Rolling Horizon Research Articles

Train rescheduling and platforming in large high-speed railway stations

To deal with train delays in large high-speed railway stations, a multi-objective mixed-integer nonlinear programming (MO-MINLP) optimization model was proposed. The model used the arrival time, departure time, track occupation, and route selection as the decision variables and fully considered the station infrastructure layout, train operational requirements, and time standards as limiting factors. The optimization objective was to minimize train delays and reduce track and route adjustments. To realize the large-scale and rapid solution of the MO-MINLP model, this study proposed a rolling horizon optimization algorithm that used “half an hour” as a time interval and solved the rescheduling and platforming problem of each time interval step-by-step. In numerical experiments, 227 train movements under delay circumstances in Hangzhoudong station were optimized by using the proposed model and solution algorithm. The results show that the proposed MO-MINLP model could resolve route conflicts, compress unnecessary dwell times, and reduce train delays; the solution algorithm could efficiently increase the computational speed. The maximum solution time for optimizing the 227 train movements is 15 min 24 s.

Rolling horizon strategies for a dynamic and stochastic ridesharing problem with rematches

We study a dynamic matching and rematching problem with applications in ridesharing systems. Transportation requests for riders and passengers arrive dynamically and are represented as nodes of a bipartite graph, connected by edges that correspond to compatible requests. Matching requests by selecting the corresponding edge earns a profit. We further allow for unmatching previously matched requests. While this increases the system’s flexibility to adjust to new matching opportunities, unmatching may degrade customer experience and therefore implies penalty costs. We evaluate myopic and stochastic multi-period mixed-integer programming models in a rolling horizon framework. All models are compared against a static model that has perfect knowledge about future requests, using a novel and extensive benchmark set of realistic instances. Our results demonstrate the value of being able to unmatch, as well as the benefits of the stochastic strategies over the myopic strategy.

A rolling horizon planning approach for short-term demand supply matching

Demand fulfillment and order management are important functions in semiconductor supply chains to interact with customers. In this paper, an iterative short-term demand supply matching (STDSM) algorithm based on mixed-integer linear programming (MILP) is proposed. This approach repromises orders taking into account the finite capacity of the shop floor. Decomposition is used to obtain computationally tractable subproblems. The STDSM approach is applied together with master planning and allocation planning in a rolling horizon setting. A simulation model of a simplified semiconductor supply chain is used for the rolling horizon experiments. The experiments demonstrate that the proposed STDSM scheme outperforms conventional business rule-based heuristics with respect to several delivery performance-related measures and with respect to stability.

Wasserstein distributionally robust surgery scheduling with elective and emergency patients

We study a surgery scheduling problem with regard to both elective and emergency patients, where surgery durations are uncertain and emergency patients arrive dynamically. The problem determines, at the beginning of a day, how many operating rooms to open and how to allocate elective and (possibly dummy) emergency patients into them to minimize the operating room opening and expected overtime costs. Incorporating (possibly dummy) emergency patients provides a novel approach for reserving emergency capacity. We propose a robust data-driven model that allows for distributional ambiguity via the Wasserstein metric. We derive its mixed-integer conic reformulation and develop an exact branch-and-cut algorithm. We also uncover our model’s connections to its sample average approximation counterpart. Since emergency patients necessitate adequate and timely treatments, we formalize a rolling horizon scheme to dynamically reschedule and prioritize the emergency patients upon their arrivals. Our scheme handles practical features such as dynamic emergency arrivals and uncertain service duration. We perform simulation studies based on real data and numerical experiments show that our method outperforms the benchmark ones in a variety of performance indicators.

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.

