arXiv subjects

Sophie N. Parragh

Publications and source records attributed to Sophie N. Parragh.

At least 19 recordsLinked to original sources

arXiv2026

Accelerated Benders decomposition for bi-objective mixed integer programming

We investigate bi-objective mixed integer programming to which Benders decomposition can be applied, a widely used technique for exploiting problem structures in real-world applications. Our study focuses on a sustainable supply chain network design problem that aims to minimise both economic and environmental objectives. To address the bi-objective nature, we employ the weighted sum method, which requires solving similar problems repeatedly with different weight values. To tackle this, we propose a straightforward acceleration technique that reuses Benders cuts generated in previous iterations of the weighted sum method. This approach enables the Benders decomposition master problem to be initialised with pre-generated cuts. Our computational experiments demonstrate that reusing these cuts significantly reduces computing time.

math.OC↗

arXiv2026

Enhancing Rolling Horizon Production Planning Through Stochastic Optimization Evaluated by Means of Simulation

Production planning must account for uncertainty in a production system, arising from fluctuating demand forecasts and execution-level friction. This article integrates scenario-based stochastic programming into a rolling horizon framework for capacitated lot sizing, evaluated via discrete-event simulation. We compare this stochastic approach against deterministic optimization and standard Material Requirements Planning (MRP) across varying customer update behaviors, shop loads, and diverse multi-stage topologies (divergent, convergent, and mixed). To accurately capture shop-floor dynamics, the framework introduces a non-anticipativity parameter controlling schedule flexibility, alongside probabilistic setup-time feedback and soft overtime constraints. Results indicate that optimization consistently outperforms MRP. In unbuffered, highly congested settings, stochastic optimization natively smooths workloads and reduces costs by up to 68%. However, introducing explicit safety stocks fundamentally shifts system dynamics: physical buffers effectively absorb shop-floor noise, diminishing the stochastic model's anticipative advantage and enabling deterministic optimization to dominate. Ultimately, this study offers critical managerial insights for aligning planning algorithms, inventory buffering, and schedule flexibility.

econ.EM↗

arXiv2025

The Bi-objective Electric Autonomous Dial-a-Ride Problem

The electric autonomous dial-a-ride problem (E-ADARP) introduces electric, autonomously driving vehicles and their unique requirements into the classic dial-a-ride problem, where people are transported between pickup and drop-off locations. Next to an electric autonomous vehicle fleet, in the literature, a weighted-sum objective function, which combines the classic routing cost-oriented objective with a user-oriented objective function, has usually been considered. The user-oriented objective function minimizes the total excess user ride time. In this work, we treat them as two separate objective functions, which are optimized concurrently. In order to address the resulting bi-objective E-ADARP, we develop a novel exact framework (called fragment-based checker), whose core part is a smart ``select-and-check" algorithm that iteratively constructs feasible solutions using fragments. Several enhancements are proposed to enforce the computational efficiency of the proposed method. In the computational experiments, we evaluate several variants of our checker algorithm by leveraging a previously developed branch-and-price algorithm. We benchmark the checker-based framework against state-of-the-art criterion space frameworks as well as a generalized branch-and-price algorithm. Numerical results on both bi-objective DARP and E-ADARP instances demonstrate the effectiveness of the proposed framework. With our proposed approaches, 21 out of 38 instances are solved optimally, where small-to-medium-sized instances are solved within seconds. On larger-scale instances, especially those requiring high battery end levels are computationally challenging to solve, our approaches provide high-quality approximations of the Pareto frontiers. Efficient solutions with varying energy restrictions are compared and we obtain valuable managerial insights for different kinds of service providers.

math.OC↗

arXiv2025

An exact approach for the multi-depot electric vehicle scheduling problem

The "avoid - shift - improve" framework and the European Clean Vehicles Directive set the path for improving the efficiency and ultimately decarbonizing the transport sector. While electric buses have already been adopted in several cities, regional bus lines may pose additional challenges due to the potentially longer distances they have to travel. In this work, we model and solve the electric bus scheduling problem, lexicographically minimizing the size of the bus fleet, the number of charging stops, and the total energy consumed, to provide decision support for bus operators planning to replace their diesel-powered fleet with zero emission vehicles. We propose a graph representation which allows partial charging without explicitly relying on time variables and derive 3-index and 2-index mixed-integer linear programming formulations for the multi-depot electric vehicle scheduling problem. While the 3-index model can be solved by an off-the-shelf solver directly, the 2-index model relies on an exponential number of constraints to ensure the correct depot pairing. These are separated in a cutting plane fashion. We propose a set of instances with up to 80 service trips to compare the two approaches, showing that, with a small number of depots, the compact 3-index model performs very well. However, as the number of depots increases the developed branch-and-cut algorithm proves to be of value. These findings not only offer algorithmic insights but the developed approaches also provide actionable guidance for transit agencies and operators, allowing to quantify trade-offs between fleet size, energy efficiency, and infrastructure needs under realistic operational conditions.

