Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing approaches rely on integer L-shaped (ILS) cuts, whose coefficients are tailored for specific recourse policies. In contrast, we propose a framework that casts recourse policies as solutions of a higher-dimensional mixed-integer program, and we characterize its convex hull in the original lower-dimensional space via a new class of inequalities called scenario recourse inequalities (SRIs). We show that SRIs are valid for any recourse policy satisfying mild assumptions and are sufficient for formulating the VRPSD under a scenario-optimal recourse policy, where the recourse actions are chosen optimally for each scenario. Under this latter policy, we also show that SRIs dominate several ILS cuts. We conduct computational experiments on the VRPSD with scenarios under both the classical and the scenario-optimal recourse policies. By using the SRIs, our algorithm solves 329 more instances to optimality than the previous state-of-the-art ILS algorithm.
In this paper, we study the performance of affine policies for two-stage adjustable robust optimization problem with fixed recourse and uncertain right hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets widely used in practice where we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than $Ω\left( \frac{\log n}{\log \log n} \right)$ even for budget of uncertain…
This paper considers a Markovian model for the optimal dynamic routing of homogeneous traffic to parallel heterogeneous queues, each having its own finite input buffer and server pool, where buffer and server-pool sizes, as well as service rates, may differ across queues. The main goal is to identify a heuristic index-based routing policy with low complexity that consistently attains a nearly minimum average loss rate (or, equivalently, maximum throughput rate). A second goal is to compare alternative policies, with respect to computational demands and empirical performance. A novel routing po…
We consider the vehicle routing problem with stochastic demands (VRPSD), a problem in which customer demands are known in distribution at the route planning stage and revealed during route execution upon arrival at each customer. A long-standing open question on the VRPSD concerns the benefits of allowing, during route execution, partial reordering of the planned customer visits. Given the practical importance of this question and the growing interest on the VRPSD under optimal restocking, we study the VRPSD under a recourse policy known as the switch policy. The switch policy is a canonical r…
Motivated by time-sensitive e-service applications, we consider the design of effective policies in a Markovian model for the dynamic control of both admission and routing of a single class of real-time transactions to multiple heterogeneous clusters of web servers, each having its own queue and server pool. Transactions come with response-time deadlines, staying until completion if the latter are missed. Per job rejection and deadline-miss penalties are incurred. Since computing an optimal policy is intractable, we aim to design near optimal heuristic policies that are tractable for large-sca…
There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from …
In this paper, we study the joint routing-scheduling problem in energy harvesting communication networks. Our policies, which are based on stochastic subgradient methods on the dual domain, act as an energy harvesting variant of the stochastic family of backpresure algorithms. Specifically, we propose two policies: (i) the Stochastic Backpressure with Energy Harvesting (SBP-EH), in which a node's routing-scheduling decisions are determined by the difference between the Lagrange multipliers associated to their queue stability constraints and their neighbors'; and (ii) the Stochastic Soft Backpr…
In this paper, a learning-based optimal transportation algorithm for autonomous taxis and ridesharing vehicles is presented. The goal is to design a mechanism to solve the routing problem for multiple autonomous vehicles and multiple customers in order to maximize the transportation company's profit. As a result, each vehicle selects the customer whose request maximizes the company's profit in the long run. To solve this problem, the system is modeled as a Markov Decision Process (MDP) using past customers data. By solving the defined MDP, a centralized high-level planning recommendation is ob…
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs with limited flow capacities on the links and constant external inflows at certain origin nodes. Under monotonicity assumptions on the routing policies, it is proven that a globally asymptotically stable equilibrium exists so that the network achieves maximal throughput, provided that no cut capacity constraint is violated by the external inflows. On the contra…
We investigate the performance of two size-based routing policies: the Size Interval Task Assignment (SITA) and Task Assignment based on Guessing Size (TAGS). We consider a system with two servers and Bounded Pareto distributed job sizes with tail parameter 1 where the difference between the size of the largest and the smallest job is finite. We show that the ratio between the mean waiting time of TAGS over the mean waiting time of SITA is unbounded when the largest job size is large and the arrival rate times the largest job size is less than one. We provide numerical experiments that show th…
This paper considers a Markov decision model for profit maximization of a cloud computing service provider catering to customers submitting jobs with firm real-time random deadlines. Customers are charged on a per-job basis, receiving a full refund if deadlines are missed. The service provider leases computing resources from an infrastructure provider in a two-tier scheme: long-term leasing of basic infrastructure, consisting of heterogeneous parallel service nodes, each modeled as a multi-server queue, and short-term leasing of external servers. Given the intractability of computing an optima…
