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A Two-Stage stochastic Integer programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

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OPERATIONS RESEARCH 2015年第6期63卷 1431-1451页

作者： Kim, Kibaek Mehrotra, Sanjay Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We study the problem of integrated staffing and scheduling under demand uncertainty. This problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules. The wait-and-see decision is to adjust these schedules at a time closer to the actual date of demand realization. We show that the mixed-integer rounding inequalities for the second-stage problem convexify the recourse function. As a result, we present a tight formulation that describes the convex hull of feasible solutions in the second stage. We develop a modified multicut approach in an integer L-shaped algorithm with a prioritized branching strategy. We generate 20 instances (each with more than 1.3 million integer and 4 billion continuous variables) of the staffing and scheduling problem using 3.5 years of patient volume data from Northwestern Memorial Hospital. Computational results show that the efficiency gained from the convexification of the recourse function is further enhanced by our modifications to the L-shaped method. The results also show that compared with a deterministic model, the two-stage stochastic model leads to a significant cost savings. The cost savings increase with mean absolute percentage errors in the patient volume forecast.

关键词： stochastic programming hospitals personnel scheduling

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Two-stage chance-constrained programming based on Gaussian mixture model and piecewise linear decision rule for refinery optimization

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COMPUTERS & CHEMICAL ENGINEERING 2024年 184卷

作者： Yang, Yu Calif State Univ Long Beach Dept Chem Engn Long Beach CA 90840 USA

The two -stage chance -constrained program (CCP) is studied for a refinery optimization problem. In stage -I, the refinery decision -makers determine the type and quantity of crude oil procurement under operational uncertainties to maximize the expected profit under all possibilities. In stage -II, process unit flowrates are adjusted based on the realized uncertainties and available crude oil, while introducing probabilistic constraints to manage the off -spec risk. To solve such a two -stage optimization problem, we propose a novel approach using Gaussian mixture model (GMM) to characterize uncertainties, and piecewise linear decision rule for stage -II operations. Comparing to the conventional scenario -based mixed -integer linear program (MILP), our new approach offers three advantages. First, it leverages a well -developed global optimization scheme for joint CCP to avoid scenario generation and potential bias. Second, the data -driven GMM enables CCP to handle uncertainties with general distributions. Third, the stage -II variables are parameterized via Gaussian component induced piecewise linear decision rule to strike an excellent trade-off between optimality and computational time. A simplified refinery plant, consisting of distillation, cracker, reformer, isomerization, and desulfurization units, is used as a test bed to demonstrate the superiority of the proposed optimization method in solution time, probabilistic feasibility, and optimality over the large-scale scenario -based MILP.

关键词： stochastic programming Chance-constrained optimization Gaussian mixture model Piecewise linear decision rule

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A Literature Review of stochastic programming and Unit Commitment

A Literature Review of Stochastic Programming and Unit Commi...

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The 7th Asia-Pacific Power and Energy Engineering Conference (APPEEC 2015)

作者： Hang Dai Ni Zhang Wencong Su Department of Electrical and Computer Engineering University of Michigan

The study of unit commitment(UC) aims to find reasonable schedules for generators to optimize power systems' operation. Many papers have been published that solve UC through different me-thods. Articles that systematically summarize UC problems' progress in order to update research-ers interested in this field are needed. Because of its promising performance, stochastic pro-gramming(SP) has become increasingly researched. Most papers, however, present SP's UC solv-ing approaches differently, which masks their relationships and makes it hard for new research-ers to quickly obtain a general idea. Therefore, this paper tries to give a structured bibliographic survey of SP's applications in UC problems.

关键词： Unit Commitment stochastic programming Review

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stochastic dynamic programming approach for proactive replacement of power cables

Stochastic dynamic programming approach for proactive replac...

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CIRED Workshop 2016

作者： Swati Sachan Chengke Zhou Geraint Bevan Babakalli Alkali Glasgow Caledonian University Glasgow Glasgow GB Glasgow Caledonian University - UK

ISBN: (纸本)9781510834675

The purpose of this paper is to present a stochastic dynamic programming based model to solve the optimization problem of cable replacement. The proposed methodology can be implemented on cables with known failure distribution and insulation degradation level; the methodology to estimate both of the elements is based on previously developed Non-homogenous Poisson Process model (NHPP) and stochastic degradation model, respectively. The model gives the sequence of decisions for each year of the planning horizon such that it optimizes the overall cost and improves the reliability by lowering the frequency of unplanned outage. The model was tested on an unjacketed XLPE cable.

