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

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

Budgeting in International Humanitarian Organizations

Problem definition: International humanitarian organizations (IHOs) prepare a detailed annual allocation plan for operations that are conducted in the countries they serve. The annual plan is strongly affected by the available financial budget. The budget of IHOs is derived from donations, which are typically limited, uncertain, and to a large extent earmarked for specific countries or programs. These factors, together with the specific utility function of IHOs, render budgeting for IHOs a challenging managerial problem. In this paper, we develop an approach to optimize budget allocation plans for each country of operations. Academic/practical relevance: The current research provides a better understanding of the budgeting problem in IHOs given the increasing interest of the operations management community for nonprofit operations. Methodology: We model the problem as a two-stage stochastic optimization model with a concave utility function and identify a number of analytical properties for the problem. We develop an efficient generalized Benders decomposition algorithm as well as a fast heuristic. Results: Using data from the International Committee of the Red Cross, our results indicate 21.3% improvement in the IHO’s utility by adopting stochastic programming instead of the expected value solution. Moreover, our solution approach is computationally more efficient than other approaches. Managerial implications: Our analysis highlights the importance of nonearmarked donations for the overall performance of IHOs. We also find that putting pressure on IHOs to fulfill the targeted missions (e.g., by donors or media) results in lower beneficiaries’ welfare. Moreover, the IHOs benefit from negative correlation among donations. Finally, our findings indicate that, if donors allow the IHO to allocate unused earmarked donations to other delegations, the performance of the IHO improves significantly

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 $b$ 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)

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