Rolling Horizon Approach Research Articles

Formulation of Kerosene Routing Problem and a Rolling-Horizon Approach Based Heuristic

Formulation of Kerosene Routing Problem and a Rolling-Horizon Approach Based Heuristic

Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity

AbstractWe investigate a new family of distributionally robust optimization problem under marginal and copula ambiguity with applications to portfolio optimization problems. The proposed model considers the ambiguity set of portfolio returns in which the marginal distributions and their copula are close—in terms of the Wasserstein distance—to their nominal counterparts. We develop a cutting-surface method to solve the proposed problem, in which the distribution separation subproblem is nonconvex and includes bilinear terms. We propose three approaches to solve the bilinear formulation, namely (1) linear relaxation via McCormick inequalities, (2) exact mixed-integer linear program reformulation via disjunctive inequalities, and (3) inner approximation method via a novel iterative procedure that exploits the structural properties of the bilinear optimization problem. We further carry out a comprehensive set of computational experiments with distributionally robust portfolios featuring Conditional Value-at-Risk (CVaR) measures. These tests aim to compare the accuracy of the proposed algorithms, analyze the impact of the radius of the Wasserstein ambiguity ball on the portfolio, and assess portfolio performance. We use a rolling-horizon approach to conduct the out-of-sample tests, which show the superior performance of the portfolios under marginal and copula ambiguity over the equally weighted and ambiguity-free Mean-CVaR benchmark portfolios.

Collaborative rescheduling of train timetables to relieve passenger congestions in an urban rail transit network: A rolling horizon approach

At some urban rail transit (URT) stations, large activities, emergencies, or holidays usually lead to a significant surge in passenger flow demand quickly, known as Large Passenger Flow (LPF) events. The passenger congestion will spread quickly via transfer stations and affect other stations and lines in the URT network. This study develops a timetable rescheduling and coordinating method for the URT network under LPF events. Firstly, a collaborative adjustment model of train timetables with an implement backup vehicle strategy is formulated to simultaneously consider rescheduling and coordinating problems, to reduce the congestion influence for an URT network. Then, a rolling horizon approach is developed to divide the whole adjustment problem into several decision-making stages to ensure solution efficiency. In each decision-making stage, the influence of LPF propagation within the URT network is firstly evaluated. Based on the congestion evaluation results, the proposed method determines whether it’s necessary to adjust timetables of the LPF Line or other lines. The proposed method is applied to the Xi’an Metro network in China. The results indicate that the proposed method can effectively evaluate and adjust the train timetables for large URT networks under the LPF events.

Efficient routing in robotic movable fulfillment systems with integer programming: A rolling horizon and heuristic approach

This paper addresses an integrated rack assignment and robot routing problem arising in robotic movable fulfillment systems (RMFS). This NP-hard planning task goes beyond current literature by simultaneously optimizing movable rack selection and multi-agent collision-free path finding, rather than decomposing them. A mixed integer programming (MIP) model with a new level-space-time network representation is proposed, jointly considering reusable racks, robot-rack pairings, storage repositioning, and collision avoidance. To improve computational efficiency, a fast rolling horizon heuristic and greedy algorithm are developed. Extensive experiments demonstrate that the integrated method's solutions can improve by 30 % upon conventional decomposed approaches. Intriguing test cases reveal the model, suggesting non-intuitive robot carryover policies that are unfound by separate selection and routing methods. This indicates potential optimization benefits from explicitly coordinating task assignment, scheduling, and routing decisions in complex automated warehousing systems. The rolling horizon heuristic solutions approach optimality with much greater efficiency than directly solving one large MIP, validating its practical value. This research provides useful integrated modeling insights, efficient solution algorithms, and decision support for efficiently controlling next-generation robotic movable fulfillment systems.

