Uncertain Arrival Times Research Articles

Robust optimization algorithm for integrated crane assignment and scheduling in slab yard with uncertain arrival time

A slab yard served as a key component of the iron and steel plant. Effective slab yard crane assignment and scheduling directly affect the overall efficiency of the steel production process. This work addresses an uncertain slab yard crane assignment and scheduling problem (SYCAS) with the fluctuating arrival time. A stochastic programming model is established to obtain a robust solution that minimises the completion time of slab groups under uncertainty. Due to its NP-hardness, we developed an improved column and cut generation method (IC&CG), which divides the problem into a relaxed master problem (RMP) and a slave problem (SP). A new initialisation strategy for obtaining high-quality solutions and an acceleration strategy for discarding irrelevant scenarios are proposed. We use small-size instances to compare the performance of IC&CG with CPLEX and a generalised column and cut generation method in both deterministic and uncertain environments to validate the effectiveness of the method. For large-size instances, a lower bound (LB) of the optimal objective function is proposed to show the effectiveness of IC&CG. Furthermore, we prove the robustness of the method by sensitive analysis.

Distributionally robust chance-constrained optimization for the integrated berth allocation and quay crane assignment problem

In this paper, we are the first to propose a distributionally robust chance-constrained (DRCC) optimization model for the integrated berth allocation and quay crane assignment problem (BACAP) in container terminals. In contrast to the classical deterministic BACAP model, we consider the arrival time to be uncertain due to the frequent arrival delays in ports. We then impose a chance constraint that the service time must start after the uncertain arrival time with a probability of at least 1−ϵ, where 1−ϵ represents the target service level in container terminals (ϵ represents the target risk tolerance of the port manager). Under the moment-based ambiguity set, we reformulate the DRCC model into a mixed integer semi-definite programming (MISDP) model. Additionally, we develop an efficient decomposition branch-and-bound algorithm to solve the MISDP model and obtain the exact solution. Fortunately, a special case of the DRCC model arises when the mean and covariance utilized in the ambiguity set are precise, allowing for the transformation of the DRCC model into a mixed integer programming (MIP) model. This conversion significantly reduces the complexity of the problem. Impressively, the solving time of the MISDP model with the decomposition branch-and-bound algorithm is comparable to that of the transformed MIP model. The numerical results show that our model can achieve a schedule with high service at low cost. Meanwhile, we have made an intriguing discovery that the correlation between the target risk tolerance and the actual service level can be depicted as a staircase function regardless of the datasets. This finding offers crucial insights for port management, enabling them to strike a balance between the cost and actual service level by determining an appropriate target service level.

WITHDRAWN: Non-work conserving dynamic scheduling of moldable gang tasks on multicore systems

In the realm of cyber-physical systems, the prevalence of multicore/many-core systems equipped with multiple or numerous cores is evident. To efficiently handle these systems, multicore task scheduling techniques are imperative. Particularly in recent cyber-physical systems, the dynamism of these systems renders task scheduling a complex endeavor. In this paper, we introduce a dynamic scheduling algorithm for moldable gang tasks on multicore systems. Our proposed algorithm determines when and with how many cores a task should be executed, especially for tasks with uncertain arrival times. In our experiments, we evaluate whether our algorithm reduces the makespan compared to the latest dynamic scheduling algorithms for moldable gang tasks. We demonstrate that, given a sufficient number of cores relative to the number of incoming tasks, our algorithm can reduce the makespan by approximately 10%.

Research on the scheduling method of ground resource under uncertain arrival time

We present a two-stage scheduling approach including proactive and reactive scheduling to solve the ground resource scheduling problem with uncertain arrival time. In the first stage, an integer programming model is constructed to minimize the delay and transfer costs. After solving this model, we obtain a baseline scheduling plan that considers the service arrival time uncertainty. In the second stage, the feasibility of the subsequent benchmark plan is evaluated based on the current state of the services and resources. The reactive scheduling model is enabled when trigger conditions are met. Moreover, an improved adaptive large neighborhood search is designed to solve the proactive scheduling model effectively. Real data from an international airport in South China is used as a test case to compare different scheduling strategies. The results show that it is difficult to handle the uncertainty of the problem with the benchmark plan that simply considered buffer time. Compared with rolling time-domain scheduling, the average transfer cost of the scheduling strategy proposed in this paper increased slightly, but the average service delay cost can be reduced significantly. Algorithm-wise, instances of different scales are designed to verify the effectiveness of the improved adaptive large neighborhood search algorithm. The efficiency of the algorithm scheme is better than that of the Gurobi solver scheme in medium to large-scale problems. Therefore, the forward and reactive strategies can better handle the uncertainty of airport ground protection services as they can simultaneously guide the allocation and utilization of airport ground protection resources.