math.OC↗

arXiv2025

Progressive hedging for multi-stage stochastic lot sizing problems with setup carry-over under uncertain demand

We investigate multi-stage demand uncertainty for the multi-item multi-echelon capacitated lot sizing problem with setup carry-over. Considering a multi-stage decision framework helps to quantify the benefits of being able to adapt decisions to newly available information. The drawback is that multi-stage stochastic optimization approaches lead to very challenging formulations. This is because they usually rely on scenario tree representations of the uncertainty, which grow exponentially in the number of decision stages. Thus, even for a moderate number of decision stages it becomes difficult to solve the problem by means of a compact optimization model. To address this issue, we propose a progressive hedging algorithm and we investigate and tune the crucial penalty parameter that influences the conflicting goals of fast convergence and solution quality. While low penalty parameters usually lead to high quality solutions, this comes at the cost of slow convergence. To tackle this problem, we adapt metaheuristic adjustment strategies to guide the algorithm towards a consensus more efficiently. Furthermore, we consider several options to compute the consensus solution. While averaging the subproblem decisions is a common choice, we also apply a majority voting procedure. We test different algorithm configurations and compare the results of progressive hedging to the solutions obtained by solving a compact optimization model on well-known benchmark instances. For several problem instances the progressive hedging algorithm converges to solutions within 1% of the cost of the compact model's solution, while requiring shorter runtimes.

math.OC↗

arXiv2024

A Branch-and-Price Algorithm for the Electric Autonomous Dial-A-Ride Problem

The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in scheduling a fleet of electric autonomous vehicles to provide ride-sharing services for customers that specify their origins and destinations. The E-ADARP differs from the classical DARP in two aspects: (i) a weighted-sum objective that minimizes both total travel time and total excess user ride time; (ii) the employment of electric autonomous vehicles and a partial recharging policy. This paper presents a highly-efficient labeling algorithm, which is integrated into Branch-and-Price (B&P) algorithms to solve the E-ADARP. To handle (i), we introduce a fragment-based representation of paths. A novel approach is invoked to abstract fragments to arcs while ensuring excess-user-ride-time optimality. We then construct a new graph that preserves all feasible routes of the original graph by enumerating all feasible fragments, abstracting them to arcs, and connecting them with each other, depots, and recharging stations in a feasible way. On the new graph, partial recharging (ii) is tackled exactly by tailored Resource Extension Functions (REFs). We apply strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. These methods construct the first labeling algorithm that can deal with minimizing (excess) user ride time. In the computational experiments, the B&P algorithm achieves optimality in 71 out of 84 instances. Remarkably, among these instances, 50 were solved optimally at the root node without branching. We identify 26 new best solutions, improve 30 previously reported lower bounds, and provide 17 new lower bounds for large-scale instances with up to 8 vehicles and 96 requests. In total 42 new best solutions are generated on previously solved and unsolved instances.

math.OC↗

arXiv2023

Adaptive Improvements of Multi-Objective Branch and Bound

Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly attracting interest. However, the larger number of objectives raises additional difficulties for implicit enumeration approaches like branch and bound. Since bounding and pruning is considerably weaker in multiple objectives, many branches have to be (partially) searched and may not be pruned directly. The adaptive use of objective space information can guide the search in promising directions to determine a good approximation of the Pareto front already in early stages of the algorithm. In particular we focus in this article on improving the branching and queuing of subproblems and the handling of lower bound sets. In our numerical test we evaluate the impact of the proposed methods in comparison to a standard implementation of multiobjective branch and bound on knapsack problems, generalized assignment problems and (un)capacitated facility location problems.

math.OC↗

arXiv2023

Bi-objective risk-averse facility location using a subset-based representation of the conditional value-at-risk

For many real-world decision-making problems subject to uncertainty, it may be essential to deal with multiple and often conflicting objectives while taking the decision-makers' risk preferences into account. Conditional value-at-risk (CVaR) is a widely applied risk measure to address risk-averseness of the decision-makers. In this paper, we use the subset-based polyhedral representation of the CVaR to reformulate the bi-objective two-stage stochastic facility location problem presented in Nazemi et al. (2021). We propose an approximate cutting-plane method to deal with this more computationally challenging subset-based formulation. Then, the cutting plane method is embedded into the epsilon-constraint method, the balanced-box method, and a recently developed matheuristic method to address the bi-objective nature of the problem. Our computational results show the effectiveness of the proposed method. Finally, we discuss how incorporating an approximation of the subset-based polyhedral formulation affects the obtained solutions.