A dynamic two-phased approach for planning downstream oil supply chain network under uncertainty

This paper introduces an innovative approach for designing a downstream oil supply chain network under uncertain conditions, aiming to bridge existing gaps in tactical decision-making and day-to-day operational management. In the initial phase, the focus lies on tactical and operational decisions related to network planning, while the second phase emphasizes real-time transshipment decisions for daily operations. This two-phased strategy proves to be adaptable and proficient in effectively handling uncertainties. Applying the mixed possibilistic-flexible programming and a rolling horizon approach, we enhance the overall performance of the oil supply chain network. To validate the efficacy of our proposed method, we conduct a comprehensive case study utilizing a database sourced from governmental agencies, specifically tailored to the Iranian oil supply chain. Our results demonstrate the efficiency of the proposed approach in addressing uncertainties, including demand fluctuations and network costs. Furthermore, the methodology exhibits potential for broader applications in other supply chain systems and industries grappling with similar challenges.

Rational capacity investment for renewable hydrogen-based steelmaking systems: A multi-stage expansion planning strategy

To improve energy efficiency and mitigate environmental impact, the iron and steel industry (ISI) is responsible for implementing a low-carbon transition. The renewable hydrogen-based steelmaking system (RHSS) has emerged as an innovative energy system in the pathway of reducing the carbon footprint of ISI. Nonetheless, the sustainable development requirements of RHSS emphasize the critical need for well-planned capacity investments to boost its economic viability. This study introduces a novel planning strategy for RHSS referred to as a multi-stage expansion planning (MSEP) model, which is aimed to minimize the levelized cost of crude steel over the planning horizon from 2025 to 2050 (EU climate neutrality year). The MSEP model incorporates the construction sequence and dynamic techno-economic parameters to formulate investment strategies that adapt to changing system requirements and external conditions over the planning horizon. To address the complexity of the MSEP model, a rolling-horizon approach (RHA) is proposed to solve the model sequentially while integrating updated information. The proposed approach is benchmarked against both the single-stage approach and the perfect-sight approach through case studies. The numerical results show that the proposed RHA (i) guarantees a rational capacity investment strategy for RHSS considering the construction sequence and dynamic techno-economic parameters over multiple planning stages; (ii) achieves a reduction in the levelized cost of crude steel by approximately 50% relative to the single-stage approach; (iii) resolves the convergence issues encountered with the perfect-sight approach while achieving an optimal solution in a reasonable time frame. Additionally, sensitivity analysis evaluates the uncertainties of multiple factors on the planning results, while the robustness analysis confirms the applicability and adaptability of RHA across various scenarios.

Modeling a closed-loop inventory routing problem for returnable transport items under horizontal logistics collaborations and dynamic demand structure

ABSTRACT This paper addresses a closed-loop inventory routing problem with multiple suppliers, products, and periods under horizontal collaboration assumptions. Our problem encompasses various decision aspects, including routing, inventory management, product delivery, returnable transport item collection and cleaning. We analyze various logistics collaboration scenarios. The effects of demand dynamicity are also assessed. The problem has been mathematically defined as a Mixed Integer Linear Programming model. A rolling horizon approach and a hybrid heuristic algorithm are proposed for instances that exceed the computational requirements of solving the exact MILP model. The applicability and potential benefits of the MILP model and the proposed solution methodologies are demonstrated through a base case and additional numerical analyses on larger-sized instances and networks. The results show that supplier collaboration significantly reduces routing costs, while customer collaboration reduces inventory costs. Numerical comparisons reveal that the proposed algorithms outperform the MILP model for large-scale problem instances.

Efficiently routing a fleet of autonomous vehicles in a real-time ride-sharing system

The advent of new communication technologies (e.g., smartphone) and autonomous vehicles (AVs) is enabling real-time ride-sharing systems where the travel requests arrives in the system on very short notice or even en-route, i.e., when AVs are already serving other users. Each request specifies an origin, a destination and a time window of pick-up, and must be immediately either accepted or rejected. Each request accepted must be assigned to an AV and both scheduled and inserted in its route considering the other possible requests already assigned to the same AV. In a lexicographic way, first we want to maximize the total number of new requests accepted, then we want to minimize the total traveled distance and finally, the total time of serving the requests. The problem is formulated as a Mixed Integer Linear Program and solved by a rolling horizon approach (MILP-RH). To efficiently address medium/large-sized instances, a rolling horizon Local Search (RHLS) is also designed, with moves properly tailored for the problem Numerical comparisons show that, on both the small-sized and some medium-sized instances, the RHLS outperforms the MILP-RH concerning the total computational time. Instead, on some medium-sized and on the large-sized instances, the RHLS is the only viable method since the MILP-RH is not able to even find a feasible solution in the given time limit. A sensitivity analysis on possible variation of some parameters is also performed deriving some useful managerial insights.

