Intra-day Scheduling Research Articles

The effect of cancelled appointments on outpatient clinic operations

This paper studies how appointment cancellations affect scheduling strategies in outpatient healthcare clinics. While cancellation rates in outpatient clinics have been reported to be as high as 27%, cancelled appointments are often ignored, or grouped with no-shows in healthcare scheduling models. We find that there exists a value of total demand that, when calculated over a scheduling horizon, marks the boundary between where cancellations hurt or help a clinic. We refer to that value as the switch point. Up to the switch point, clinics can achieve a greater reward when patients do not cancel. However, for values of expected total demand greater than the switch point, the clinic reward is reduced if more patients retain (do not cancel) appointments. To assist us in evaluating the switch point, we construct a mixed-integer nonlinear programming model to solve a multi-day outpatient scheduling problem. The model accounts for both inter-day (appointment day) and intra-day (appointment time slot) scheduling decisions, while balancing service benefits against service costs. We include probabilities of no-show and cancellation, which allows us to discuss how cancellations affect scheduling decisions through the switch point. The knowledge of the switch point allows a clinic to understand when appointment no-shows and cancellations negatively affect clinic service, and can assist the clinic in determining the number of patients for which it is committed to provide service, i.e., its panel size. In this paper, we discuss methodologies for calculating the switch point, and discuss its sensitivity to model parameters.

Multi-time Scale Optimal Power Flow Strategy for Medium-voltage DC Power Grid Considering Different Operation Modes

Direct current (DC) power grids based on flexible high-voltage DC technology have become a common solution of facilitating the large-scale integration of distributed energy resources (DERs) and the construction of advanced urban power grids. In this study, a typical topology analysis is performed for an advanced urban medium-voltage DC (MVDC) distribution network with DERs, including wind, photovoltaic, and electrical energy storage elements. Then, a multi-time scale optimal power flow (OPF) strategy is proposed for the MVDC network in different operation modes, including utility grid-connected and off-grid operation modes. In the utility grid-connected operation mode, the day-ahead optimization objective minimizes both the DER power curtailment and the network power loss. In addition, in the off-grid operation mode, the day-ahead optimization objective prioritizes the satisfaction of loads, and the DER power curtailment and the network power loss are minimized. A dynamic weighting method is employed to transform the multi-objective optimization problem into a quadratically constrained quadratic programming (QCQP) problem, which is solvable via standard methods. During intraday scheduling, the optimization objective gives priority to ensure minimum deviation between the actual and predicted values of the state of charge of the battery, and then seeks to minimize the DER power curtailment and the network power loss. Model predictive control (MPC) is used to correct deviations according to the results of ultra short-term load forecasting. Furthermore, an improved particle swarm optimization (PSO) algorithm is applied for global intraday optimization, which effectively increases the convergence rate to obtain solutions. MATLAB simulation results indicate that the proposed optimization strategy is effective and efficient.

Multi-time scale optimization scheduling of integrated energy system considering demand side response

As the physical carrier of the energy Internet, the integrated energy system has become the focus of current research. Considering the renewable energy and demand side load fluctuations, using the price type and the alternative demand side response characteristics, a day-ahead and intraday optimization scheduling model that takes into account the demand side response is established, in which the intraday, according to the difference of electricity, cold/heat and natural gas scheduling time, a three-layer rolling optimization scheduling model is proposed. The example analysis shows that this model can suppress the fluctuation of renewable energy and load in the day, improve the stability of the system, and further reduce the operating cost of the system.

Coordinated operation of multi-energy microgrid with flexible load

Aiming at the economy of microgrid operation and the uncertainty of renewable energy, a coordinated operation schedule of a multienergy microgrid based on a flexible load is proposed in this paper. Considering the difference in price and demand characteristics of multienergy, a multienergy interaction model based on a demand side response is established in day-ahead scheduling. In the intraday rolling optimization phase, according to the state of charge of battery and the demand of load, different battery function models are established at different time intervals, cooperating with the flexible load to obtain the optimal value of each unit's output. The main purpose of day-ahead scheduling and intraday scheduling is to achieve economic optimal scheduling and real-time scheduling is to guarantee the stability of the system. Finally, the simulation results verify the effectiveness of the proposed strategy. The proposed coordinated operation schedule of the multienergy microgrid achieves an integrated optimization for multienergy-type supply.