math.OC↗

arXiv2023

Adaptive large neighborhood search for a personnel task scheduling problem with task selection and parallel task assignments

Motivated by a real-world application, we model and solve a complex staff scheduling problem. Tasks are to be assigned to workers for supervision. Multiple tasks can be covered in parallel by a single worker, with worker shifts being flexible within availabilities. Each worker has a different skill set, enabling them to cover different tasks. Tasks require assignment according to priority and skill requirements. The objective is to maximize the number of assigned tasks weighted by their priorities, while minimizing assignment penalties. We develop an adaptive large neighborhood search (ALNS) algorithm, relying on tailored destroy and repair operators. It is tested on benchmark instances derived from real-world data and compared to optimal results obtained by means of a commercial MIP-solver. Furthermore, we analyze the impact of considering three additional alternative objective functions. When applied to large-scale company data, the developed ALNS outperforms the previously applied solution approach.

cs.DM↗

arXiv2022

Bi-objective facility location under uncertainty with an application in last-mile disaster relief

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the $ε$-constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.

math.OC↗

arXiv2022

Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming

In the bi-objective branch-and-bound literature, a key ingredient is objective branching, i.e. to create smaller and disjoint sub-problems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound set. When considering three or more objective functions, however, applying objective branching becomes more complex, and its benefit has so far been unclear. In this paper, we investigate several ingredients which allow to better exploit objective branching in a multi-objective setting. We extend the idea of probing to multiple objectives, enhance it in several ways, and show that when coupled with objective branching, it results in significant speed-ups in terms of CPU times. We also investigate cut generation based on the objective branching constraints. Besides, we generalize the best-bound idea for node selection to multiple objectives and we show that the proposed rules outperform the, in the multi-objective literature, commonly employed depth-first and breadth-first strategies. We also analyze problem specific branching rules. We test the proposed ideas on available benchmark instances for three problem classes with three and four objectives, namely the capacitated facility location problem, the uncapacitated facility location problem, and the knapsack problem. Our enhanced multi-objective branch-and-bound algorithm outperforms the best existing branch-and-bound based approach and is the first to obtain competitive and even slightly better results than a state-of-the-art objective space search method on a subset of the problem classes.

cs.DS↗

arXiv2022

Modeling and solving the multimodal car- and ride-sharing problem

We introduce the multimodal car- and ride-sharing problem (MMCRP), in which a pool of cars is used to cover a set of ride requests while uncovered requests are assigned to other modes of transport (MOT). A car's route consists of one or more trips. Each trip must have a specific but non-predetermined driver, start in a depot and finish in a (possibly different) depot. Ride-sharing between users is allowed, even when two rides do not have the same origin and/or destination. A user has always the option of using other modes of transport according to an individual list of preferences. The problem can be formulated as a vehicle scheduling problem. In order to solve the problem, an auxiliary graph is constructed in which each trip starting and ending in a depot, and covering possible ride-shares, is modeled as an arc in a time-space graph. We propose a two-layer decomposition algorithm based on column generation, where the master problem ensures that each request can only be covered at most once, and the pricing problem generates new promising routes by solving a kind of shortest-path problem in a time-space network. Computational experiments based on realistic instances are reported. The benchmark instances are based on demographic, spatial, and economic data of Vienna, Austria. We solve large instances with the column generation based approach to near optimality in reasonable time, and we further investigate various exact and heuristic pricing schemes.

cs.AI↗

arXiv2022

Modeling and solving a vehicle-sharing problem considering multiple alternative modes of transport

Motivated by the change in mobility patterns, we present a scheduling approach for a vehicle-sharing problem, considering several alternative modes of transport, from a company viewpoint with centralized planning. We consider vehicle-sharing in a company having one or more depots and a fixed number of users, i.e. employees. The users have appointments with a fixed location and fixed start and end times. A vehicle must be used for a full trip of a user from depot to depot. We aim at assigning vehicles to user trips so as to maximize savings compared to other modes of transport. We first consider that only one type of vehicle is used, and second that multiple vehicle types can be used. For the first case, we show that the vehicle-sharing problem can be formulated as a minimum-cost flow problem. Secondly, if multiple types of vehicles are available the problem can be formulated as a multi-commodity flow problem. These formulations make the problem applicable in daily operations due to efficient solution methods. We provide a comprehensive computational study for both cases on instances based on demographic, spatial, and economic data of Vienna. We show that our formulations for this problem solve these instances in a few seconds, which makes them usable in an online booking system. In the analysis we discuss different potential settings. We study the optimal composition of a shared fleet, restricted sets of modes of transport, and variations of the objective function.

