Latency

Motivated by the tactical planning level of demand adaptive public transportation systems, we present the stochastic symmetric traveling salesman problem with generalized latency (STSP-GL), a stochastic extension to the symmetric traveling salesman problem with generalized latency (TSP-GL). The STSP-GL aims to choose a subset of nodes of an undirected graph and determines a Hamiltonian tour amongst those nodes, minimizing an objective function that is a weighted combination of route design and passenger routing costs. These nodes are selected to ensure that a predefined percentage of uncertain passenger demand is served with a given probability. We formulate the STSP-GL as a stochastic program and propose a branch-and-price algorithm for solving its deterministic equivalent. We also develop a local search approach with which we improve the performance of the B&P approach. We assess the efficiency of the proposed methods on a set of instances from the literature. We demonstrate that the proposed methods outperform a known benchmark, improving upper bounds by up to 85% and lower bounds by up to 55%. Finally, we show that solutions of the stochastic model are both more cost-effective and robust than those of the deterministic model.

math.OC↗

arXiv2023

Ambulance Demand Prediction via Convolutional Neural Networks

Minimizing response times is crucial for emergency medical services to reduce patients' waiting times and to increase their survival rates. Many models exist to optimize operational tasks such as ambulance allocation and dispatching. Including accurate demand forecasts in such models can improve operational decision-making. Against this background, we present a novel convolutional neural network (CNN) architecture that transforms time series data into heatmaps to predict ambulance demand. Applying such predictions requires incorporating external features that influence ambulance demands. We contribute to the existing literature by providing a flexible, generic CNN architecture, allowing for the inclusion of external features with varying dimensions. Additionally, we provide a feature selection and hyperparameter optimization framework utilizing Bayesian optimization. We integrate historical ambulance demand and external information such as weather, events, holidays, and time. To show the superiority of the developed CNN architecture over existing approaches, we conduct a case study for Seattle's 911 call data and include external information. We show that the developed CNN architecture outperforms existing state-of-the-art methods and industry practice by more than 9%.

cs.LG↗

arXiv2023

Hybrid Multi-agent Deep Reinforcement Learning for Autonomous Mobility on Demand Systems

We consider the sequential decision-making problem of making proactive request assignment and rejection decisions for a profit-maximizing operator of an autonomous mobility on demand system. We formalize this problem as a Markov decision process and propose a novel combination of multi-agent Soft Actor-Critic and weighted bipartite matching to obtain an anticipative control policy. Thereby, we factorize the operator's otherwise intractable action space, but still obtain a globally coordinated decision. Experiments based on real-world taxi data show that our method outperforms state of the art benchmarks with respect to performance, stability, and computational tractability.

cs.LG↗

arXiv2023

Robust Charging Network Planning for Metropolitan Taxi Fleets

We study the robust charging station location problem for a large-scale commercial taxi fleet. Vehicles within the fleet coordinate on charging operations but not on customer acquisition. We decide on a set of charging stations to open to ensure operational feasibility. To take this decision, we propose a novel solution method situated between the Location Routing Problems with Intraroute Facilities and Flow Refueling Location Problems. Additionally, we introduce a problem variant that makes a station sizing decision. Using our exact approach, charging stations for a robust operation of city-wide taxi fleets can be planned. We develop a deterministic core problem employing a cutting plane method for the strategic problem and a branch-and-price decomposition for the operational problem. We embed this problem into a robust solution framework based on adversarial sampling, which allows for planner-selectable risk tolerance. We solve instances derived from real-world data of the metropolitan area of Munich, containing 1,000 vehicles and 60 potential charging station locations. Our investigation of the sensitivity of technological developments shows that increasing battery capacities show a more favorable impact on vehicle feasibility of up to 10 percentage points compared to increasing charging speeds. Allowing for depot charging dominates both of these options. Finally, we show that allowing just 1% of operational infeasibility risk lowers infrastructure costs by 20%.

math.OC↗

arXiv2023

Combinatorial Optimization enriched Machine Learning to solve the Dynamic Vehicle Routing Problem with Time Windows

