32 research outputs found
Location of charging stations in electric car sharing systems
Electric vehicles are prime candidates for use within urban car sharing systems, both from economic and environmental perspectives. However, their relatively short range necessitates frequent and rather time-consuming recharging throughout the day. Thus, charging stations must be built throughout the system's operational area where cars can be charged between uses. In this work, we introduce and study an optimization problem that models the task of finding optimal locations and sizes for charging stations, using the number of expected trips that can be accepted (or their resulting revenue) as a gauge of quality. Integer linear programming formulations and construction heuristics are introduced, and the resulting algorithms are tested on grid-graph-based instances, as well as on real-world instances from Vienna. The results of our computational study show that the best-performing exact algorithm solves most of the benchmark instances to optimality and usually provides small optimality gaps for the remaining ones, whereas our heuristics provide high-quality solutions very quickly. Our algorithms also provide better solutions than a sequential approach that considers strategic and operational decisions separately. A cross-validation study analyzes the algorithms' performance in cases where demand is uncertain and shows the advantage of combining individual solutions into a single consensus solution, and a simulation study investigates their behavior in car sharing systems that provide their customers with more flexibility regarding vehicle selection
Reinforcement Learning Approaches for the Orienteering Problem with Stochastic and Dynamic Release Dates
In this paper, we study a sequential decision making problem faced by
e-commerce carriers related to when to send out a vehicle from the central
depot to serve customer requests, and in which order to provide the service,
under the assumption that the time at which parcels arrive at the depot is
stochastic and dynamic. The objective is to maximize the number of parcels that
can be delivered during the service hours. We propose two reinforcement
learning approaches for solving this problem, one based on a policy function
approximation (PFA) and the second on a value function approximation (VFA).
Both methods are combined with a look-ahead strategy, in which future release
dates are sampled in a Monte-Carlo fashion and a tailored batch approach is
used to approximate the value of future states. Our PFA and VFA make a good use
of branch-and-cut-based exact methods to improve the quality of decisions. We
also establish sufficient conditions for partial characterization of optimal
policy and integrate them into PFA/VFA. In an empirical study based on 720
benchmark instances, we conduct a competitive analysis using upper bounds with
perfect information and we show that PFA and VFA greatly outperform two
alternative myopic approaches. Overall, PFA provides best solutions, while VFA
(which benefits from a two-stage stochastic optimization model) achieves a
better tradeoff between solution quality and computing time
An Exact Method for Assortment Optimization under the Nested Logit Model
We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we provide a general exact method that embeds a tailored Branch-and-Bound algorithm into a fractional programming framework. Contrary to the existing literature, in which assumptions are imposed on either the structure of nests or the combination and characteristics of products, no assumptions on the input data are imposed, and hence our approach can solve the most general problem setting. We show that the parameterized subproblem of the fractional programming scheme, which is a binary highly non-linear optimization problem, is decomposable by nests, which is a main advantage of the approach. To solve the subproblem for each nest, we propose a two-stage approach. In the first stage, we identify those products that are undoubtedly beneficial to offer, or not, which can significantly reduce the problem size. In the second stage, we design a tailored Branch-and-Bound algorithm with problem-specific upper bounds. Numerical results show that the approach is able to solve assortment instances with up to 5,000 products per nest. The most challenging instances for our approach are those in which the dissimilarity parameters of nests can be either less or greater than one
A bilevel approach for compensation and routing decisions in last-mile delivery
In last-mile delivery logistics, peer-to-peer logistic platforms play an
important role in connecting senders, customers, and independent carriers to
fulfill delivery requests. Since the carriers are not under the platform's
control, the platform has to anticipate their reactions, while deciding how to
allocate the delivery operations. Indeed, carriers' decisions largely affect
the platform's revenue. In this paper, we model this problem using bilevel
programming. At the upper level, the platform decides how to assign the orders
to the carriers; at the lower level, each carrier solves a profitable tour
problem to determine which offered requests to accept, based on her own profit
maximization. Possibly, the platform can influence carriers' decisions by
determining also the compensation paid for each accepted request. The two
considered settings result in two different formulations: the bilevel
profitable tour problem with fixed compensation margins and with margin
decisions, respectively. For each of them, we propose single-level
reformulations and alternative formulations where the lower-level routing
variables are projected out. A branch-and-cut algorithm is proposed to solve
the bilevel models, with a tailored warm-start heuristic used to speed up the
solution process. Extensive computational tests are performed to compare the
proposed formulations and analyze solution characteristics
Mathematical Programming Formulations for the Collapsed k-Core Problem
In social network analysis, the size of the k-core, i.e., the maximal induced
subgraph of the network with minimum degree at least k, is frequently adopted
as a typical metric to evaluate the cohesiveness of a community. We address the
Collapsed k-Core Problem, which seeks to find a subset of users, namely the
most critical users of the network, the removal of which results in the
smallest possible k-core. For the first time, both the problem of finding the
k-core of a network and the Collapsed k-Core Problem are formulated using
mathematical programming. On the one hand, we model the Collapsed k-Core
Problem as a natural deletion-round-indexed Integer Linear formulation. On the
other hand, we provide two bilevel programs for the problem, which differ in
the way in which the k-core identification problem is formulated at the lower
level. The first bilevel formulation is reformulated as a single-level sparse
model, exploiting a Benders-like decomposition approach. To derive the second
bilevel model, we provide a linear formulation for finding the k-core and use
it to state the lower-level problem. We then dualize the lower level and obtain
a compact Mixed-Integer Nonlinear single-level problem reformulation. We
additionally derive a combinatorial lower bound on the value of the optimal
solution and describe some pre-processing procedures and valid inequalities for
the three formulations. The performance of the proposed formulations is
compared on a set of benchmarking instances with the existing state-of-the-art
solver for mixed-integer bilevel problems proposed in (Fischetti et al., A New
General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs, Operations
Research 65(6), 2017)
A branch-and-cut algorithm for the Edge Interdiction Clique Problem
Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim of reducing the clique number of the graph. The EICP optimal solutions, called optimal interdiction policies, determine the subset of most vital edges of a graph which are crucial for preserving its clique number. We propose a new set-covering-based Integer Linear Programming (ILP) formulation for the EICP with an exponential number of constraints, called the clique-covering inequalities. We design a new branch-and-cut algorithm which is enhanced by a tailored separation procedure and by an effective heuristic initialization phase. Thanks to the new exact algorithm, we manage to solve the EICP in several sets of instances from the literature. Extensive tests show that the new exact algorithm greatly outperforms the state-of-the-art approaches for the EICP
Solving Two-Stage Stochastic Steiner Tree Problems by Two-Stage Branch-and-Cut
We consider the Steiner tree problem under a two-stage stochastic model with recourse and finitely many scenarios. In this prob- lem, edges are purchased in the first stage when only probabilistic infor- mation on the set of terminals and the future edge costs is known. In the second stage, one of the given scenarios is realized and additional edges are puchased in order to interconnect the set of (now known) ter- minals. The goal is to decide on the set of edges to be purchased in the first stage while minimizing the overall expected cost of the solution. We provide a new semi-directed cut-set based integer programming formula- tion, which is stronger than the previously known undirected model. We suggest a two-stage branch-and-cut (B&C) approach in which L-shaped and integer-L-shaped cuts are generated. In our computational study we compare the performance of two variants of our algorithm with that of a B&C algorithm for the extensive form of the deterministic equiva- lent (EF). We show that, as the number of scenarios increases, the new approach significantly outperforms the (EF) approach