arXiv subjects

Ivana Ljubic

Publications and source records attributed to Ivana Ljubic.

6 recordsLinked to original sources

arXiv2025

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.

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arXiv2024

Emerging Optimization Problems for Distribution in Same-day Delivery

Same-day deliveries (SDD) have become a new standard to satisfy the "instant gratification" of online customers. Despite the existing powerful technologies deployed in last-mile delivery, SDD services face new decision-making challenges related to the trade-off between delivery cost and time. In addition, new challenges related to environmental issues, customer satisfaction, or fairness arise. Researchers have explored various approaches to face these challenges in the context of SDD, where stochastic and dynamic data uncertainty plays a fundamental role. In this paper, we carefully review the emerging routing problems and solutions proposed in the existing literature for SDD services. We survey papers related to how to deal with dynamic arrival times of orders, how to allocate time slots to deliveries, how to select the right delivery options, how to design pickup and delivery routes, or how to partition the delivery areas and decide the composition of the fleet. We also formulate and compare models for representative problems elaborating on the pros and cons that might guide practitioners in choosing the most appropriate objectives and constraints. Finally, we sketch challenges and identify future research directions.

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arXiv2024

The Multi-Commodity Flow Problem with Outsourcing Decisions

We address a new prize-collecting problem of routing commodities in a given network with hub and non-hub nodes, in which the service of the non-hub nodes will be outsourced to third-party carriers. The problem is modeled as a Stackelberg game: there is a major firm (leader) that decides to serve a subset of commodities. The leader aims to outsource first and third legs of transportation services to smaller carriers (who act as followers) by allocating at most one carrier to each non-hub node. The carriers try to maximize their own profits, which are influenced by the leader's offers. The goal of the leader is to determine the optimal outsourcing fees, along with the allocation of carriers to the non-hub nodes, so that the profit from the routed commodities is maximized. The optimal response of the followers must be taken into account, as the followers might refuse to serve some legs in case they are negative or do not maximize their profit. We also study two alternative settings: one in which the outsourcing fees are fixed, and the other one in which the carriers accept any offer, as long as the resulting profit is non-negative. We prove that the set of possible outsourcing fees can be discretized and formulate the problem as a single-level mixed-integer nonlinear program. For all considered problem variants, we prove NP-hardness and propose and computationally investigate several MIP formulations. We study the computational scalability of these MIP formulations and analyze solutions obtained by varying the reservation prices of the carriers. Finally, by comparing the introduced problem variants, we derive some interesting managerial insights.

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arXiv2024

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 expected number of parcels that can be delivered during service hours. We propose two reinforcement learning (RL) approaches for solving this problem. These approaches rely on a look-ahead strategy in which future release dates are sampled in a Monte-Carlo fashion and a batch approach is used to approximate future routes. Both RL approaches are based on value function approximation - one combines it with a consensus function (VFA-CF) and the other one with a two-stage stochastic integer linear programming model (VFA-2S). VFA-CF and VFA-2S do not need extensive training as they are based on very few hyper-parameters and make good use of integer linear programming (ILP) and 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 VFA-CF/VFA-2S. In an empirical study, we conduct a competitive analysis using upper bounds with perfect information. We also show that VFA-CF and VFA-2S greatly outperform alternative approaches that: 1) do not rely on future information, or 2) are based on point estimation of future information, or 3) employ heuristics rather than exact methods, or 4) use exact evaluations of future rewards.

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arXiv2024

Three Network Design Problems for Community Energy Storage

In this paper, we develop novel mathematical models to optimize utilization of community energy storage (CES) by clustering prosumers and consumers into energy sharing communities/microgrids in the context of a smart city. Three different microgrid configurations are modeled using a unifying mixed-integer linear programming formulation. These configurations represent three different business models, namely: the island model, the interconnected model, and the Energy Service Companies model. The proposed mathematical formulations determine the optimal households' aggregation as well as the location and sizing of CES. To overcome the computational challenges of treating operational decisions within a multi-period decision making framework, we also propose a decomposition approach to accelerate the computational time needed to solve larger instances. We conduct a case study based on real power consumption, power generation, and location network data from Cambridge, MA. Our mathematical models and the underlying algorithmic framework can be used in operational and strategic planning studies on smart grids to incentivize the communitarian distributed renewable energy generation and to improve the self-consumption and self-sufficiency of the energy sharing community. The models are also targeted to policymakers of smart cities, utility companies, and Energy Service Companies as the proposed models support decision making on renewable energy related projects investments.

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arXiv2023

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 $b$ 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).

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