An integrated two-level distributed dispatch for interconnected microgrids considering unit commitment and transmission loss

Interconnected microgrids or a microgrid cluster (MGC) can enable mutual power support among microgrids and can improve the utilization of renewable energy sources. However, most of the distributed optimization focuses only on day-ahead or day-in dispatch, and few studies have attempted to study the integrated two-level distributed optimization. On the basis of the alternating direction method of multipliers (ADMM), this paper describes an efficient two-level distributed algorithm framework to solve multi-area ED problems in MGC considering unit commitment and transmission loss. Specifically, to overcome the non-convexity, a choice and comparison approach is introduced to cooperate with power-based ADMM for searching feasible binary variables in the first level, i.e., day-ahead dispatch. Voltage-based ADMM is adopted to obtain the relevant intra-day scheduling plan considering tie-line transmission loss among different areas in the second level. Moreover, a spinning reserve-based chance-constrained programming procedure is added to address uncertainty factors such as renewable energy fluctuations and load forecasting errors in isolated microgrids. Finally, a consensus-based cost allocation is proposed to fairly clear the expenses among microgrids. A case study with several networked microgrids is tested to demonstrate the effectiveness of the proposed approach.

Data‐driven multi‐time scale robust scheduling framework of hydrothermal power system considering cascade hydropower station and wind penetration

A data-driven multi-time scale robust scheduling model for a wind–hydro–thermal power system is presented in this study, according to the characteristic that wind power prediction accuracy increases with the decrease of the time scale. In day-ahead scheduling, a generation plan is formulated with the target of minimising the total operating cost, and a data-driven robust optimisation method based on the robust kernel density estimation (RKDE) is employed to deal with the uncertainty of wind power. That is, the distributional information of wind power is extracted by the RKDE from the big data, then the distributional information is incorporated into a data-driven uncertainty set, and finally, a robust optimisation model is formed. During the intraday scheduling stage, the objective is to minimise the total water spillage in cascade hydropower stations and the adjustment cost of thermal units, and the task is to readjust the outputs of units based on the base outputs obtained by the day-ahead scheduling, combined with the rolling forecast data of wind power and load. The real-time scheduling is aimed at satisfying the power balance with minimum power adjustment. Finally, a test system is carried out to verify the efficiency and practicability of the proposed framework.

Intraday Scheduling with Patient Re-Entries and Variability in Behaviours

Problem definition: We consider the intraday scheduling problem in a group of Orthopaedic clinics where the planner schedules appointment times given a sequence of appointments. We consider patient re-entry - where patients may be required to go for an X-ray examination, returning to the same doctor they have seen - and variability in patient behaviours such as walk-ins, lateness, and no-shows, which leads to inefficiency such as long patient waiting time and physician overtime. Academic/Practical relevance: In our dataset, 25% of the patients are required to go for X-ray examination. We also found significant variability in patient behaviours. Hence patient re-entry and variability in behaviours are common, but we found little in the literature that could handle them. Our model has potential wider applications, e.g. in machine scheduling and ride-sharing. Methodology: We formulate the problem as a two-stage optimization problem, where scheduling decisions are made in the first stage. Queue dynamics in the second stage is modeled under a P-Queue (Bandi and Loke, 2018) paradigm which minimizes a risk index, representing the chance of violating performance targets such as patient waiting times. The model reduces to a sequence of mixed-integer linear optimization problems. Results: Simulations shows that our model can achieve as much as 15% reduction on various metrics including patient waiting time and server overtime over the benchmark policy. Managerial insights: We present an optimization model that is easy to implement in practice and tractable to compute. Our simulation indicates that not accounting for patient re-entry or variability in patient behaviours will lead to sub-optimal policies, especially when X-ray rate is high and lateness has a large spread.

Hierarchical Distributed Robust Optimization for Demand Response Services

This paper presents a hierarchical robust distributed optimization for day-ahead and intra-day scheduling of the operation of flexible devices (electro-thermal heating units) within a city district. An aggregation service provider, which acts as an aggregator, performs this distributed optimization to maximize the flexibility potential of its customers to provide services to other actors, such as to a balance responsible party or the distribution system operator. Our optimization algorithm is based upon the alternating direction method of multipliers and prioritizes each individual customer and its own private objective. A model predictive control and robust design guarantee that uncertainty, e.g., electrical or thermal demand, is managed within the optimization process. The work includes a customer versus system level objective (aggregator) analysis under uncertainty.

