Rolling Horizon Research Articles

Rolling horizon optimization for real-time operation of prosumers with Peer-to-Peer energy trading

Peer-to-Peer energy trading is recognized as a promising approach for prosumers to improve the operational economics. However, the uncertainty of renewable energy poses challenges to the reliable and economical operations of prosumers. This paper focuses on the real-time operation of prosumers. An efficient rolling horizon optimization-based real-time operation strategy for prosumers is proposed to minimize the total operational cost in one-day, in which the thermal comfort demand of the prosumers is also considered. The case study is finally conducted for 94 prosumers located at an urban community microgrid in a typical summer day scenario. Simulation results show that the proposed rolling horizon operation strategy can make full use of the flexible energy resources of prosumers, realizing the local energy supply–demand balance while improving prosumers’ operational economics. Moreover, the negative impact of day-ahead forecasting errors on the intra-day operation can be reduced significantly.

Real-time optimization of train regulation and passenger flow control for urban rail transit network under frequent disturbances

Urban rail transit networks face frequent delays and oversaturation resulting from unexpected disturbances and high demands during rush hours, which inevitably leads to unstable train operations, poor service experiences, and potential accidents on crowded platforms. This paper explores the train regulation and passenger flow control strategies for large-scale urban rail transit networks. Specifically, we develop a mixed-integer nonlinear programming (MINLP) formulation to improve the punctuality and regularity in train operations, reduce the passenger waiting time, and alleviate the passenger flow burden of platforms, where the dynamic coupling interactions among network-wide passengers, trains and stations are systematically considered. To reduce the computational complexity and satisfy real-time requirements, we particularly devise a real-time optimization approach based on iterative nonlinear programming (INP) combined with Lagrangian relaxation (LR) under the rolling horizon (RH) framework, which effectively disposes of the intractable nonconvexity and constructs the desirable properties of decomposability and parallelism. The original problem is transformed into a sequence of line-level subproblems that can be solved quickly, so as to circumvent the computational burden. Moreover, to verify the effectiveness of our approach, we apply it to address numerical examples on a simplified network and the real-world Beijing Subway network. The realistic case studies illustrate that the proposed approach can reduce the train deviation from the original timetable, the passenger waiting time, and the passenger accumulation risk on the platform, by around 84.92%, 30.34% and 61.42% in comparison with the common rule-based strategy. Additionally, the computation time for the realistic large-scale experiment is acceptable for a real-time implementation.

Designing of Integrated Tactical Production-Quality Planning in a Rolling Horizon Under Demand Uncertainty: Case Study in the Automotive Wire Harness Industry

To minimize waste and scrap, reworking becomes an integral part of many manufacturing companies. In this study, the integrated production-quality planning in the tactical horizon considering the customer demand uncertainty is presented. A mixed-integer programming model is developed to find optimal dynamic planning production which minimizes costs and reduces the scrap. After each production cycle, the quality indicators and relative costs for good and poor quality are performed. These indicators are introduced into the developed model to determine the optimal production orders and stock levels considering the reworked and scrapped products. A real case study is presented to illustrate the applicability of the proposed model. By comparing the obtained results with real results from studied company, we proved that this new model gives an optimal production plan.

Maritime inventory routing with transshipment: the case of Yamal LNG

The LNG-ADP problem is a tactical planning problem for creating an annual delivery program (ADP) for a liquefied natural gas (LNG) producer. An ADP specifies the departure dates of the LNG carriers as well as the delivery dates at the different customers for a period of 12–18 months. The problem can be formulated as maritime inventory routing problem, as it is an important requirement to plan the deliveries such that inventory levels are kept within minimum and maximum limits at the customers as well as the LNG production facility. Inspired by the case of Yamal LNG, we propose a novel discrete-time formulation for the LNG-ADP problem with transshipment and intermediate storage. Our formulation also allows for waiting at the unloading ports. The problem is solved using a rolling horizon heuristic (RHH) for a case based on the Yamal LNG project. We study the impact of different RHH configurations on run time and solution quality. The results show that using a central period that is shorter than the forecast period provides the best objective function, whereas a central period that is longer than the forecast period improves run time. We also explore the effect of allowing waiting at the unloading ports. Waiting does not necessarily improve the objective function value, despite increasing the solution space. However, we observe a reduction in run time for instances where waiting is allowed.