Optimal Sequencing of Arrival Flights at Metroplex Airports: A Study on Shared Waypoints Based on Path Selection and Rolling Horizon Control

The civil aviation industry is experiencing significant growth in air traffic density within terminal areas, necessitating improved air traffic efficiency. In China’s pursuit of world-class airport clusters, operational complexities arise due to the co-location of these airports in the same terminal area airspace, resulting in lower operational efficiency. To mitigate congestion and flight delays, this study proposes an integrated model that considers multiple runways and route selections, accounting for actual route point restrictions. Utilizing actual operational data from Shanghai metroplex, the proposed model is validated. The study focuses on the airport metroplex system and presents a comprehensive mixed-integer programming (MIP) model for arrival sequencing, considering multiple airports, runways, and routes. The maximum landing efficiency is adopted as the objective function, optimizing arrival scheduling while considering time intervals, route selection, and landing constraints. The Multi-waypoint Rolling Horizon Control (MWRHC) algorithm is employed to tackle time-efficiency challenges, ensuring flight safety by continuous monitoring of flights in the terminal area. Comparative analysis reveals the algorithm’s superior optimization performance for single-runway airports compared to dual-runway airports. Overall, the proposed model and algorithm effectively improve the efficiency of multi-airport arrival scheduling in airport metroplex systems.

A rolling horizon framework for the time‐dependent multi‐visit dynamic safe street snow plowing problem

AbstractAs a major real‐world problem, snow plowing has been studied extensively. However, most studies focus on deterministic settings with little urgency yet enough time to plan. In contrast, we assume a severe snowstorm with little known data and little time to plan. We introduce a novel time‐dependent multi‐visit dynamic safe street snow plowing problem and formulate it on a rolling‐horizon‐basis. To solve this problem, we develop an adaptive large neighborhood search as the underlying method and validate its efficacy on team orienteering arc routing problem benchmark instances. We create real‐world‐based instances for the city of Vienna and examine the effect of (i) different snowstorm movements, (ii) having perfect information, and (iii) different information‐updating intervals and look‐aheads for the rolling horizon method. Our findings show that different snowstorm movements have no significant effect on the choice of rolling horizon settings. They also indicate that (i) larger updating intervals are beneficial, if prediction errors are low, and (ii) larger look‐aheads are better suited for larger updating intervals and vice versa. However, we observe that less look‐ahead is needed when prediction errors are low.

Sensitivity analysis of the hyperparameters of an ensemble Kalman filter application on a semi-distributed hydrological model for streamflow forecasting

Data Assimilation (DA) is an important step for improving prediction accuracy and real-time correction of hydrological models for operational forecasting purposes. The Ensemble Kalman filter (EnKF) is one of the most popular techniques used to address the issues of updating the model states and parameters by creating a novel set of initial conditions in real-time. This study aims at identifying optimal seasonal EnKF parametrizations to reduce the uncertainty associated with the initial conditions in a semi-distributed hydrological model of a snow-dominated catchment in Canada. Sensitivity analysis is performed to evaluate the effects of the EnKF individual hyperparameters (temperature, precipitation and inflow uncertainties) and the updating of three state variables (vadose zone, saturated zone and snowpack) on the skill of short-term (up to 9 days lead-time) forecasts. Results show that the performance of the forecasts is sensitive to the individual hyperparameters and particularly so to the temperature uncertainty, which varies between seasons. Additionally, the forecast skill is related to the choice of the state variables to be updated depending on the season. The vadose zone state variable displays higher importance and sensitivity than the other states, and the results indicate that all state variables should not be systematically updated on this catchment and with the implemented hydrological model. Finally, combining the best hyperparameter values with the optimal combination of state variables to update, insight is provided on the success of the data assimilation scheme that is evaluated on a rolling horizon using a set of seasonal rules to gain forecast performance over the span of multiple years.