Deep learning adaptive dynamic programming for real time energy management and control strategy of micro-grid

With the widespread application of distributed renewable energy in power systems, energy management problems in micro-grids have become increasingly significant. Offline or static optimization methods are frequently employed to solve the problems which are typically discrete and nonlinear. There are few online optimization methods and they are not only complex but also normally consider the distributed generations and loads in micro-grid as a whole. The outcome is that the online methods fail to reflect the composing characteristic of distributed multi-energy and the contribution made by developing renewable energy to reduce the consumption of traditional fossil energy. Moreover, results obtained by either the offline or the on-line methods can deviate to certain extents from the true values. This paper treats the management of distributed energy in micro-grids as an optimal control problem. Using the system control theory, a framework of real-time management of distributed energy in micro-grids is proposed. A deep learning adaptive dynamic programming is proposed for this framework. Due to the introduction of the concept of closed-loop feedback, the proposed management and control strategy is a real-time algorithm. Furthermore, the accuracy of managing and controlling the objective function can be improved. The gap of the flexible load after the optimization can be helpful in terms of guiding the flexible load consumers to change their habits of energy consumption, thereby reducing the coal-fired power generation and providing room for reducing carbon emissions. Because it is real-time, micro-grid operators can also realize intra-day scheduling, which can be done through combining this optimized management and control strategy with the mechanism of energy operating and managing. Moreover, some data sets of the real-time optimal control strategy are obtained in this paper. These intuitive and accurate data sets can be used to further optimize energy operating and managing of micro-grids, thereby realizing effective energy management for micro-grids. Finally, the real-time and effectiveness of the proposed management and control strategy are proved by the simulations. Some positive conclusions are drawn.

Optimal Dispatching of Active Distribution Networks Based on Load Equilibrium

This paper focuses on the optimal intraday scheduling of a distribution system that includes renewable energy (RE) generation, energy storage systems (ESSs), and thermostatically controlled loads (TCLs). This system also provides time-of-use pricing to customers. Unlike previous studies, this study attempts to examine how to optimize the allocation of electric energy and to improve the equilibrium of the load curve. Accordingly, we propose a concept of load equilibrium entropy to quantify the overall equilibrium of the load curve and reflect the allocation optimization of electric energy. Based on this entropy, we built a novel multi-objective optimal dispatching model to minimize the operational cost and maximize the load curve equilibrium. To aggregate TCLs into the optimization objective, we introduced the concept of a virtual power plant (VPP) and proposed a calculation method for VPP operating characteristics based on the equivalent thermal parameter model and the state-queue control method. The Particle Swarm Optimization algorithm was employed to solve the optimization problems. The simulation results illustrated that the proposed dispatching model can achieve cost reductions of system operations, peak load curtailment, and efficiency improvements, and also verified that the load equilibrium entropy can be used as a novel index of load characteristics.

Multi-time scale energy management of wind farms based on comprehensive evaluation technology

A novel energy management of wind farms is proposed in this paper. Firstly, a novel comprehensive evaluation system is proposed to quantify economic properties of each wind farm to make the energy management more economical and reasonable. Then, a combination of multi time-scale schedule method is proposed to develop a novel energy management. The day-ahead schedule optimizes unit commitment of thermal power generators. The intraday schedule is established to optimize power generation plan for all thermal power generating units, hydroelectric generating sets and wind power plants. At last, the power generation plan can be timely revised in the process of on-line schedule. The paper concludes with simulations conducted on a real provincial integrated energy system in northeast China. Simulation results have validated the proposed model and corresponding solving algorithms.

The value of stochastic programming in day-ahead and intra-day generation unit commitment

The recent expansion of renewable energy supplies has prompted the development of a variety of efficient stochastic optimization models and solution techniques for hydro-thermal scheduling. However, little has been published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intra-day unit commitment under wind uncertainty, we compare two-stage and multi-stage stochastic models to deterministic ones and quantify their added value. We present a modification of the WILMAR scenario generation technique designed to match the properties of the errors in our wind forecasts, and show that this is needed to make the stochastic approach worthwhile. Our evaluation is done in a rolling horizon fashion over the course of two years, using a 2020 central scheduling model based on the British power system, with transmission constraints and a detailed model of pump storage operation and system-wide reserve and response provision. We show that in day-ahead scheduling the stochastic approach saves 0.3% of generation costs compared to the best deterministic approach, but the savings are less in intra-day scheduling.

Multi-Period Generation Scheduling Optimization Model and its Application

Generation scheduling depended on accurate boundary conditions. Before the actual implementation, optimization result of day-ahead schedule was needed to be rolling corrected by two periods of intraday scheduling and real-time scheduling. It was key problem to establish optimization models which adapt to different dispatch period and coordinate different period generation scheduling for to achieving the best optimization results. This paper first discussed coordination mode of different period generation scheduling; Then, the mathematical models were established for day-ahead scheduling, intraday scheduling and real-time scheduling; Day-ahead scheduling and intraday scheduling including SCUC and SCED, intraday scheduling including SCED, and optimization goals were the minimum total cost of generation. In addition to boundary conditions, the difference between day-ahead scheduling and intraday scheduling model was that the optimal range from all units into AGC units; In real-time operation stage, the optimized objective was the minimum deviation between real-time schedule and intraday schedule for AGC units. Through practical application in a provincial, it proves that the proposed model is correct and effective.

Network flow models for intraday personnel scheduling problems

Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem.