Dynamic Pricing and Routing for Same-Day Delivery

2020 ◽  
Vol 54 (4) ◽  
pp. 1016-1033 ◽  
Author(s):  
Marlin W. Ulmer
Keyword(s):  
Dynamic Pricing ◽  
Function Approximation ◽  
Computational Study ◽  
Routing Problem ◽  
Value Function Approximation ◽  
Routing Policy ◽  
State Dependent ◽  
Markov Decision ◽  
Fixed Prices ◽  
Number Of Customers

An increasing number of e-commerce retailers offers same-day delivery. To deliver the ordered goods, providers dynamically dispatch a fleet of vehicles transporting the goods from the warehouse to the customers. In many cases, retailers offer different delivery deadline options, from four-hour delivery up to next-hour delivery. Due to the deadlines, vehicles often only deliver a few orders per trip. The overall number of served orders within the delivery horizon is small and the revenue low. As a result, many companies currently struggle to conduct same-day delivery cost-efficiently. In this paper, we show how dynamic pricing is able to substantially increase both revenue and the number of customers we are able to serve the same day. To this end, we present an anticipatory pricing and routing policy (APRP) method that incentivizes customers to select delivery deadline options efficiently for the fleet to fulfill. This maintains the fleet’s flexibility to serve more future orders. We model the respective pricing and routing problem as a Markov decision process (MDP). To apply APRP, the state-dependent opportunity costs per customer and option are required. To this end, we use a guided offline value function approximation (VFA) based on state space aggregation. The VFA approximates the opportunity cost for every state and delivery option with respect to the fleet’s flexibility. As an offline method, APRP is able to determine suitable prices instantly when a customer orders. In an extensive computational study, we compare APRP with a policy based on fixed prices and with conventional temporal and geographical pricing policies. APRP outperforms the benchmark policies significantly, leading to both a higher revenue and more customers served the same day.

Dynamic Optimization for Airline Maintenance Operations

2020 ◽  
Vol 54 (4) ◽  
pp. 998-1015 ◽  
Author(s):  
Carlos Lagos ◽  
Felipe Delgado ◽  
Mathias A. Klapp
Keyword(s):  
Dynamic Optimization ◽  
Function Approximation ◽  
Economies Of Scale ◽  
Maintenance Scheduling ◽  
Limited Attention ◽  
Aircraft Maintenance ◽  
Value Function Approximation ◽  
Markov Decision ◽  
Airline Maintenance

The occurrence of unexpected aircraft maintenance tasks can produce expensive changes in an airline’s operation. When it comes to critical tasks, it might even cancel programmed flights. Despite this, the challenge of scheduling aircraft maintenance operations under uncertainty has received limited attention in the scientific literature. We study a dynamic airline maintenance scheduling problem, which daily decides the set of aircraft to maintain and the set of pending tasks to execute in each aircraft. The objective is to minimize the expected costs of expired maintenance tasks over the operating horizon. To increase flexibility and reduce costs, we integrate maintenance scheduling with tail assignment decisions. We formulate our problem as a Markov decision process and design dynamic policies based on approximate dynamic programming, including value function approximation, rolling horizon techniques, and a hybrid policy between the latter two that delivers the best results. In a case study based on LATAM airline, we show the value of dynamic optimization by testing our best policies against a simple airline decision rule and a deterministic relaxation with perfect future information. We suggest to schedule tasks requiring less resources first to increase utilization of residual maintenance capacity. Finally, we observe strong economies of scale when sharing maintenance resources between multiple airlines.