Tri-level hybrid interval-stochastic optimal scheduling for flexible residential loads under GAN-assisted multiple uncertainties

Various building loads, such as heating, ventilation, and air conditioners (HVACs), electric water heaters (EWHs), and electric vehicles (EVs), can introduce opportunities for improving the flexibility of electricity consumption while satisfying the needs of building owners as well as benefiting the resilience of distribution system. To utilize such flexibility, a tri-level distribution market framework is established, including residential consumers, load aggregators (LAs), and the distribution system operator (DSO). The uncertainties from all three levels are considered. The random consumption behavior at the consumer level is modeled as a Gaussian noise that is also aggregated and transmitted to the LA level. The weather temperature in the LA level is forecasted as an interval, and the photovoltaic (PV) power in the market-clearing level is modeled by a set of power scenarios generated by Generative Adversarial Networks (GANs). Then, a hybrid interval-stochastic programming is proposed to transform the uncertain problems in the first two levels into deterministic ones. For real-time implementations, a rolling horizon optimization (RHO) scheme is employed to continuously optimize the power consumption based on the latest operating information. Finally, case studies on a modified IEEE 69-bus system validate the effectiveness of the proposed uncertainty modeling strategies and the RHO scheme.

Time window optimization for attended home service delivery under multiple sources of uncertainties

We consider a vehicle routing problem variant to optimize time window assignments together with vehicle routing and scheduling decisions, under the uncertainties of trip time, service time and possible customers’ cancellations. We minimize the expected cost of vehicles’ overtime, idleness, and customer waiting, when also allowing to add new customers to existing schedules. We formulate a two-stage stochastic mixed-integer programming model using finite samples of the uncertain parameters, where in the first stage, we optimize vehicle routes and assign service time windows to customers, and in the second stage, we construct a linear program to compute the resultant undesirable cost given routes and time windows. We also propose a re-optimization method and an insertion-based linear program for accommodating real-time requests in a rolling horizon way for dynamic operations. To speed up computation, we further decompose the problem into three phases and propose Assignment–Routing–Scheduling heuristics. We first design three clustering algorithms based on spatial similarities to assign customers to vehicles, and then combine the nearest-neighbor and smallest-variance rules to decide the route for each vehicle. Finally, we cast the scheduling part as a Newsvendor problem variant and apply inventory approximations to derive closed-form solutions for determining time windows. We conduct numerical studies on diverse instances generated using both well-established benchmark data sets and Ford’s mobile service data, to compare different approaches and demonstrate the benefits of allowing flexible time-window assignments.

Rack retrieval and repositioning optimization problem in robotic mobile fulfillment systems

Robotic mobile fulfillment systems provide a new solution for e-commerce retailers to fulfill customers’ orders, wherein racks are moved by mobile robots to workstations so pickers can retrieve the purchased products. While such automated parts-to-picker systems can save on labor costs, they raise new operational challenges. In this paper, we investigate the rack storage and robot assignment to racks problem during order processing. We formulate this problem with the goal of minimizing the makespan of the system. Based on a rolling horizon framework and the simulated annealing method, we develop a matheuristic decomposition approach, which involves the solution of a special axial 3-index assignment problem in each stage to solve the problem. We test the performance of the proposed method for both large-scale cases based on a real-world dataset and small-scale instances generated synthetically. Computational results demonstrate the good performance of the proposed approach.

Connected automated vehicle trajectory optimization along signalized arterial: A decentralized approach under mixed traffic environment

Trajectory optimization, as a key connected automated vehicles (CAVs) operation task, has the potential to mitigate traffic congestion, lower energy consumption, and increase the efficiency of traffic operation. This study proposes a decentralized approach to optimization CAV trajectories in both longitudinal and lateral dimensions along a signalized arterial under the mixed traffic environment, where human vehicles (HVs) and CAVs co-exist. More specifically, a 2-stage model is developed to optimize CAV trajectories based on traffic signal plans of downstream intersections and trajectory information of surrounding vehicles. The stage-1 is formulated to provide a rough estimate of the minimal travel time required for a single CAV traveling along this arterial with minimum stops. The stage-2 model is then designed to optimize the longitudinal and lateral behavior of CAVs with the objective of minimizing delay and lane-changing costs. This model is solved by a dynamic programming algorithm to satisfy the real-time optimization needs. A rolling horizon approach is adapted to dynamically implement the proposed model in light of changing traffic conditions. Numerical experiments have been conducted on a real-world arterial to evaluate the model performances. By comparing the optimized trajectories to the no optimization benchmark, the proposed model can reduce average stop delays of CAVs. Moreover, it can also reduce the stop delays of HVs and mixed traffic.