关键词： XLPE insulation dynamic programming power cable insulation stochastic processes stochastic programming Power cables stochastic programming dynamic programming cable degradation model stochastic models stochastic Processes Markov chain Power cable insulation stochastic XLPE insulation Planning Horizon

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Medium-Term Hydrothermal Scheduling of the Infiernillo Reservoir Using stochastic Dual Dynamic programming (SDDP): A Case Study in Mexico

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ENERGIES 2023年第17期16卷 6288页

作者： Marin Cruz, Ignacio Badaoui, Mohamed Mota Palomino, Ricardo Inst Politecn Nacl Escuela Super Ingn Mecan & Elect Ave Luis Enrique Erro S-N Mexico City 07738 DF Mexico

This article aims to obtain and evaluate medium-term operating policies for the hydrothermal scheduling problem by using the stochastic dual dynamic programming (SDDP) approach. To this end, to feed the mathematical model and build the probability distribution functions that best fit each month of the actual inflow volume, monthly inflow data recorded from 1938 to 2018 for the Infiernillo reservoir located in Mexico were employed. Moreover, we simulated inflow volume scenarios using the Monte Carlo method for each month of a one-year planning period. The SDDP approach to solving the optimization problem consisted of the simulation of one forward scenario per iteration and the stabilization of the total operating cost as a convergence criterion, which results in an operating policy. We then assessed its quality by estimating the one-sided optimality gap. It is worth mentioning that the best operation policy required scenario trees of up to 17,000 inflow realizations per stage. Additionally, to study the evolution of the expected value along the planning horizon of the main variables involved in the medium-term hydrothermal scheduling problem, we simulated the best operation policy over 10,000 inflow scenarios. Finally, to show the practical value of the proposed approach, we report its computational complexity.

关键词： stochastic programming medium-term hydrothermal scheduling stochastic dual dynamic programming Infiernillo reservoir

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A mathematical programming based decision support system for waste to resource market trading

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JOURNAL OF CLEANER PRODUCTION 2024年 437卷

作者： Mah, Angel Xin Yee Ng, Tsan Sheng Wang, Bo Tiong, Yong Wei Lee, Jonathan T. E. Wang, Chi-Hwa Natl Univ Singapore NUS Environm Res Inst Singapore City 138602 Singapore Campus Res Excellence & Technol Enterprise CREATE Energy & Environm Sustainabil Solut Megac E2S2 Singapore City 138602 Singapore Natl Univ Singapore Dept Ind Syst Engn & Management Singapore City 117576 Singapore Natl Univ Singapore Dept Chem & Biomol Engn Singapore City 117585 Singapore Natl Univ Singapore Energy Studies Inst Singapore City 119620 Singapore

In a linear economy, consumers typically dispose end-of-life products which are eventually incinerated or landfilled. Digital platforms could unlock rich waste reutilization opportunities and economic benefits by connecting the waste producers with potential waste buyers in online marketplaces. While previous studies mostly focus on input-output matching, this study proposes a decision support system that can be incorporated to an online marketplace to optimize the waste trading based on economic considerations. Moreover, the decision support system could facilitate higher level decisions such as capacity planning and incentive design. Based on a case study on Singapore's organic waste streams, the waste trading platform presents economic benefits for agents that sell their waste. Additionally, enforcing waste reutilization targets would require relevant policy support in terms of incentives or levies, where the levies can be implemented as co-payment rate for the agents. For instance, results showed that when the food waste reutilization target is set as 6 t/d, increasing the copayment rate from 0 to 20% allows the waste trading network to be self-sustaining without external funding. Finally, sensitivity analyses show that collecting more waste records in the database helps in optimizing the investment decisions, preferably when the number of records exceeds 64.

关键词： Circular economy Industrial symbiosis Mathematical optimization Waste to resource Digital platform stochastic programming

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An Exponential Cone programming Approach for Managing Electric Vehicle Charging

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OPERATIONS RESEARCH 2024年第5期72卷 iii-vii, 1751-2261, C2-C3页

作者： Chen, Li He, Long Zhou, Yangfang (Helen) Natl Univ Singapore Inst Operat Res & Analyt Singapore 117602 Singapore Univ Sydney Discipline Business Analyt Sydney NSW 2006 Australia George Washington Univ Sch Business Washington DC 20052 USA Singapore Management Univ Lee Kong Chian Sch Business Singapore 178899 Singapore