Railway crew planning with fairness over time

Passenger railway operators typically employ large numbers of drivers and guards, and are interested in providing them with fair and attractive working conditions. At Netherlands Railways (NS), the largest passenger railway operator in The Netherlands, this challenge is addressed through the use of Sharing-Sweet-and-Sour rules, which specify a fair allocation of sweet (attractive) and sour (unattractive) work over the different crew bases. While these rules are currently implemented at the crew base level and in the tactical planning phase, NS is considering formulating these rules at the individual level, in the operational planning phase, and with respect to a given planning period. This gives rise to a new problem, which we call the railway crew planning problem with fairness over time. We propose a rolling horizon approach with a penalty-based feedback mechanism and a column generation heuristic to solve this problem. On several real-life instances from NS, including up to 572 unique guards, this method is able to satisfy the individual rules for on average 95.2% of the employees.

Dynamic joint decision of matching parameters and relocation strategies in ride-sourcing systems interacting with traffic congestion

As the ride-sourcing market expands, ride-sourcing fleets have increased urban traffic congestion, and in turn, road congestion is affecting ride-sourcing operations. It is crucial to incorporate this interaction mechanism into the operational decision of ride-sourcing systems. This mechanism can be described in detail by simulation models. Applying simulation-based optimization methods to the real-time operation of ride-sourcing systems is challenging due to the limitations of simulation efficiency. To tackle this issue, this study first proposes a modular simulation model combining time-driven and event-driven mechanisms. The simulation model comprises two layers: the traffic flow module at the bottom, defined by trip-based and multi-region macroscopic fundamental diagrams and cell transmission models, and the ride-sourcing operation module at the top, which considers the interaction between the traffic congestion and ride-sourcing operation and models the random behavior of passengers and drivers. We verify the efficiency and accuracy of the simulation model. The simulation model is utilized as an evaluator of the objective functions and performance measures. Then, we integrate the Bayesian optimization, parallel sampling, and rolling horizon approaches to develop an efficient and effective simulation-based optimization framework for the dynamic joint decision-making of matching radius, matching intervals, and threshold relocation strategies. Six groups of experiments for the traffic scenario in Berlin reveal some interesting findings. (1) The matching rate first increases and then decreases with the matching radius (a concave function), while the closest study does not think so. (2) As the fleet size grows, passenger waiting time reaches its minimum and then rises because of the increased endogenous congestion generated by ride-sourcing fleets. (3) The optimal operation strategy considering endogenous congestion not only leads to an increase in the system revenue and efficiency but also leads to congestion relief, even though the latter was not our initial objective. This benefit is the most pronounced when the fleet size and background traffic are moderate.

Dynamic repositioning in bike-sharing systems with uncertain demand: An improved rolling horizon framework

The bike-sharing system (BSS) serves as a vital shared mobility mechanism, providing first- and last-mile services in urban transportation. However, one ongoing challenge in the BSS is the spatiotemporal imbalance caused by fluctuating user demand. To address this issue, this paper studies a dynamic bike repositioning problem under scenario-based demand to achieve a balance in inventory levels for electronic fences. Specifically, a multi-period two-stage stochastic model is proposed to make the trade-off between operational costs and service quality. The model incorporates a vehicle no-return (VNR) strategy, which allows vehicles to remain at the last station at the end of each period, awaiting the next repositioning task. To solve the model, an improved rolling horizon framework is introduced to effectively handle the temporal dimension complexity of the multi-period problem. Then a customized hybrid heuristic algorithm based on parallel genetic algorithm and variable neighborhood search is developed to obtain high-quality solutions. To validate the effectiveness and applicability of the proposed method, small-scale and practical-scale numerical experiments are specifically conducted based on real-world BSS data from Beijing, China. The results demonstrate the proposed method (i) creates a substantial reduction in the number of unmet demands when multiple scenarios potentially occur compared to the determined model, (ii) yields an average reduction of 29.04% in operational costs compared to the scheme without the VNR strategy, (iii) overcomes the short-sightedness inherent in the conventional single-period rolling horizon approach, exhibiting closer to optimal performance, and (iv) is superior to baseline approaches in terms of solution quality and efficiency.

Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint

This paper investigates a multi-period stochastic cash flow inventory problem with the aim of maximizing the long-term survival probability, which may be the objective of some retailers especially in periods of economic distress. Demand in each period is stochastic and can be non-stationary. In order to avoid too many lost sales under this objective, we introduce a joint chance constraint requiring the probability of no stockouts during the planning horizon to be higher than a specified service level. We develop a scenario-based model and a sample average approximation (SAA) model to solve the problem. A statistical upper bound on the survival probability based on SAA is provided and we discuss upper and lower bounds for the problem based on stochastic dynamic programming. We also propose a rolling horizon approach with service rate updating to test the out-of-sample performance of the two stochastic models and solve problems with long planning horizons. We test the two methods in large numerical tests and find that the rolling horizon approach together with the stochastic models can solve realistically sized problems in reasonable time.

Continuity of care in home health care scheduling: a rolling horizon approach

Continuity of care in home health care scheduling: a rolling horizon approach

A robust LP-based approach for a dynamic surgical case scheduling problem with sterilisation constraints

The purpose of this article is to investigate a practical scheduling problem in which a group of elective surgical cases are scheduled over time, while considering their unpredictable durations and potential delays in the sterilisation of surgical instruments. The primary objectives were to schedule the maximum number of surgeries and decrease overtime for the surgical staff, as well as limit the number of instruments requiring emergency sterilisation. The study was conducted in collaboration with the University Hospital of Angers in France, which also contributed historical data for the experiments. We propose two robust mixed integer linear programming models, which are then solved iteratively through a rolling horizon approach, in which the objective functions are taken into account in lexicographic order. Experiments on randomly generated instances indicated which of the two approaches had better performance. Comparison of the results for a real-world scenario involving actual planning at the hospital indicated a greater than 69% decrease in overtime, and a minimum of 92% fewer stressful situations in the sterilising unit.

Rolling Horizon Approach for Real-Time Charging and Routing of Autonomous Electric Vehicles

Rolling Horizon Approach for Real-Time Charging and Routing of Autonomous Electric Vehicles

Online flash delivery from multiple depots

ABSTRACT We study routing for on-demand last-mile logistics with two crucial novel features: i) Multiple depots, optimizing where to pick-up every order, ii) Allowing vehicles to perform depot returns prior to being empty, thus adapting their routes to include new orders online. Both features result in shorter distances and more agile planning.We propose a scalable dynamic method to deliver orders as fast as possible. Following a rolling horizon approach, each time step the following is executed. First, define potential pick-up locations and identify which groups of orders can be transported together, with which vehicle and following which route. Then, decide which of these potential groups of orders will be executed and by which vehicle by solving an integer linear program. We simulate one day of service in Amsterdam that considers 10,000 requests, compare results to several strategies and test different scenarios. Results underpin the advantages of the proposed method.

Optimization of the power output scheduling of a renewables-based hybrid power station using MILP approach: The case of Tilos island