A robust rolling horizon framework for empty repositioning

Naturally imbalanced freight flows force transportation service providers to reposition empty resources. When constructing empty repositioning plans, the cost of repositioning empty resources needs to be weighed against the cost of corrective actions in case of unavailable resources. This is especially challenging given the uncertainty of future demand. We design and implement a robust rolling horizon framework for constructing effective empty repositioning plans. An extensive computational study demonstrates the benefits of explicitly accounting for uncertainty in future demand by using robust optimization, and pragmatically controlling the level of conservatism in hedging against this uncertainty. We also investigate practical strategies for reducing the complexity of managing the repositioning of empty resources in transportation service networks covering huge geographic areas.

Integrated charging infrastructure planning and charging scheduling for battery electric bus systems

• Integrated optimization of charging infrastructure and charging scheduling. • A two-phase optimization framework is proposed to solve the integrated problem. • Uncertainties in bus energy consumption and vehicle travel time are considered. • A novel rolling horizon approach is proposed to tackle real-time charging scheduling. Studies on the electric bus system planning problem have typically focused exclusively on either the deployment of charging infrastructure or the scheduling of charging events; few have examined the impact of charging facility deployment on charging activities. Considering the interdependence of system design and operational strategies, this study proposes a two-phase optimization framework for charging infrastructure planning and charging scheduling for battery electric bus systems. An integrated optimization model is first developed to simultaneously optimize charger deployment, on-board battery capacity, and charging schedules. A charging scheduling model is further proposed and a rolling horizon approach is utilized in the second phase to optimize the real-time charging scheduling of electric buses. Compared to existing electric bus system planning methods, the proposed integrated model can reduce the total system cost by 19.5%. In addition, compared to uncontrolled charging, the proposed rolling horizon-based charging strategy can reduce the total charging cost by 68.3%.

Inventory decisions for ameliorating products under consideration of stochastic demand

Product quality is a key factor in the food and drinks industry, allowing companies to distinguish themselves from their competitors and achieve higher profit margins. However, the quality of a product may be subject to change over time and thus complicate planning and decision-making processes. While most of the literature in this area focuses on quality change in the form of deterioration, there are also products that improve in quality over time, resulting in unique challenges with regard to production and inventory management. In this context, this paper introduces an inventory planning problem for ameliorating products under consideration of demand uncertainty and product loss due to evaporation over time. This problem is solved using a MILP model within a rolling horizon approach. The proposed model is illustrated on two case studies from the cheese and whisky industry and investigates different scenario settings. The general findings show that the differences in profit margins between the quality categories influence the optimal strategy of the manufacturer and that the optimal aging and storage time should be kept to a minimum. Moreover, the results show that the rolling horizon approach is well-suited to handle the stochastic setting and that high demand fulfilment can be achieved as long as an appropriate planning horizon for the different products and product categories is considered • Stochastic problem formulation to study inventory decisions for ameliorating products. • Illustration based on two case studies from the cheese and whisky industry. • Analysis of different scenario settings related to uncertainty and other aspects. • Findings show the impact of profit margins on the optimal strategy of the producer.

A Multi-Stage Optimisation Approach to Design Relocation Strategies in One-Way Car-Sharing Systems With Stackable Cars

One of the main operational challenges faced by the operators of one-way car-sharing systems is to ensure vehicle availability across the regions of the service areas with uneven patterns of rental requests. Fleet balancing strategies are required to maximise the demand served while minimising the relocation costs. However, the design of optimal relocation policies is a complex problem, and global optimisation solutions are often limited to very small network sizes for computational reasons. In this work, we propose a multi-stage decision support system for vehicle relocation that decomposes the general relocation problem into three independent decision stages to allow scalable solutions. Furthermore, we adopt a rolling horizon control strategy to cope with demand uncertainty. Our approach is highly modular and flexible, and we leverage it to design user-based, operator-based and robotic relocation schemes. Besides, we formulate the relocation problem considering both conventional cars and a new class of compact stackable vehicles that can be driven in a road train. We compare the proposed relocation schemes with two recognised benchmarks using a large data set of taxi trips in New York. Our results show that our approach is scalable and outperforms the benchmark schemes in terms of quality of service, vehicle utilisation and relocation efficiency. Furthermore, we find that stackable vehicles can achieve a relocation performance close to that of autonomous cars, even with a small workforce of relocators.

