Marlin W. Ulmer

Budgeting Time for Dynamic Vehicle Routing with Stochastic Customer Requests

Parcel services route vehicles to pick up parcels in the service area. Pickup requests occur dynamically during the day and are unknown before their actual request. Because of working hour restrictions, service vehicles only have a limited time to serve dynamic requests. As a result, not all requests can be confirmed. To achieve an overall high number of confirmed requests, dispatchers have to budget their time effectively by anticipating future requests. To determine the value of a decision, i.e., the expected number of future confirmations given a point of time and remaining free time budget, we present an anticipatory time budgeting heuristic (ATB) drawing on methods of approximate dynamic programming. ATB frequently simulates a problem’s realization to subsequently approximate the values for every vector of point of time and free time budget to achieve an approximation of an optimal decision policy. Since the number of vectors is vast, we introduce the dynamic lookup table (DLT), a general approach ad...

Anticipatory Planning for Courier, Express and Parcel Services

In recent years, the number of challenges for courier, express and parcel services has grown. Today, service providers deal with dynamic changes and uncertainty. Customers can request service at any point of time in the whole service region. Technologies like Global Positioning Systems allow a more detailed and dynamic routing. Furthermore, historical data can be used to anticipate future events. To tackle the new challenges and to utilize the new resources, we suggest modeling customer locations as spatial random variables. This allows a more detailed and therefore efficient routing and decision making. Nevertheless, it requires more complex methods to anticipate future demands, because the straightforward application of graph theoretical approaches is not possible. For an exemplary problem setting in the Euclidean Plane (EP), we introduce a new anticipatory cost benefit heuristic (CBH). Additionally, we adjust techniques of approximate dynamic programming (ADP) and compare the results of CBH and ADP with a myopic approach and an optimal ex post solution. Here, both ADP and CBH outperform the myopic approach.

On the Value and Challenge of Real-Time Information in Dynamic Dispatching of Service Vehicles

Ubiquitous computing technologies and information systems pave the way for real-time planning and management. In the process of dynamic vehicle dispatching, the adherent challenge is to develop decision support systems using real-time information in an appropriate quality and at the right moment in order to improve their value creation. As real-time information enables replanning at any point in time, the question arises when replanning should be triggered. Frequent replanning may lead to efficient routing decisions due to vehicles’ diversions from current routes while less frequent replanning may enable effective assignments due to gained information. In this paper, the authors analyze and quantify the impact of the three main triggers from the literature, exogenous customer requests, endogenous vehicle statuses, and replanning in fixed intervals, for a dynamic vehicle routing problem with stochastic service requests. To this end, the authors generalize the Markov-model of an established dynamic routing problem and embed the different replanning triggers in an existing anticipatory assignment and routing policy. They particularly analyze under which conditions each trigger is advantageous. The results indicate that fixed interval triggers are inferior and dispatchers should focus either on the exogenous customer process or the endogenous vehicle process. It is further shown that the exogenous trigger is advantageous for widely spread customers with long travel durations and few dynamic requests while the endogenous trigger performs best for many dynamic requests and when customers are accumulated in clusters.

Approximate Dynamic Programming for Dynamic Vehicle Routing

This talk addresses the emerging field of dynamic vehicle routing. For these types of problems, plans are subsequently updated with respect to newly revealed information. Furthermore, stochastic information about potential future developments is available. This talk discusses modeling of dynamic vehicle routing problems and how they can be solved. To this end, a variety of solution methods from the field of approximate dynamic programming are presented. The talk further gives an outlook on recent challenges in both applications and methodology.