We consider a two-stage robust facility location problem on a metric under an uncertain demand. The decision-maker needs to decide on the (integral) units of supply for each facility in the first stage to satisfy an uncertain second-stage demand, such that the sum of first stage supply cost and the worst-case cost of satisfying the second-stage demand over all scenarios is minimized. The second-stage decisions are only assignment decisions without the possibility of adding recourse supply capacity. This makes our model different from existing work on two-stage robust facility location and set …
Same-day delivery for e-commerce has become a popular service. Companies usually offer several time delivery options with the earliest one being next hour delivery. Due to tight delivery deadlines and thin margins, companies often find it challenging to provide efficient same-day delivery services. In this work, we propose a holistic scheme that combines the optimization of routing and pricing for same-day delivery. The proposed approach is able to take into account uncertainty in travel times, a crucial factor for delivery applications in urban environments. We model this problem as a Markov …
This paper considers the multi-armed bandit problem with multiple simultaneous arm pulls. We develop a new `irrevocable' heuristic for this problem. In particular, we do not allow recourse to arms that were pulled at some point in the past but then discarded. This irrevocable property is highly desirable from a practical perspective. As a consequence of this property, our heuristic entails a minimum amount of `exploration'. At the same time, we find that the price of irrevocability is limited for a broad useful class of bandits we characterize precisely. This class includes one of the most com…
Xerox Research Centre India（印度施乐研究中心）；Tepper School of Business, Carnegie Mellon University（卡内基梅隆大学泰珀商学院）；Marshall School of Business, University of Southern California（南加州大学马歇尔商学院）；Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）
Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed dynamically with the goal of maximizing the number of served requests. We model the DVRPSR as a multi-stage optimization problem, where the first-stage decision defines route plans for serving scheduled requests. Our main contributions are knapsack-based linear models to approximate accurately the expected reward-to-go, measured as the number of accepted requests, …
École de technologie supérieure（高等技术学院）；GERAD（GERAD（蒙特利尔高等商学院决策分析研究组））；CIRRELT（CIRRELT（企业网络、物流与运输研究中心））；Politecnico di Milano（米兰理工大学）
We study a stochastic variant of the vehicle routing problem arising in the context of domestic donor collection services. The problem we consider combines the following attributes. Customers requesting services are variable, in the sense that the customers are stochastic but are not restricted to a predefined set, as they may appear anywhere in a given service area. Furthermore, demand volumes are stochastic and observed upon visiting the customer. The objective is to maximize the expected served demands while meeting vehicle capacity and time restrictions. We call this problem the VRP with a…
We consider the long term behaviour of a Markov chain ξ(t) on \Z^N based on the N station supermarket model. Different routing policies for the supermarket model give different Markov chains. We show that for a general class of local routing policies, "join the least weighted queue" (JLW), the N one-dimensional components ξ_i(t) can be partitioned into disjoint clusters C_k. Within each cluster C_k the "speed" of each component ξ_j converges to a constant V_k and under certain conditions ξis recurrent in shape on each cluster. To establish these results we have assembled methods from two disti…
Given the rise of electric vehicle (EV) adoption, supported by government policies and dropping technology prices, new challenges arise in the modeling and operation of electric transportation. In this paper, we present a model for solving the EV routing problem while accounting for real-life stochastic demand behavior. We present a mathematical formulation that minimizes travel time and energy costs of an EV fleet. The EV is represented by a battery energy consumption model. To adapt our formulation to real-life scenarios, customer pick-ups and drop-offs were modeled as stochastic parameters.…
Bosch Center for AI（博世人工智能中心）；Technion – Israel Institute of Technology（以色列理工学院）
We study combinatorial problems with real world applications such as machine scheduling, routing, and assignment. We propose a method that combines Reinforcement Learning (RL) and planning. This method can equally be applied to both the offline, as well as online, variants of the combinatorial problem, in which the problem components (e.g., jobs in scheduling problems) are not known in advance, but rather arrive during the decision-making process. Our solution is quite generic, scalable, and leverages distributional knowledge of the problem parameters. We frame the solution process as an MDP, …
This paper studies congestion-aware route-planning policies for Autonomous Mobility-on-Demand (AMoD) systems, whereby a fleet of autonomous vehicles provides on-demand mobility under mixed traffic conditions. Specifically, we first devise a network flow model to optimize the AMoD routing and rebalancing strategies in a congestion-aware fashion by accounting for the endogenous impact of AMoD flows on travel time. Second, we capture reactive exogenous traffic consisting of private vehicles selfishly adapting to the AMoD flows in a user-centric fashion by leveraging an iterative approach. Finally…