Two-Stage Robust Programming Modeling for Continuous Berth Allocation with Uncertain Vessel Arrival Time

In order to mitigate the environmental pollution caused by sea freight, we focused on optimizing carbon emissions in container terminal operations. This paper establishes a mixed integer programming (MIP) model for a continuous berth allocation problem (CBAP) considering the tide time window. We aimed to minimize the total carbon emissions caused by the waiting time, consumption time and deviation to berth preference. In order to overcome the influence of an uncertain arrival time, the proposed MIP model was extended to mixed integer robust programming (MIRP) models, which applied a two-stage robust optimization (TSRO) approach to the optimal solution. We introduced an uncertainty set and scenarios to describe the uncertain arrival time. Due to the complexity of the resulting models, we proposed three particle swarm optimization (PSO) algorithms and made two novelties. The numerical experiment revealed that the robust models yielded a smaller variation in the objective function values, and the improved algorithms demonstrated a shorter solution time in solving the optimization problem. The results show the robustness of the constructed models and the efficiency of the proposed algorithms.

Scenario-Based Robust Remanufacturing Scheduling Problem Using Improved Biogeography-Based Optimization Algorithm

As a promising method for organizing remanufacturing production activities, remanufacturing scheduling has attracted increasing attention in recent years. However, extant studies have primarily focused on solving remanufacturing scheduling problems in a deterministic environment, while neglecting the impact of uncertainties on remanufacturing. Therefore, a new scenario-based robust remanufacturing scheduling problem was investigated in this study, and a robust optimization model for this problem was established. In the proposed model, a discrete scenario set is used to describe the uncertain arrival time and uncertain processing time of end-of-life products, and the variable start-up batch size constraint is considered to improve the practicality and flexibility of the model. To solve this model, an improved biogeography-based optimization algorithm with a new three-dimensional unequal-length representation scheme is proposed, in which, new migration and mutation operators, a local search strategy, and a new batch promotion mechanism are designed to improve the algorithmic performance. The results of the experiments demonstrate the feasibility of the proposed model and the superiority of the presented algorithm in solving the proposed model.

A bi-layer model for berth allocation problem based on proactive-reactive strategy

To reduce the impact of equipment failure, vessel arrival time delay and other unexpected factors, container terminal managers need to develop a more robust berth scheduling plan while considering the recovery costs. To deal with the berth allocation problem (BAP) with uncertain arrival time, a proactive-reactive hybrid strategy to deal with the impact of uncertainty is proposed. According to the characteristics of BAP and proactive-reactive strategy, a bi-layer programming model is constructed. A robust baseline plan with buffer time is generated in the first layer, and a recovered scheduling plan is generated in the second layer according to the actual arrival time. The decisions between the two layers of models affect each other. In addition, an Adaptive cross-entropy algorithm (ACEA) is designed to solve the first layer model. Different from the traditional cross-entropy algorithm (CEA), an adaptive search strategy is added to further search and optimize the neighborhood of the elite solutions. Furthermore, heuristic adjustment strategies (HAS) are designed to deal with the second layer. The computational results demonstrate that the bi-layer model proposed in this paper can better balance the baseline schedule cost and the recovered schedule cost. Numerical experiments are carried out to assess the effectiveness of the proposed model and the efficiency of the proposed algorithms.

Design and Implementation of Renewable Based EV Charging Station

A significant transformation occurs globally as transportation switches from fossil fuel-powered to zero emission E-Vehicles. The transition to the electric vehicle requires an infrastructure of E-Vehicle charging stations everywhere. The rapid adoption of electric vehicles (EVs) calls for the widespread installation of EV charging stations. To maximize the profitability of charging stations, intelligent controllers that provide both charging and electric grid services are in great need. However, it is challenging to determine the optimal charging schedule due to the uncertain arrival time and charging demands of EVs. In this paper, we propose solar energy based three phase voltage source inverter fed grid. In this research solar energy is maintain a consistent output voltage to the load or grid. In this research PV system with a NeuroFuzzy-based MPPT algorithm and a Switched Z source Boost converte .