Value function approximation for dynamic multi-period vehicle routing

Abstract In practical applications like parcel or technician services, customers request service during the day. Service providers decide whether to accept a customer for same-day service or to defer a customer due to resource limitations. Some requests are therefore postponed to the following day. To satisfy customer expectations, service providers aim on a high number of same-day services. Still, acceptance decisions not only affect the performance on the current, but also on the following day. Suitable acceptance, postponement, and routing decisions therefore should anticipate future routing and requests in both the current and the next day(s). The resulting decision problem is a dynamic multi-period vehicle routing problem with stochastic service requests. To approximately solve the Markov decision process of the presented problem, we present an anticipatory dynamic policy based on approximate dynamic programming. This policy estimates the potential of problem states with respect to future same-period services within and over the periods. Our policy draws on value function approximation, state space aggregation, and on a classification of the periods. We compare our policy to several policies from the literature. We analyze how and when multi-period anticipation improves the solution quality significantly and how the newly developed state space classification is essential to achieve anticipation. We finally show how multi-period anticipation changes the acceptance behavior to less discrimination of rural customers and to a fairer geographical distribution of same-day services in comparison to single-period anticipation.

Same-day delivery with heterogeneous fleets of drones and vehicles

In this paper, we analyze how drones can be combined with regular delivery vehicles to improve same-day delivery performance. To this end, we present a dynamic vehicle routing problem with heterogeneous fleets. Customers order goods over the course of the day. These goods are delivered either by a drone or by a regular transportation vehicle within a delivery deadline. Drones are faster but have a limited capacity as well as charging times. Vehicles capacities are unlimited but vehicles are slow due to urban traffic. To decide whether an order is delivered by a drone or by a vehicle, we present a policy function approximation based on geographical districting. Our computational study reveals two major implications: First, geographical districting is highly effective increasing the expected number of sameday deliveries. Second, a combination of drone and vehicle fleets may reduce routing costs significantly.

Anticipation versus reactive reoptimization for dynamic vehicle routing with stochastic requests

Due to new business models and technological advances, dynamic vehicle routing is gaining increasing interest. Solving dynamic vehicle routing problems is challenging, since it requires optimization in two directions. First, as a reaction to newly revealed information, current routing plans need to be reoptimized. Second, uncertain future changes of information need to be anticipated by explicitly quantifying the impact of future information and routing developments. Since customers or drivers usually wait for response, decisions need to be derived in real-time. This limited time often prohibits extensive optimization in both directions and the question arises how to utilize the limited calculation time effectively. In this paper, we compare the merit of route reoptimization and anticipation for a dynamic vehicle routing problem with stochastic requests. To this end, we present a policy allowing for a tunable combination of two existing approaches, each one aiming on optimization in one direction. We show that anticipation is beneficial in every case. We further reveal how the optimization direction is strongly connected to the degree of dynamism, the percentage of unknown requests.

Anticipation in Dynamic Vehicle Routing.

For many routing applications, decision making is conducted under incomplete information. The information is only revealed successively during the execution of the routing. In many cases, dispatchers adapt their decisions dynamically to new information. Nevertheless, to avoid myopic decisions, dispatchers have to anticipate future events in current decision making. In this paper, we propose the use of a Markov decision process (MDP) to model stochastic dynamic vehicle routing problems (SDVRPs). For the integration of stochasticity in dynamic decision making, we present novel methods of approximate dynamic programming (ADP). These methods are extensions and combinations of general ADP-methods and are tailored to match the characteristics of SDVRPs. A comparison with conventional state-of-the-art benchmark heuristics for a SDVRP with stochastic customer requests proves the ADP-methods to be highly advantageous.

Rich Vehicle Routing: Applications

In this chapter, we present the practical fields of routing applications inducing RVRPs. We analyze the applications regarding uncertainty and requirement for planning. We focus on routing in urban environments. The main purpose of this section is to give an overview of the important entities and underlying components in RVRPs as well as the most common objectives, constraints, and main drivers of uncertainty.

Rich Vehicle Routing: Environment

In this chapter, we first recall the development in the field of vehicle routing problems. We then describe the characteristics of rich vehicle routing problems (RVRPs) in Sect. 2.2 focusing on uncertainty and replanning aspects. We briefly describe logistics management (LM) in Sect. 2.3, embed (rich) vehicle routing in context of LM’s hierarchical planning in Sect. 2.4, and present an overview on emerging developments and challenges inducing RVRPs in Sect. 2.5.