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same day deliveries. Existing multi-stage stochastic optimization approaches that allow to solve the underlying dynamic vehicle routing problem are either computationally too expensive for an application in online settings, or -- in the case of reinforcement learning -- struggle to perform well on high-dimensional combinatorial problems. To mitigate these drawbacks, we propose a novel machine learning pipeline that incorporates a combinatorial optimization layer. We apply this general pipeline to a dynamic vehicle routing problem with dispatching waves, which was recently promoted in the EURO Meets NeurIPS Vehicle Routing Competition at NeurIPS 2022. Our methodology ranked first in this competition, outperforming all other approaches in solving the proposed dynamic vehicle routing problem. With this work, we provide a comprehensive numerical study that further highlights the efficacy and benefits of the proposed pipeline beyond the results achieved in the competition, e.g., by showcasing the robustness of the encoded policy against unseen instances and scenarios.

math.OC↗

arXiv2022

Driver-aware charging infrastructure design

Public charging infrastructure plays a crucial role in the context of electrifying the private mobility sector in particular for urban regions. Against this background, we develop a new mathematical model for the optimal placement of public charging stations for electric vehicles in cities. While existing approaches strongly aggregate traffic information or are only applicable to small instances, we formulate the problem as a specific combinatorial optimization problem that incorporates individual demand and temporal interactions of drivers, exact positioning of charging stations, as well as various charging speeds, and realistic charging curves. We show that the problem can be naturally cast as an integer program that, together with different reformulation techniques, can be efficiently solved for large instances. More specifically, we show that our approach can compute optimal placements of charging stations for instances based on traffic data for cities with up to $600\,000$ inhabitants and future electrification rates of up to $15\%$.

math.OC↗

arXiv2022

Optimizing intermodal transportation networks at scale via column generation

In light of the need for design and analysis of intermodal transportation systems, we propose an algorithmic framework to determine the system optimum of an intermodal transportation system. To this end, we model an intermodal transportation system by combining two core principles of network optimization - layered-graph structures and (partially) time-expanded networks - to formulate our problem on a graph that allows us to implicitly encode problem specific constraints related to intermodality. This enables us to solve a standard integer minimum-cost multi-commodity flow problem to obtain the system optimum for an intermodal transportation system. To solve this integer minimum-cost multi-commodity flow problem efficiently, we present a column generation approach to find continuous minimum-cost multi-commodity flow solutions, which we combine with a price-and-branch procedure to obtain integer solutions. To speed up our column generation, we further develop a pricing filter and an admissible distance approximation to utilize the $A^*$ algorithm for solving the pricing problems. We show the efficiency of our framework by applying it to a real-world case study for the city of Munich, where we solve instances with up to 56,295 passengers to optimality, and show that the computation time of our algorithm can be reduced by up to 60\% through the use of our pricing filter and by up to additional 90\% through the use of the $A^*$-based pricing algorithm.

math.OC↗

arXiv2022

Bilevel Optimization for Feature Selection in the Data-Driven Newsvendor Problem

We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse, explainable models with improved out-of-sample performance. Up to now, state-of-the-art methods utilize regularization, which penalizes the number of selected features or the norm of the solution vector. As an alternative, we introduce a novel bilevel programming formulation. The upper-level problem selects a subset of features that minimizes an estimate of the out-of-sample cost of ordering decisions based on a held-out validation set. The lower-level problem learns the optimal coefficients of the decision function on a training set, using only the features selected by the upper-level. We present a mixed integer linear program reformulation for the bilevel program, which can be solved to optimality with standard optimization solvers. Our computational experiments show that the method accurately recovers ground-truth features already for instances with a sample size of a few hundred observations. In contrast, regularization-based techniques often fail at feature recovery or require thousands of observations to obtain similar accuracy. Regarding out-of-sample generalization, we achieve improved or comparable cost performance.

cs.LG↗

arXiv2022

Coordinating charging request allocation between self-interested navigation service platforms

Current electric vehicle market trends indicate an increasing adoption rate across several countries. To meet the expected growing charging demand, it is necessary to scale up the current charging infrastructure and to mitigate current reliability deficiencies, e.g., due to broken connectors or misreported charging station availability status. However, even within a properly dimensioned charging infrastructure, a risk for local bottlenecks remains if several drivers cannot coordinate their charging station visit decisions. Here, navigation service platforms can optimally balance charging demand over available stations to reduce possible station visit conflicts and increase user satisfaction. While such fleet-optimized charging station visit recommendations may alleviate local bottlenecks, they can also harm the system if self-interested navigation service platforms seek to maximize their own customers' satisfaction. To study these dynamics, we model fleet-optimized charging station allocation as a resource allocation game in which navigation platforms constitute players and assign potentially free charging stations to drivers. We show that no pure Nash equilibrium guarantee exists for this game, which motivates us to study VCG mechanisms both in offline and online settings, to coordinate players' strategies toward a better social outcome. Extensive numerical studies for the city of Berlin show that when coordinating players through VCG mechanisms, the social cost decreases on average by 42 % in the online setting and by 52 % in the offline setting.