Optimizing the marketing of flexibility for a virtual battery in day-ahead and balancing markets: A rolling horizon case study

Industrial electricity consumers with flexible demand can profit from adjusting their load to short-term prices or by providing balancing services to the grid. Markets which support this kind of short-term position adjustment are the day-ahead market and balancing markets. We propose a formulation for a combined optimization model that computes an optimal distribution of flexibility between the balancing and day-ahead markets. The optimal solution also includes the specific bids for the day-ahead and balancing markets. Besides the expected profits of each market and their different rules for bidding, our model also takes their different roles in a continuous marketing of flexibility into account. To prevent overrating short-term profits we introduce a variable penalty term that adds a cost to unfavorable load schedules. We evaluate the optimization model in a rolling horizon case study based on the setting of a virtual battery at TRIMET Aluminum SE, which is derived from a flexible aluminum electrolysis process. For such a battery we compute a daily optimal split of flexibility and trading decisions based on data in the period 04/2021–03/2022. We show that the optimal split is more profitable than using only one market or a fixed split between the markets.

A quadrant shrinking heuristic for solving the dynamic multi-objective disaster response personnel routing and scheduling problem

In the aftermath of natural disasters there is a need to provide disaster relief services. These services are offered by diverse disaster relief personnel teams that are specialized in the provision of the required services, e.g., teams that set up temporary shelters, teams that are providing medical services. These services are provided during a rolling horizon and the demand and supply characteristics of the disaster relief system evolve dynamically over time. In this paper we are presenting a dynamic variant of the multi-objective disaster relief personnel routing and scheduling (DDRPRS) problem, which considers efficiency, fairness and transportation risk objectives. We introduce a Quadrant Shrinking Method (QSM) based heuristic algorithm to approximate the Pareto Optimal Solutions of the DDRPRS problem under consideration. The proposed algorithm considers the performance of the solutions over the entire planning horizon and their robustness over time in terms of their efficiency, fairness and transportation risk. We apply the proposed heuristic for routing and scheduling personnel involved in evacuation and medical operations using data from the 2018 Lombok Earthquake in Indonesia. Our heuristic implementation covers both the dynamic and static variants of the disaster relief personnel routing and scheduling problem. Computational results show that the proposed heuristic can generate in a short time sufficiently large number of Pareto Optimal Solutions which cover the entire Pareto frontier as indicated by the diverging behaviours of the Pareto Optimal Solutions and the associated hypervolume metrics.

Optimal control of combined heat and power station operation

Combined heat and power stations have become one of the most utilized units of district heating systems. These stations usually contain several boilers for burning fossil fuels and renewable resources used for heating up steam, which can be used either for residential and commercial heating or electricity generation. To ensure efficiency, a boiler should either run continuously (for at least a given period) on a power output higher than a given threshold or switch off. The optimal control of the plant operations should combine an efficient setup for the turbine and boilers in operation, reflecting the demand for steam and the price of electricity, and a schedule that describes which boilers should be in operation at a given time. This paper proposes a method for optimal control of combined heat and power station operation for a given time horizon. The method is based on a two-level approach. The lower-level models correspond to finding the optimal setup of the combined heat and power station parameters for an hourly demand for different kinds of steam. The upper-level model corresponds to the optimal schedule of the operations of the individual boilers, which is planned for the entire time horizon. The lower-level model is modeled as a mixed-integer linear programming problem and is solved using parametric programming. A dynamic programming algorithm solves the upper-level model with a rolling horizon. The validity of the proposed method and its computational complexity for different granularity of the time horizon, different ranges of the parameters, varying demand for various kinds of steam, and varying electricity prices are investigated in a case study. The presented approach can be readily applied to other control problems with a similar structure.

Strategic decision making of energy storage owned virtual power plant in day-ahead and intra-day markets

In this paper, a service-oriented aggregator like a virtual power plant is modeled and designed to facilitate the integration of distributed generations in both day-ahead and intra-day power markets and simultaneously collaborate with the distribution system operator to manage the grid utilization problem. To do this, a proper plan of interactions between power system and market operators, customers, and aggregators concerning participation in the electricity market is suggested and explained. The optimal arrangement of the real and reactive power flows of VPP sources is a solution used to manage the congestion of the distribution network with the aim of maximizing the integration of renewable energy into the energy market. The VPP utilizes the rolling horizon technique to decrease the uncertainties related to renewables in the scheduling horizon. To prevent unwarranted wind and solar power generation curtailments, VPP behaves flexibly and reschedules its resources according to the contracts that are concluded. In this work, a modified IEEE 33-bus distribution test system is utilized to investigate the efficiency and proficiency of the proposed method. The simulation and numerical results demonstrate that the suggested VPP model can not only improve solar and wind power integration in the energy markets but also alleviate congestion in the distribution networks.