Learning to Operate an Electric Vehicle Charging Station Considering Vehicle-Grid Integration

The rapid adoption of electric vehicles (EVs) calls for the widespread installation of EV charging stations. To maximize the profitability of charging stations, intelligent controllers that provide both charging and electric grid services are in great need. However, it is challenging to determine the optimal charging schedule due to the uncertain arrival time and charging demands of EVs. In this paper, we propose a novel centralized allocation and decentralized execution (CADE) reinforcement learning (RL) framework to maximize the charging station’s profit. In the centralized allocation process, EVs are allocated to either the waiting or charging spots. In the decentralized execution process, each charger makes its own charging/discharging decision while learning the action-value functions from a shared replay memory. This CADE framework significantly improves the scalability and sample efficiency of the RL algorithm. Numerical results show that the proposed CADE framework is both computationally efficient and scalable, and significantly outperforms the baseline model predictive control (MPC). We also provide an in-depth analysis of the learned action-value function to explain the inner working of the reinforcement learning agent.

The impacts of longitudinal separation, efficiency loss, and cruise speed adjustment in robust terminal traffic flow problem under uncertainty

ABSTRACT Minimization of approaching time and maximization of the utilization of air route and airport resources are the two ultimate goals of air traffic control. This research considers arrival sequence and the uncertain arrival times at entry waypoints of flights and investigates the impact of air traffic controller specific parameters in the model. The two-stage optimization framework will first determine a deterministic schedule and optimize the approaching time while considering additional longitudinal separation, efficiency loss from deterministic schedule, and cruise speed adjustment in the second-stage optimization model via sample average approximation. The numerical experiments suggested an efficiency loss of 20%, which can absorb the empirical probabilistic lateness at entry waypoints with the real-world data. The proposed method could determine the estimated average delay time at runways with different settings of additional buffer for longitudinal separation and trade-off parameters between the estimated average delay time and estimated penalty cost of cruise speed adjustment.

Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach

This paper considers a single‐stage make‐to‐stock production–inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost‐minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unit‐tracking/decomposition approach, taking into account the possibility of order‐crossing, which is new to the literature and relevant to other planning problems. The extended unit‐tracking/decomposition approach allows us to determine the optimal base‐stock level and to formulate the exact and an approximate expression of the per‐period cost of a base‐stock policy. The same approach is also used to develop a state‐dependent ordering policy. The numerical study reveals that our state‐dependent policy can reduce inventory‐related costs compared to the base‐stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory‐related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality.

Rolling horizon based robust optimization method of quayside operations in maritime container ports

The quayside operation is a complex system in maritime shipping, which requires an intelligent scheduling approach to cope with complex situations. This paper investigates joint berth allocation and quay crane assignment problem considering uncertain arrival time of vessels and operation efficiency of quay cranes. A nominal model of this problem considering vessel priorities is presented firstly. Meanwhile, a multi-objective robust model is built based on the idea of robust optimization. Besides, control parameters are introduced into the model for levels of uncertainties. Then, an intelligent search algorithm integrated with rolling horizon is designed for solving the problem. Finally, the model and proposed approach are validated by computational results with different instance sizes. Results point out that intelligent algorithm is superior on solution quality and solving time for large-scale examples. Besides, vessel delays show obvious impact on the scheme than uncertain quay crane productivity, especially under the medium uncertainty level.