Quantifying the impact of delivery day flexibility on last-mile delivery costs

Last-mile delivery operations are often required to uphold rigid delivery dates, such as the day after an order is placed. However, given the inherent temporal stochasticity in customer order placement, this practice can overwhelm the available vehicle fleet with long routes and the need for driver overtime. This work explores the potential benefits of customer flexibility, wherein the delivery day can be chosen by the distributor from among pre-agreed delivery day windows spanning two or more consecutive days, allowing the delivery day to be co-optimized along the associated vehicle routes and leading to distribution cost savings. To that end, we develop a rolling horizon simulation framework that integrates a novel forecasting scheme for sampling order realizations with a branch-and-cut algorithm for solving the multi-period vehicle routing instances arising on each day. Computational studies using real-life industrial data are conducted to compare various decision policies and quantify the long-term cost savings that are possible when allowing such flexibility. In certain cases, we reveal the potential of significant cost savings–up to 12%–compared to the current “next-day” delivery policy. Our study also investigates the extent of discount incentives that may be offered to customers for accepting flexible delivery days.

Bi-Level Fuzzy Expectation-Based Dynamic Anti-Missile Weapon Target Allocation in Rolling Horizons

The weapon target allocation (WTA) problem is a crucial issue in anti-missile command decisions. However, the current anti-missile weapon target allocation models ignore the dynamic complexity, cooperation, and uncertainty in the actual combat process, which results in the misclassification and omission of targets. Therefore, we propose a bi-level dynamic anti-missile weapon target allocation model based on rolling horizon optimization and marginal benefit reprogramming to achieve rapid impact on static and dynamic uncertainties in the battlefield environment. Further, we also propose an improved bi-level recursive BBO algorithm based on hybrid migration and variation to perform fast and efficient optimization of the model objective function. A simulation analysis demonstrate that the model is suitable for larger-scale, complex, dynamic anti-missile operations in uncertain environments, while the algorithm achieves better solution efficiency and solution time compared with the same type of heuristic algorithm, which meet the requirements of solution accuracy and timeliness. In addition, we obtain better rolling horizon parameters to further optimize its performance.

Scheduling and operation of RES-based virtual power plants with e-mobility: A novel integrated stochastic model

In the present paper, an Energy Management System is proposed to optimally schedule and operate a Virtual Power Plant (VPP) composed of charging stations for e-vehicles, stationary batteries, and renewable energy sources. The model is capable to optimize the bidding process on the Day-Ahead Market (DAM) through a two-stage stochastic formulation, which considers the uncertainties affecting the evaluation of the energy required for the next day. The stochastic scenarios are generated through a Monte Carlo procedure and clustered by a reduced domain k-means algorithm. To manage in real-time the operation of the VPP, a new Rolling Horizon mixed-integer linear programming model is adopted. The effectiveness of the tools developed is proved by numerical simulations reproducing the different operating conditions of the VPP. The benefits of the approach are confirmed by extensive analyses performed over a 4-month period. An increase of the profits of 23 % compared to a non-optimized strategy and of 6 % with respect to a deterministic optimization is observed.

Hybrid rolling-horizon optimization for berth allocation and quay crane assignment with unscheduled vessels

Port operations usually suffer from uncertainties, such as vessels’ arrival time and handling time and unscheduled vessels. To address this, this study presents a dynamic berth allocation and crane assignment specific problem (BACASP) when unscheduled vessels arrive at the port, which is branded the berth allocation and quay crane assignment specific problem with unscheduled vessels (UBACASP). A rolling-horizon based method is proposed to decompose the UBACASP into a multi-stage static decision BACASP, wherein a rescheduling margin-based hybrid rolling-horizon optimization method is developed by incorporating the event-driven and periodical rolling-horizon strategies as the urgency of dynamic events is evaluated. In each rolling horizon, a mixed integer linear programming model (MILP) is presented for the BACASP to minimize the total port stay time of vessels and the penalties of delays associated with the spatial and temporal constraints, such as the length of continuous berth, number of quay cranes (QCs) and non-crossing of QCs. A discretization strategy is designed to divide the continuous berth into discrete segments, and convert the BACASP to a discrete combinatorial optimization problem, which is efficiently solved by the proposed adaptive large neighborhood search algorithm (ALNS). Case studies with different problem characteristics are conducted to prove the effectiveness of the solution methods proposed in this study. Moreover, the performances of the ALNS and the existing methods for solving the BACASP are compared, and the advantages and disadvantages of different rolling strategies under different degrees of uncertainties are deeply analyzed.