Workforce Scheduling in the Era of Crowdsourced Delivery

2020 ◽  
Vol 54 (4) ◽  
pp. 1113-1133
Author(s):  
Marlin Ulmer ◽  
Martin Savelsbergh
Keyword(s):  
Function Approximation ◽  
Value Function ◽  
Computational Study ◽  
Minimum Cost ◽  
Service Level ◽  
Workforce Scheduling ◽  
Negative Effects ◽  
Start Time ◽  
Value Function Approximation ◽  
Delivery Options

Using crowdsourced delivery capacity, that is, individuals offering their vehicle and their time to perform deliveries, can allow companies to provide faster delivery options and more easily accommodate fluctuations in demand. However, because of the uncertainty associated with crowdsourced delivery capacity, ensuring service quality is more challenging. To prevent or mitigate any negative effects of the uncertainty associated with crowdsourced delivery capacity, companies may choose to also have a scheduled delivery workforce that they can control more effectively. We investigate continuous approximation and value function approximation methods for scheduling this workforce, that is, deciding their shifts (start time and duration) to achieve a service level target at minimum cost. An extensive computational study demonstrates the efficacy of our methods and provides insights into the use of crowdsourced delivery capacity.

scholarly journals Stochastic Comparative Statics in Markov Decision Processes

2021 ◽  
Author(s):  
Bar Light
Keyword(s):  
Markov Decision Processes ◽  
Dynamic Pricing ◽  
Optimization Problems ◽  
Transition Probability ◽  
Random Variable ◽  
Comparative Statics ◽  
Decision Processes ◽  
Optimal Decision ◽  
Initial State ◽  
Markov Decision

In multiperiod stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. I analyze how the expected value of this random variable changes as a function of the dynamic optimization parameters in the context of Markov decision processes. I call this analysis stochastic comparative statics. I derive both comparative statics results and stochastic comparative statics results showing how the current and future optimal decisions change in response to changes in the single-period payoff function, the discount factor, the initial state of the system, and the transition probability function. I apply my results to various models from the economics and operations research literature, including investment theory, dynamic pricing models, controlled random walks, and comparisons of stationary distributions.

scholarly journals On the Selective Vehicle Routing Problem

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 771 ◽  
Author(s):  
Cosmin Sabo ◽  
Petrică C. Pop ◽  
Andrei Horvat-Marc
Keyword(s):  
Mathematical Model ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Mixed Integer ◽  
The Novel ◽  
Routing Problem ◽  
Proposed Model ◽  
Benchmark Instances ◽  
Number Of Customers ◽  
Optimal Set

The Generalized Vehicle Routing Problem (GVRP) is an extension of the classical Vehicle Routing Problem (VRP), in which we are looking for an optimal set of delivery or collection routes from a given depot to a number of customers divided into predefined, mutually exclusive, and exhaustive clusters, visiting exactly one customer from each cluster and fulfilling the capacity restrictions. This paper deals with a more generic version of the GVRP, introduced recently and called Selective Vehicle Routing Problem (SVRP). This problem generalizes the GVRP in the sense that the customers are divided into clusters, but they may belong to one or more clusters. The aim of this work is to describe a novel mixed integer programming based mathematical model of the SVRP. To validate the consistency of the novel mathematical model, a comparison between the proposed model and the existing models from literature is performed, on the existing benchmark instances for SVRP and on a set of additional benchmark instances used in the case of GVRP and adapted for SVRP. The proposed model showed better results against the existing models.

Diffusion Approximation of State-Dependent G-Networks Under Heavy Traffic

2008 ◽  
Vol 45 (2) ◽  
pp. 347-362 ◽  
Author(s):  
Saul C. Leite ◽  
Marcelo D. Fragoso
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Diffusion Approximation ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Weak Sense ◽  
Feedforward Network ◽  
State Dependent ◽  
Number Of Customers

This paper is concerned with the characterization of weak-sense limits of state-dependent G-networks under heavy traffic. It is shown that, for a certain class of networks (which includes a two-layer feedforward network and two queues in tandem), it is possible to approximate the number of customers in the queue by a reflected stochastic differential equation. The benefits of such an approach are that it describes the transient evolution of these queues and allows the introduction of controls, inter alia. We illustrate the application of the results with numerical experiments.

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