To support the rapid growth in global electric vehicle adoption, public charging of electric vehicles is crucial. We study the problem of an electric vehicle charging service provider, which faces (1) stochastic arrival of customers with distinctive arrival/departure times and energy requirements and (2) a total electricity cost including demand charges, which are costs related to the highest per-period electricity used in a finite horizon. We formulate its problem of scheduling vehicle charging to minimize the expected total cost as a stochastic program (SP). As this SP is large-scale, we solve it using exponential cone program (ECP) approximations. For the SP with unlimited chargers, we derive an ECP as an upper bound and characterize the bound on the gap between their theoretical performances. For the SP with limited chargers, we then extend this ECP by also leveraging the idea from distributionally robust optimization (DRO) of using an entropic dominance ambiguity set: Instead of using DRO to mitigate distributional ambiguity, we use it to derive an ECP as a tractable upper bound of the SP. We benchmark our ECP approach with sample average approximation (SAA) and a DRO approach using a semidefinite program (SDP) on numerical instances calibrated to real data. As our numerical instances are large-scale, we find that although SDP cannot be solved, ECP scales well and runs efficiently (about 50 times faster than SAA) and consequently results in a lower mean total cost than SAA. We then show that our ECP continues to perform well considering practical implementation issues, including a data-driven setting and an adaptive charging environment. We finally extend our ECP approaches (for both the uncapacitated and capacitated cases) to include the pricing decision and propose an alternating optimization algorithm, which performs better than SAA on our numerical instances. Our method of constructing ECPs can be potentially applicable to approximate more general two-stage

关键词： stochastic programming exponential cone programming electric vehicle demand charge robust optimization

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Dynamic capacity planning of hospital resources under COVID-19 uncertainty using approximate dynamic programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2024年第1期75卷 13-25页

作者： Gokalp, Elvan Cakir, M. Selim Satis, Hasan Univ Bath Bath England Univ Bristol Bristol England Gazi Univ Fac Med Ankara Turkiye

COVID-19 pandemic has resulted in an inflow of patients into the hospitals and overcrowding of healthcare resources. Healthcare managers increased the capacities reactively by utilizing expensive but quick methods. Instead of this reactive capacity expansion approach, we propose a proactive approach considering different realizations of demand uncertainties in the future due to COVID-19. For this purpose, a stochastic and dynamic model is developed to find the right amount of capacity increase in the most critical hospital resources. Due to the problem size, the model is solved with Approximate Dynamic programming. Based on the data collected in a large tertiary hospital in Turkey, the experiments show that ADP performs better than a benchmark myopic heuristic. Finally, sensitivity analysis is performed to explore the impact of different epidemic dynamics and cost parameters on the results.

关键词： stochastic programming dynamic programming health services simulation

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Joint optimal congestion control and power allocation for MCMR mesh networks based on stochastic programming

Joint optimal congestion control and power allocation for MC...

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11th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM 2015)

作者： Kewei Li Xiaoqian Li Yunfei Peng Bo Jiang Wuhan Second Ship Design and Research Institute Hubei China

ISBN: (纸本)9781510821279

A stochastic model for joint optimal congestion control and power allocation in multi-channel multi-radio wireless mesh networks is proposed. The design problem characterizes the stochastic traffic of the network data flows and the capacity of radio channels in multi-channel multi-radio wireless mesh networks as some random variables. The corresponding design problem is formulated as the stochastic network utility maximization problem subject to some stochastic constrains, which is a chance constrained programming. The genetic algorithm is used to solve this stochastic maximization problem. The simulation is conducted in the Hyacinth network, and the result shows the quantitative relationship between the network performance and the confidence level.

关键词： Congestion Control Cross-Layer Genetic Algorithm stochastic programming Wireless Mesh Network Wireless mesh networks stochastic models Genetic Algorithm (GA) power splitting stochastic programming design problems Mesh networks wireless channels

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Dispersion Sensitive Optimal Control: A Conditional Value-at-Risk-Based Tail Flattening Approach via Sequential Convex programming

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2024年第6期32卷 2468-2475页

作者： Echigo, Kazuya Sheridan, Oliver Buckner, Samuel Acikmese, Behcet Univ Washington William E Boeing Dept Aeronaut & Astronaut Seattle WA 98195 USA

In this brief, we propose a sequential convex programming (SCP) framework for minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination-an important property in high-risk contexts such as spacecraft landing. Our proposed approach seeks to minimize the conditional value-at-risk (CVaR) of the dispersion, thereby shifting the probability distribution away from the tails. This approach provides an optimization framework that is not overly conservative and can accurately capture more information about true distribution, compared with methods which consider only the expected value, or robust optimization methods. The main contribution of this brief is to present an approach that: 1) establishes an optimization problem with CVaR dispersion cost 2) approximated with one of the two novel surrogates which is then 3) solved using an efficient SCP algorithm. In 2), two approximation methods, a sampling approximation (SA) and a symmetric polytopic approximation (SPA), are introduced for transforming the stochastic objective function into a deterministic form. The accuracy of the SA increases with sample size at the cost of problem size and computation time. To overcome this, we introduce the SPA, which avoids sampling by using an alternative approximation and thus offers significant computational benefits. Monte Carlo simulations indicate that our proposed approaches minimize the CVaR of the dispersion successfully.

关键词： Dispersion Cost function Optimization Optimal control Gaussian distribution Tail Uncertainty Convex programming nonlinear programming stochastic programming

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