Data-driven inventory policy: Learning from sequentially observed non-stationary data

This paper aims to find dynamic inventory policies for retailers that have limited knowledge about future demand and sequentially observe the unprecedented demand data. We assume the demand is non-stationary; it follows different distributions for different time periods, and the data distributions and the transition behavior are unknown. Two solution approaches are presented to tackle this problem. Integrated-Bayesian (IB) approach is a parametric approach and is introduced for the case when an uncertainty set of possible demand distributions is available. A non-parametric approach, separate-lasso (SL), is proposed for the case that the uncertainty set possible demand distributions is not known. Both methods are theoretically analyzed and empirically benchmarked against several state-of-the-art heuristics. The theoretical analyses provide easy-to-implement algorithms for both approaches, while performance guarantees are derived for the separate-lasso approach. Computational studies show that the proposed methods outperform state-of-the-art heuristics–namely, sample average approximation, rolling horizon, and exponential smoothing–in nine different data environments. The optimal dynamic policy is not obtainable in this dynamic setting as reliable demand forecasts are not available. Therefore, we derive an approximated optimal policy, OPT, assuming the complete knowledge of the demand data in advance. The empirical results reveal that the cost of the proposed approaches is only 12% higher than that of OPT on average. Furthermore, we show that the proposed methods capture the hidden patterns inside the highly non-stationary real-world demand data of one of the largest e-commerce websites.

Overall Equipment Effectiveness Prediction with Multiple Linear Regression for Semi-automatic Automotive Assembly Lines

In the field of industry, especially in the production areas, it is particularly important that the monitoring of assembly efficiency takes place in real-time mode, and that the related data-based estimation also works quickly and reliably. The Manufacturing Execution System (MES), Enterprise Resource Planning (ERP) and Customer Relationship Management (CRM) systems used by companies provide excellent support in data recording, processes, and storing. For Overall Equipment Effectiveness (OEE) data showing the efficiency of assembly lines, there is a regular need to determine expected values. This paper focuses on OEE values prediction with Multiple Linear Regression (MLR) as supervised machine learning. Many factors affecting OEE (e.g., downtimes, cycle time) are examined and analyzed in order to make a more accurate estimation. Based on real industrial data, we used four different methods to perform prediction with various machine learning algorithms, these were the cumulative, fix rolling horizon, optimal rolling horizon and combined techniques. Each method is evaluated based on similar mathematical formulas.

How to Deploy Robotic Mobile Fulfillment Systems

Many warehouses involved in e-commerce order fulfillment use robotic mobile fulfillment systems. Because demand and variability can be high, scheduling orders, robots, and storage pods in interaction with manual workstations are critical to obtaining high performance. Simultaneously, the scheduling problem is extremely complicated because of interactions between decisions, many of which must be taken timely because of short planning horizons and a constantly changing environment. This paper models all such scheduling decisions in combination to minimize order fulfillment time. We propose two decision methods for the above scheduling problem. The models batch the orders using different batching methods and assign orders and batches to pods and workstations in sequence and robots to jobs. Order picking and stock replenishment operations are included in the models. We conduct numerical experiments based on a real-world case to validate the efficacy and efficiency of the model and algorithm. Instances with 14 workstations, 400 orders, 300 stock-keeping units (SKUs), 160 pods, and 160 robots can be solved to near optimality within four minutes. Our methods can be applied to large instances, for example, using a rolling horizon. Because our model can be solved relatively fast, it can be used to take managerial decisions and obtain executive insights. Our results show that making integrated decisions, even when done heuristically, is more beneficial than sequential, isolated optimization. We also find that positioning pick stations close together along one of the system’s long sides is efficient. The replenishment stations can be grouped along another side. Another finding is that SKU diversity per pod and SKU dispersion over pods have strong and positive impacts on the total completion time of handling order batches. Funding: This work was supported by National Natural Science Foundation of China [72025103, 72361137001, 71831008, 72071173] and the Research Grants Council of the Hong Kong Special Administrative Region, China [HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0265 .