econ.TH↗

arXiv2022

Electric vehicle charge scheduling with flexible service operations

Operators who deploy large fleets of electric vehicles often face a challenging charge scheduling problem. Specifically, time-ineffective recharging operations limit the profitability of charging during service operations such that operators recharge vehicles off-duty at a central depot. Here, high investment cost and grid capacity limit available charging infrastructure such that operators need to schedule charging operations to keep the fleet operational. In this context, flexible service operations, i.e. allowing to delay or expedite vehicle departures, can potentially increase charger utilization. Beyond this, jointly scheduling charging and service operations promises operational cost savings through better utilization of Time-of-Use energy tariffs and carefully crafted charging schedules designed to minimize battery wear. Against this background, we study the resulting joint charging and service operations scheduling problem accounting for battery degradation, non-linear charging, and Time-of-Use energy tariffs. We propose an exact Branch & Price algorithm, leveraging a custom branching rule and a primal heuristic to remain efficient during the Branch & Bound phase. Moreover, we develop an exact labeling algorithm for our pricing problem, constituting a resource-constrained shortest path problem that considers variable energy prices and non-linear charging operations. We benchmark our algorithm in a comprehensive numerical study and show that it can solve problem instances of realistic size with computational times below one hour, thus enabling its application in practice. Additionally, we analyze the benefit of jointly scheduling charging and service operations. We find that our integrated approach lowers the amount of charging infrastructure required by up to 57% besides enabling operational cost savings of up to 5%.

eess.SY↗

arXiv2022

Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cuts

The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as the hard-margin loss, which associates a constant penalty to any misclassified or within-margin sample. Applying this loss function yields much-needed robustness for critical applications but it also leads to an NP-hard model that makes training difficult, since current exact optimization algorithms show limited scalability, whereas heuristics are not able to find high-quality solutions consistently. Against this background, we propose new integer programming strategies that significantly improve our ability to train the hard-margin SVM model to global optimality. We introduce an iterative sampling and decomposition approach, in which smaller subproblems are used to separate combinatorial Benders' cuts. Those cuts, used within a branch-and-cut algorithm, permit to converge much more quickly towards a global optimum. Through extensive numerical analyses on classical benchmark data sets, our solution algorithm solves, for the first time, 117 new data sets to optimality and achieves a reduction of 50% in the average optimality gap for the hardest datasets of the benchmark.

cs.LG↗

arXiv2022

Optimal Decision Diagrams for Classification

Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly, decision diagrams are usually less prone to data fragmentation in internal nodes. However, the inherent complexity of training these classifiers acted as a long-standing barrier to their widespread adoption. In this context, we study the training of optimal decision diagrams (ODDs) from a mathematical programming perspective. We introduce a novel mixed-integer linear programming model for training and demonstrate its applicability for many datasets of practical importance. Further, we show how this model can be easily extended for fairness, parsimony, and stability notions. We present numerical analyses showing that our model allows training ODDs in short computational times, and that ODDs achieve better accuracy than optimal decision trees, while allowing for improved stability without significant accuracy losses.

cs.LG↗

arXiv2022

Coordinated Charging Station Search in Stochastic Environments: A Multi-Agent Approach