Hybrid energy systems comprising renewables (mainly wind and solar) and storage systems are increasingly welcome to serve small communities or areas, such as small islands. In particular, the present study deals with the hybrid power station of Tilos, a little island located in the Greek Dodecanese, which includes a 800 kW wind turbine, a 160kWp PV field, and a 2.88 MWh NaNiCl2 battery; the system is also connected to the Kos-Kalymnos electrical network via a submarine cable. Currently, it is used to export its whole energy production under the management of the Greek company Eunice Energy Group. The agreement with the grid regulator is conceived to involve a remuneration for the energy output in three power levels (0 kW, 200 kW, 400 kW), with hourly dispatch provided the day before. Economic penalties will be applied in the near future for failure to respect power levels, whether in the form of excess or deficiency. This must be done in accordance with the available power to avoid surpluses or deficits, as well as excessive curtailment of renewable energy. In this work, a way to optimize energy fluxes of the island is proposed to better exploit the potential revenue, without excessively resorting to curtailments. The optimizations are performed in a Python environment through the “Gurobi” optimization solver, which is based on Mixed Integer Linear Programming (MILP). Scheduling emerges as a result of a rolling horizon approach. The new scheduling method reveals that there is potential for an increase in exported energy by 87.1% and potentially doubles the earnings over the current operation. Furthermore, novel scenarios are proposed to explore how different agreements with the grid operator would shift the optimal solution. Compared to an ideal optimized control under the current restrictions, a scenario that introduces the possibility of shutting down the wind turbine may increase the annual earnings by 10%, while a scenario that introduces a higher power band has the potential to increase annual earnings by 29.1%.

Robust optimization for a dynamic emergency materials supply chain network under major infectious disease epidemics

ABSTRACT The COVID-19 outbreak has posed serious challenges to logistics and supply chain management. This study examines how living materials can be provided to a population under quarantine control due to the spread of infectious diseases. First, we present a modified SEIR model for predicting the number of people and materials demanded. Considering the dynamic evolution and other characteristics of infectious diseases, and the resulting demand uncertainty, we develop a robust optimization model for a multi-period dynamic emergency materials supply chain network with the objective of minimising total cost. We then transform it into a solvable robust counterpart model, propose a dynamic adjustment strategy, and cope with it using the Rolling Horizon approach to obtain dynamic location and materials distribution decisions. Finally, we conduct a case study of the Shanghai epidemic in 2022 to verify the feasibility and effectiveness of our model and method.

Collaborative passenger flow control optimization of urban rail transit network based on sliding window mechanism

In order to enhance the operational performance of urban rail transit networks under overloaded conditions, this study proposes a novel network-level collaborative passenger flow strategy based on a sliding window mechanism. The main idea is to categorize arriving passengers at stations into different groups using variable-length windows and allocate them to specific trains. With the aim of minimizing the total passenger extra waiting time under cost budget, we establish a mixed integer programming model with sliding window constraints, flow distribution constraints, and node flow constraints to build the optimal matching relation between passenger flow demands and transportation resources. Specifically, the model incorporates precise quantity constraints related to transfers, facilitating the accurate quantification of both internal and external demands of network passenger flow. Then we use logical constraint transformation and linearization techniques to enable the model to be solved directly by commercial optimization solvers. For large-scale problems, we adopt a rolling horizon approach to improve computing efficiency. To validate the effectiveness of the sliding-window based passenger control method, we conduct case studies including a small designed example and real-world research on the Beijing Subway network. The experimental results demonstrate that our proposed model assists managers in developing flexible and accurate network-level collaborative passenger flow control schemes.

Long-term operation of isolated microgrids with renewables and hybrid seasonal-battery storage

With the progress of decarbonization, renewable-powered microgrids are attracting wide attention. To cope with the fluctuation of renewable power at different timescales, both long-term and short-term energy storage devices are required. This paper studies the operation of renewable-dominated isolated microgrids integrated with hybrid seasonal-battery storage. A data-driven scheduling-correction framework is proposed. By leveraging the historical data of renewable power and load, the scheduling module generates ex-post optimal state-of-charge (SoC) sequences of the seasonal energy storage ahead of the operating year. In each period of real-time operation, the correction module performs two steps: the first step is to update the reference SoC for the seasonal storage based on the ex-post optimal SoC sequences and the newly observed data; the second step is to solve a bi-objective rolling-horizon optimization problem which minimizes the instant operating cost while steering the SoC of seasonal storage to its reference value. An appealing feature of the proposed method is that the long-term renewable power forecasts are not required. A microgrid system is devised to verify the proposed framework. Numerical tests show that the scheduling-correction framework outperforms existing rolling horizon approaches in compromising economy, power supply reliability, and renewable energy utilization.