Mobility support for disadvantaged and disabled travelers during pandemic or similar situations

The COVID-19 lockdown has reduced public transportation service to the disadvantaged and disabled people who urgently need adequate mobility to obtain essential suppliers. This paper aims to improve the life quality of people with disabilities and elderly people by addressing social exclusion, accessibility, and mobility issues. Demand responsive transport services are frequently offered in the context of door-to-door transportation of the elderly and persons with disabilities. We study and compare two frameworks. We apply both Sample average approximation (SAA) and Rolling Horizon (RH) to optimize a car sharing system for the total cost, including initiation cost and operation cost after fleet size is determined. The model is implemented with given geographic conditions and other local information to be tailored for specific applications for local communities. Given that no historical data is available, random sample data is generated to simulate expected demands. We consider three types of probability distributions for daily demand data, and the results generated using three different distributions are being examined and compared. The research shows that the demand data following a normal distribution results in the minimum total cost. Additionally, we study the impact of several factors on total cost, including demand fulfillment rates and operation hours. Our results suggest that the impact of fulfillment rate on fleet size is exponential after a threshold under all three types of daily demand data, and extended operation hours can significantly reduce the total cost. Finally, the paper provides applicable frameworks for city planners, NPOs, and policymakers to better allocate limited resources to implement the carsharing system when little to no historical travel information is available for low-density population areas. It is anticipated that the outcome from this research would benefit disadvantaged and disabled travelers during COVID-19 or similar difficult situations in the future.

A framework for researching energy optimization of factory operations

Energy optimization of factory operations has gained increasing importance over recent years since it is understood as one way to counteract climate change. At the same time, the number of research teams working on energy-optimized factory operations has also increased. While many tools are useful in this area, our team has recognized the importance of a comprehensive framework to combine functionality for optimization, simulation, and communication with devices in the factory. Therefore, we developed a framework that provides a standardized interface to research energy-optimized factory operations with a rolling horizon approach. The optimization part of the framework is based on the OpenAI gym environment. The framework also provides connectors for multiple communication protocols including Open Platform Communication Unified Architecture and Modbus via Transmission Control Protocol. These facilities can be utilized to implement rolling horizon optimizations for factory systems easily and directly control devices in the factory with the optimization results. In this article, we present the framework and show some examples to prove the effectiveness of our approach.

Unrelated parallel machine scheduling with multiple time windows: An application to earth observation satellite scheduling

In this paper, we investigate a variant of the unrelated parallel machine scheduling problem with multiple time windows that is widely employed in the scheduling of earth observation satellites. Two mixed-integer linear programming formulations are proposed based on the concept of non-immediate precedence and the deep analysis of the relationship of time windows. To facilitate the problem solving, we develop a bidirectional rolling horizon preprocessing algorithm to reduce the problem size. Based on detailed overlapping analysis, more inequalities are obtained to tighten the formulations. Furthermore, the dominance among derived inequalities is analyzed, and only nondominated inequalities are appended to limit the size of the problem. The proposed formulation and algorithm can optimally solve instances of up to 800 jobs and 20 machines within 20 min. Moreover, to verify the practicality of our method, we also conducted numerous experiments on realistic instances of satellite scheduling. The experimental results prove that our algorithm is effective for obtaining optimal solutions and can be applied in practice.

Scenario-Based Stochastic Optimization for Energy and Flexibility Dispatch of a Microgrid

Energy storage is one of the most important components of microgrids with non-dispatchable generators and can offer both energy and flexibility services when the microgrid operates in grid-connected mode. This paper proposes a scenario-based stochastic optimization model that can be used to determine the energy and flexibility dispatch of a residential microgrid with solar and stationary battery systems. The objective of the model is to minimize the expected energy and peak power cost as well as the battery aging cost, while maximizing the expected revenue from flexibility. The formulated stochastic optimization problem is solved in rolling horizon with the uncertainty model being dynamically updated to consider the most recent forecast profiles for solar power and electricity demand. The benefits of the proposed approach were demonstrated by simulating the daily operation of a real building. The results showed that the estimated flexibility was successfully dispatched yielding an economic value of at least 7% of the operation cost of the building microgrid. The model can be used by flexibility providers to assess their flexibility and design a bidding strategy as well as by system operators to design incentives for flexibility providers.