cs.OH↗

arXiv2022

The bi-objective multimodal car-sharing problem

The aim of the bi-objective multimodal car-sharing problem (BiO-MMCP) is to determine the optimal mode of transport assignment for trips and to schedule the routes of available cars and users whilst minimizing cost and maximizing user satisfaction. We investigate the BiO-MMCP from a user-centred point of view. As user satisfaction is a crucial aspect in shared mobility systems, we consider user preferences in a second objective. Users may choose and rank their preferred modes of transport for different times of the day. In this way we account for, e.g., different traffic conditions throughout the planning horizon. We study different variants of the problem. In the base problem, the sequence of tasks a user has to fulfill is fixed in advance and travel times as well as preferences are constant over the planning horizon. In variant 2, time-dependent travel times and preferences are introduced. In variant 3, we examine the challenges when allowing additional routing decisions. Variant 4 integrates variants 2 and 3. For this last variant, we develop a branch-and-cut algorithm which is embedded in two bi-objective frameworks, namely the $ε$-constraint method and a weighting binary search method. Computational experiments show that the branch-and cut algorithm outperforms the MIP formulation and we discuss changing solutions along the Pareto frontier.

cs.AI↗

arXiv2022

A matheuristic for tri-objective binary integer programming

Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither objective can be improved without deteriorating another objective. Motivated by the success of matheuristics in the single-objective domain, we propose a linear programming-based matheuristic for tri-objective binary integer programming. To achieve a high-quality approximation of the optimal set of trade-off solutions, a lower bound set is first obtained using the vector linear programming solver Bensolve. Then, feasibility pump-based ideas in combination with path relinking are applied in novel ways so as to obtain a high quality upper bound set. Our matheuristic is compared to a recently-suggested algorithm that is, to the best of our knowledge, the only existing matheuristic method for tri-objective integer programming. In an extensive computational study, we show that our method generates a better approximation of the true Pareto front than the benchmark method on a large set of tri-objective benchmark instances. Since the developed approach starts from a potentially fractional lower bound set, it may also be used as a primal heuristic in the context of linear relaxation-based multi-objective branch-and-bound algorithms.

math.OC↗

arXiv2022

An outer approximation algorithm for multi-objective mixed-integer linear and non-linear programming

In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems. It produces the non-dominated extreme points as well as the facets of the convex hull of these points. The algorithm relies on an oracle which solves single-objective weighted-sum problems and we show that the required number of oracle calls is polynomial in the number of facets of the convex hull of the non-dominated extreme points in the case of multiobjective mixed-integer programming (MOMILP). Thus, for MOMILP problems for which the weighted-sum problem is solvable in polynomial time, the facets can be computed with incremental-polynomial delay. From a practical perspective, the algorithm starts from a valid lower bound set for the non-dominated extreme points and iteratively improves it. Therefore it can be used in multi-objective branch-and-bound algorithms and still provide a valid bound set at any stage, even if interrupted before converging. Moreover, the oracle produces Pareto optimal solutions, which makes the algorithm also attractive from the primal side in a multi-objective branch-and-bound context. Finally, the oracle can also be called with any relaxation of the primal problem, and the obtained points and facets still provide a valid lower bound set. A computational study on a set of benchmark instances from the literature and new non-linear multi-objective instances is provided.

math.OC↗

arXiv2021

A LP relaxation based matheuristic for multi-objective integer programming

Motivated by their success in the single-objective domain, we propose a very simple linear programming-based matheuristic for tri-objective binary integer programming. To tackle the problem, we obtain lower bound sets by means of the vector linear programming solver Bensolve. Then, simple heuristic approaches, such as rounding and path relinking, are applied to this lower bound set to obtain high-quality approximations of the optimal set of trade-off solutions. The proposed algorithm is compared to a recently suggested algorithm which is, to the best of our knowledge, the only existing matheuristic method for tri-objective integer programming. Computational experiments show that our method produces a better approximation of the true Pareto front using significantly less time than the benchmark method on standard benchmark instances for the three-objective knapsack problem.

math.OC↗

arXiv2020

Resource-constrained multi-project scheduling with activity and time flexibility

Project scheduling in manufacturing environments often requires flexibility in terms of the selection and the exact length of alternative production activities. Moreover, the simultaneous scheduling of multiple lots is mandatory in many production planning applications. To meet these requirements, a new resource-constrained project scheduling problem (RCPSP) is introduced where both decisions (activity flexibility and time flexibility) are integrated. Besides the minimization of makespan, two new alternative objectives are presented: maximization of balanced length of selected activities (time balance) and maximization of balanced resource utilization (resource balance). New mixed integer and constraint programming (CP) models are proposed for the developed integrated flexible project scheduling problem. Benchmark instances on an already existing flexible RCPSP and the newly developed problem are solved to optimality. The real-world applicability of the suggested CP models is shown by additionally solving a large industry case.

cs.AI↗