Matheuristics for Waiting Time Minimization for Trailers with Uncertain Arrival Times

Matheuristics for Waiting Time Minimization for Trailers with Uncertain Arrival Times

A Data-Driven Approach for Baggage Handling Operations at Airports

Before each flight departs, baggage has to be loaded into containers, which are then forwarded to the airplane. Planning the loading process consists of setting the start times for the loading process and depletion of the baggage storage as well as assigning handling facilities and workers. Flight delays and uncertain arrival times of passengers at the check-in counters require plans that are adjusted dynamically every few minutes and, hence, an efficient planning procedure. We propose a model formulation and a solution procedure that utilize historical flight data to generate reliable plans in a rolling planning fashion, allowing problem parameters to be updated in each reoptimization. To increase the tractability of the problem, we employ a column generation–based heuristic in which new schedules and work profiles are generated in subproblems, which are solved as dynamic programs. In a computational study, we demonstrate the robust performance of the proposed procedure based on real-world data from a major European airport. The results show that (i) the procedure outperforms both a constructive heuristic that mimics human decision making and a meta heuristic (tabu search) and (ii) being able to dynamically (re)allocate baggage handlers leads to improved solutions with considerably fewer left bags.

Research on Time Inventory Control Model of 3PL Warehousing of Furniture Products under Uncertain Lead Time

3PL warehousing has become an important link between suppliers and retailers in the cross-border e-commerce supply chain. During the COVID-19, product shortage became one of the biggest concerns with the overseas 3PL warehouse integration using ocean shipment. Therefore it has become the focus of the cross-border e-commerce industry and research. Due to the large volume and low-value density, furniture products are generally replenished by ocean transportation. The shortage of such products can be caused by ocean transportation which brings uncertain arrival times and difficult inventory control. This paper, considering the uncertain lead time, uncertain demand, and 3PL warehouse free storage period, introduces a replenishment inventory control model. Utilizing the mathematical dynamic simulation model, it takes refrigerators as a product example into the calculations to prove the validity and accuracy. The experimental results demonstrate that the warehouse free-storage period is a vital factor affecting inventory control for cross-border e-commerce enterprises. When the lead time is uncertain, it is the most optimized solution to use the maximum lead time to determine the maximum inventory.

An M/M/c queue model for vehicle routing problem in multi-door cross-docking environments

Cross-docking is a strategy to facilitate a persistent process from suppliers to the consumer points, without long-term storage of products at a distribution warehouse. Products are collected from various origins by inbound trucks, unloaded to the cross-dock, reconsolidated with other products, and finally loaded onto outbound trucks within the same or next day. Because of the limited number of dock-doors as the main resources and the uncertain arrival time of trucks at the cross-dock, queue problems in such environments are unavoidable. This study considers a vehicle routing problem (VRP) for a multi-door cross-docking system with a queuing approach. A real application of the proposed model can be found in congestion conditions at the cross-docking yard, when the queuing time of the vehicles (i.e., the queuing delay) may reducethe quality of service. Moreover, in some cases, improper queue management at a facility such as a cross-dock may incur an economic cost associated with the waiting time in the queue. In this study, we focus on the receiving doors of a cross-dock and assume that the rate of truck arrivals at the cross-dock is a random variable. Moreover, the cross-dock is not able to provide service to all vehicles simultaneously; it has some limitations such as capacity constraints and service time restrictions. Thus, an M/M/c queuing formulation is proposed to model this cross-docking environment, in which the vehicles’ dispatch plan for starting the pickup process would also be determined. In the proposed multi-channel queuing system, the arrival flow of trucks to the cross-docking terminal can be deemed as a Poisson process, resulting in a nonlinear mathematical formulation to optimize the problem. The model is then linearized. To handle its computational complexity, we develop a new Genetic Algorithm (GA) to obtain near-optimal solutions to the problem and compare them with those of the optimization software GAMS. Then, a sensitivity analysis is done on different parameters of the model, and their effect on transportation cost and waiting cost of vehicles in the queue is investigated. The results show that considering a queuing approach in this problem, even for a small-scale problem derived from a real case study, can improve the average waiting time of trucks in the queue considerably compared with the situation in which all parameters are assumed deterministic.