A service network design for scheduled advanced air mobility using human-driven and autonomous air metro

Emerging modes of advanced air mobility are potential alternatives to current ground transport. This study proposes a service network design approach for the air metro, a pre-scheduled service with fixed routes that accommodate passengers for intra- or inter-city trips. The scenarios of human-driven and autonomous air metro are then compared, where the former has a labour cost for pilots and the latter has a higher capital costs such as vehicle and automation costs. Then, a rolling horizon optimisation approach is proposed, where the temporal length of a single rolling horizon is an early confirmation period plus a safety margin. The rolling horizon introduces decision and marginal arcs with different fleet, passenger, and pilot network capabilities. The optimised outputs on critical arcs are determined and fixed, while the marginal arcs can be continuously adjusted in the subsequent rolling horizons. Numerical studies are undertaken across all variables in the context of the Greater Metropolitan Area of Sydney, Australia. Results suggest that the human-driven air metro would be economically preferable until the utilisation cost of an autonomous aircraft can reduce by 60%. Furthermore, confirming the actual passenger demand at least 45 min in advance is recommended, and a single rolling horizon should be longer than 150 min.

A constraint equivalent model of heat network for combined heat and power systems cooperation considering uncertainties

The cooperation of combined heat and power (CHP) systems can improve efficiency in energy utilization by fully utilizing the complementarity between heat and power. However, heat and power systems are operated by different companies where data sharing is restricted for privacy reasons, thus posing significant obstacles to collaboration. This paper proposes a coordinated operation method for CHP systems based on the constraint equivalent model. To preserve the operational constraints of heat networks and protect data privacy, a boundary point search method is firstly developed, where the operational constraints of heat networks are mapped to the feasible region of CHP units. Then, a multi-period cooperation model considering uncertainties of both networks is established based on the proposed constraint equivalent model and the rolling horizon strategy. Moreover, the impact of heat storage tanks and uncertainties of heat loads on the boundaries of the feasible region for heat networks is further analyzed. Simulation results demonstrate the effectiveness of the proposed constraint equivalent model and the cooperation method.

Flexible renewable energy planning based on multi-step forecasting of interregional electricity supply and demand: Graph-enhanced AI approach

Jeju Island faces curtailment problems when renewable energy generation exceeds the facility capacity. In addition, the renewable energy system cannot achieve consistent operation because of the uncertainty of renewable energy sources (RES) and their complex spatiotemporal patterns. Climate change and extreme meteorological phenomena also affect the energy system of the island. Therefore, it is essential to maximize RES exploitation to accomplish carbon-free energy production. This study developed a rolling horizon optimization–based flexible renewable energy distribution planning (FxRE-Plan) based on an artificial intelligence-driven spatiotemporal RES prediction model. An adaptive graph convolutional recurrent network (AGCRN) was used to develop a spatiotemporal prediction model. Then, FxRE-Plan was determined using a multiobjective genetic algorithm to maximize the RES potential under climate change scenarios. The FxRE-Plan was evaluated and compared with the current operation of the electric grid in Jeju Island through economic, environmental cost, and climate change vulnerability assessment index. The results of this research show that the AGCRN–based spatiotemporal prediction model exhibited superior prediction performance, achieving a 95% R2. In addition, the FxRE-Plan reduced greenhouse gas emissions by approximately 11.5% at maximum and climate change vulnerability. Hence, the proposed FxRE-Plan can be used to solve curtailments in real electric grids by pursuing carbon-free islands.

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.

A Linear-Parameter-Varying Formulation for Model Predictive Perimeter Control in Multi-Region MFD Urban Networks

An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].