Range and charge anxiety remain essential barriers to a faster electric vehicle market diffusion. To this end, quickly and reliably finding suitable charging stations may foster an electric vehicle uptake by mitigating drivers' anxieties. Here, existing commercial services help drivers to find available stations based on real-time availability data but struggle with data inaccuracy, e.g., due to conventional vehicles blocking the access to public charging stations. In this context, recent works have studied stochastic search methods to account for availability uncertainty in order to minimize a driver's detour until reaching an available charging station. So far, both practical and theoretical approaches ignore driver coordination enabled by charging requests centralization or sharing of data, e.g., sharing observations of charging stations' availability or visit intentions between drivers. Against this background, we study coordinated stochastic search algorithms, which help to reduce station visit conflicts and improve the drivers' charging experience. We model a multi-agent stochastic charging station search problem as a finite-horizon Markov decision process and introduce an online solution framework applicable to static and dynamic policies. In contrast to static policies, dynamic policies account for information updates during policy planning and execution. We present a hierarchical implementation of a single-agent heuristic for decentralized decision making and a rollout algorithm for centralized decision making. Extensive numerical studies show that compared to an uncoordinated setting, a decentralized setting with visit-intentions sharing decreases the system cost by 26%, which is nearly as good as the 28% cost decrease achieved in a centralized setting, and saves up to 23% of a driver's search time while increasing her search reliability.

eess.SY↗

arXiv2021

Online Traffic Routing: Deterministic Limits and Data-driven Enhancements

Over the past decade, GPS enabled traffic applications, such as Google Maps and Waze, have become ubiquitous and have had a significant influence on billions of daily commuters' travel patterns. A consequence of the online route suggestions of such applications, e.g., via greedy routing, has often been an increase in traffic congestion since the induced travel patterns may be far from the system optimum. Spurred by the widespread impact of traffic applications on travel patterns, this work studies online traffic routing in the context of capacity-constrained parallel road networks and analyzes this problem from two perspectives. First, we perform a worst-case analysis to identify the limits of deterministic online routing and show that the ratio between the total travel cost of the online solution of any deterministic algorithm and that of the optimal offline solution is unbounded, even in simple settings. This result motivates us to move beyond worst-case analysis. Here, we consider algorithms that exploit knowledge of past problem instances and show how to design data-driven algorithms whose performance can be quantified and formally generalized to unseen future instances. We present numerical experiments based on an application case for the San Francisco Bay Area to evaluate the performance of our approach. Our results show that the data-driven algorithms we develop outperform commonly used greedy online-routing algorithms.

math.OC↗

arXiv2021

The Customer is Always Right: Customer-Centered Pooling for Ride-Hailing Systems

Today's ride-hailing systems experienced significant growth and ride-pooling promises to allow for efficient and sustainable on-demand transportation. However, efficient ride-pooling requires a large pool of participating customers. To increase the customers' willingness for participation, we study a novel customer-centered pooling (CCP) mechanism, accounting for individual customers' pooling benefits. We study the benefit of this mechanism from a customer, fleet operator, and system perspective, and compare it to existing provider-centered pooling (PCP) mechanisms. We prove that it is individually rational and weakly dominant for a customer to participate in CCP, but not for PCP. We substantiate this analysis with complementary numerical studies, implementing a simulation environment based on real-world data that allows us to assess both mechanisms' benefit. To this end, we present results for both pooling mechanisms and show that pooling can benefit all stakeholders in on-demand transportation. Moreover, we analyze in which cases a CCP mechanism Pareto dominates a PCP mechanism and show that a mobility service operator would prefer CCP mechanisms over PCP mechanisms for all price segments. Simultaneously, CCP mechanisms reduce the overall distance driven in the system up to 32% compared to not pooling customers. Our results provide decision support for mobility service operators that want to implement and improve pooling mechanisms as they allow us to analyze the impact of a CCP and a PCP mechanism from a holistic perspective. Among others, we show that CCP mechanisms can lead to a win-win situation for operators and customers while simultaneously improving system performance and reducing emissions.

eess.SY↗

arXiv2021

A Concise Guide on the Integration of Battery Electric Buses into Urban Bus Networks

With the increasing market penetration of battery-electric buses into urban bus networks, practitioners face many novel planning problems. As a result, the interest in optimization-based decision-making for these planning problems increases but practitioners' requirements on planning solutions and current academic approaches often diverge. Against this background, this survey aims to provide a concise guide on optimization-based planning approaches for integrating battery-electric buses into urban bus networks for both practitioners and academics. First, we derive practitioners' requirements for integrating battery-electric buses from state-of-the-art specifications, project reports, and expert knowledge. Second, we analyze whether existing optimization-based planning models fulfill these practitioners' requirements. Based on this analysis, we carve out the existing gap between practice and research and discuss how to address these in future research.

eess.SY↗