Stochastic Programming for Liner Ship Routing and Scheduling under Uncertain Sea Ice Conditions

It is anticipated that in the foreseeable future the Northern Sea Route (NSR) will be able to serve commercial shipping as an alternative transportation shortcut between East Asia and Europe, especially in the summer season. The sailing time, however, is heavily subject to the variation of sea ice conditions along this route. Any participating shipping company must consider how to mitigate the ill effects on itinerary planning caused by sailing time and cost uncertainty. Finding a good trade-off between the benefit from a tight schedule and the risk caused by an unexpected delay is a key element in relevant routing and scheduling decisions, and may be beyond the reach of traditional deterministic planning models. With the aim of maximizing profit over all possible shipping environment scenarios, this article proposes a two-stage stochastic nonlinear integer programming model for liner ship routing and scheduling with uncertain shipping time and cost, the nonlinearity of which arises from the coexistence of schedule-sensitive shipping demand and uncertain arrival time variables in the objective function. The model is converted into an equivalent linear integer programming counterpart by introducing a set of nominal delay variables, and Benders decomposition is applied to solve the linearized problem. Numerical experiments and sensitivity analyses are conducted to validate the efficacy and effectiveness of the model, the results of which suggest several managerial insights that can be used to guide liner ship route and schedule planning under uncertain shipping conditions.

An exact robust approach for the integrated berth allocation and quay crane scheduling problem under uncertain arrival times

We consider an integrated berth allocation and quay crane assignment and scheduling problem where the arrival times of the vessels may be affected by uncertainty. The problem is modelled as a two-stage robust mixed integer program where the berth allocation decisions are taken before the exact arrival times are known, and the crane assignment and scheduling operations are adjusted to the arrival times. To solve the robust two-stage model, we follow a decomposition algorithm that decomposes the problem into a master problem and a separation problem. A new scenario reduction procedure for solving the separation problem is proposed as well as a warm start technique for reducing the number of iterations performed by the decomposition algorithm. To scale the proposed decomposition algorithm for large size instances, it is combined with a rolling horizon heuristic.The efficiency and effectiveness of the proposed algorithms are demonstrated through extensive computational experiments carried out on randomly generated instances with both homogeneous and heterogeneous cranes as well as on instances from the literature.

Airline ground operations: Optimal schedule recovery with uncertain arrival times

Airline operations are subject to a number of stochastic influences which result into variable ground and block times for same flights on different days. Our research explores how airline operations control centers may benefit from an integrated decision support system for schedule recovery during aircraft ground operations. In this paper, we study the sensitivity of an optimal set of schedule recovery options towards uncertain arrival times. The calculation of recovery options is based upon an integrated and iterative scheduling and optimization algorithm, which incorporates uncertainties for arrival flights as a function of a given look-ahead time. Potential recovery options include stand re-allocation, quick-turnaround, quick passenger transfer, waiting for transfer passengers, cancellation of passenger or crew connections, and arrival prioritization. Within a case study setting at Frankfurt Airport, 20 aircraft turnarounds are analysed during a morning peak with their respective estimated arrival times (including potential arrival delays). The analysis of simulation results reveals an almost identical set of selected recovery options under high uncertainty circumstances and from post-operational point-of-view, which indicates high solution stability.

Scheduling ships with uncertain arrival times through the Kiel Canal

The Kiel Canal is a two-way waterway that connects the Baltic Sea and the North Sea. The canal consists of an alternating sequence of narrow transit segments and wider siding segments. This calls for solving a ship scheduling problem to decide which ships have to wait in sidings to let opposing traffic pass through such that the total traversing time of all ships is minimized. This paper extends previous studies on scheduling ships through the Kiel Canal by considering that the arrival times of the ships at the entrance to the canal are subject to uncertainty. This is a major challenge in the planning as it gives frequent need of replanning to make the schedules feasible. We propose a mathematical formulation for the problem to mitigate the negative effects of the uncertainty. This formulation incorporates time-corridors, so that the schedule will still be valid as long as the ships arrive within their given time-corridors. To solve real-sized instances of the problem, we adapt a matheuristic that adds violated constraints iteratively to the problem. The matheuristic was tested within a rolling horizon simulation framework to study the effect of arrival time uncertainty. We show by experiment that solutions of the matheuristic for different time-corridor widths can be used to identify a suitable corridor width that trades off the average traversing time of ships and the number of reschedules required in the planning. A simple myopic heuristic, reflecting the current scheduling practice, was used to generate benchmark results, and tests on real data showed that the matheuristic provides solutions with significantly less need of replanning, while at the same time keeping the total traversing times for the ships short. We also provide simulations to gain insight about the effect on the ships’ average traversing time from upgrading the narrow transit segments.