Distributionally robust optimization for planning and scheduling under uncertainty

Integration of machine learning prediction and heuristic optimization for mask delivery in COVID-19

The novel coronavirus pneumonia (COVID-19) has created huge demands for medical masks that need to be delivered to a lot of demand points to protect citizens. The efficiency of delivery is critical to the prevention and control of the epidemic. However, the huge demands for masks and massive number of demand points scattered make the problem highly complex. Moreover, the actual demands are often obtained late, and hence the time duration for solution calculation and mask delivery is often very limited. Based on our practical experience of medical mask delivery in response to COVID-19 in China, we present a hybrid machine learning and heuristic optimization method, which uses a deep learning model to predict the demand of each region, schedules first-echelon vehicles to pre-distribute the predicted number of masks from depot(s) to regional facilities in advance, reassigns demand points among different regions to balance the deviations of predicted demands from actual demands, and finally routes second-echelon vehicles to efficiently deliver masks to the demand points in each region. For the subproblems of demand point reassignment and two-batch routing whose complexities are significantly lower, we propose variable neighborhood tabu search heuristics to efficiently solve them. Application of the proposed method in emergency mask delivery in three megacities in China during the peak of COVID-19 demonstrated its significant performance advantages over other methods without pre-distribution or reassignment. We also discuss key success factors and lessons learned to facilitate the extension of our method to a wider range of problems.

Distributionally robust optimization of a Canadian healthcare supply chain to enhance resilience during the COVID-19 pandemic

This paper presents a multi-period multi-objective distributionally robust optimization framework for enhancing the resilience of personal protective equipment (PPE) supply chains against disruptions caused by pandemics. The research is motivated by and addresses the supply chain challenges encountered by a Canadian provincial healthcare provider during the COVID-19 pandemic. Supply, price, and demand of PPE are the uncertain parameters. The ∊ -constraint method is implemented to generate efficient solutions along the trade-off between cost minimization and service level maximization. Decision makers can easily adjust model conservatism through the ambiguity set size parameter. Experiments investigate the effects of model conservatism on optimal procurement decisions such as the portion of the supply base dedicated to long-term fixed contracts. Other types of PPE sources considered by the model are one-time open-market purchases and federal emergency PPE stockpiles. The study recommends that during pandemics health care providers use distributionally robust optimization with the ambiguity set size falling in one of three intervals based on decision makers' relative preferences for average cost performance, worst-case cost performance, or cost variance. The study also highlights the importance of surveillance and early warning systems to allow supply chain decision makers to trigger contingency plans such as locking contracts, reinforcing logistical capacities and drawing from emergency stockpiles. These emergency stockpiles are shown to play efficient hedging functions in allowing healthcare supply chain decision makers to compensate variations in deliveries from contract and open-market suppliers.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches.

Distributionally robust optimization for fire station location under uncertainties

Emergency fire service (EFS) systems provide rescue operations for emergencies and accidents. If properly designed, they can decrease property loss and mortality. This paper proposes a distributionally robust model (DRM) for optimizing the location of fire stations, the number of fire trucks, and demand assignment for long term planning in an EFS system. This is achieved by minimizing the worst-case expected total cost, including fire station construction cost, purchase cost for fire trucks, transportation cost, and penalty cost for not providing adequate service. The ambiguity in demands and travel durations distributions are captured through moment information and mean absolute deviation. A cutting plane method is used to solve the problem. Due to fact that it is computationally intensive for larger problems, two approximate methods are introduced; one that uses linear decision rules (LDRs), and another that adopts three-point approximations of the distributions. The results show that the heuristic method is especially useful for solving large instances of DRM. Extensive numerical experiments are conducted to analyze the model’s performance with respect to different parameters. Finally, data obtained from Hefei (China) demonstrates the practical applicability and value of the model in designing an EFS system in a large metropolitan setting.

Probabilistic Optimization Techniques in Smart Power System

Uncertainties are the most significant challenges in the smart power system, necessitating the use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations. The topics of probabilistic optimization in smart power systems are covered in this review paper. In order to account for uncertainty in optimization processes, stochastic optimization is essential. Robust optimization is the most advanced approach to optimize a system under uncertainty, in which a deterministic, set-based uncertainty model is used instead of a stochastic one. The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving the constraints optimization problems, where finite probability get violated. This review paper discusses microgrid and home energy management, demand-side management, unit commitment, microgrid integration, and economic dispatch as examples of applications of these techniques in smart power systems. Probabilistic mathematical models of different scenarios, for which deterministic approaches have been used in the literature, are also presented. Future research directions in a variety of smart power system domains are also presented.

Big data analytics opportunities for applications in process engineering

Big data is an expression for massive data sets consisting of both structured and unstructured data that are particularly difficult to store, analyze and visualize. Big data analytics has the potential to help companies or organizations improve operations as well as disclose hidden patterns and secret correlations to make faster and intelligent decisions. This article provides useful information on this emerging and promising field for companies, industries, and researchers to gain a richer and deeper insight into advancements. Initially, an overview of big data content, key characteristics, and related topics are presented. The paper also highlights a systematic review of available big data techniques and analytics. The available big data analytics tools and platforms are categorized. Besides, this article discusses recent applications of big data in chemical industries to increase understanding and encourage its implementation in their engineering processes as much as possible. Finally, by emphasizing the adoption of big data analytics in various areas of process engineering, the aim is to provide a practical vision of big data.

Robust Single Machine Scheduling with Random Blocks in an Uncertain Environment

While scheduling problems in deterministic models are quite well investigated, the same problems in an uncertain environment require very often further exploration and examination. In the paper we consider a single machine tabu search method with block approach in an uncertain environment modeled by random variables with the normal distribution. We propose a modification to the tabu search method which improves the robustness of the obtained solutions. The conducted computational experiments show that the proposed improvement results in a much more robust solutions than the ones obtained in the classic block approach.

Data-Driven Robust Optimization for Steam Systems in Ethylene Plants under Uncertainty

In an ethylene plant, steam system provides shaft power to compressors and pumps and heats the process streams. Modeling and optimization of a steam system is a powerful tool to bring benefits and save energy for ethylene plants. However, the uncertainty of device efficiencies and the fluctuation of the process demands cause great difficulties to traditional mathematical programming methods, which could result in suboptimal or infeasible solution. The growing data-driven optimization approaches offer new techniques to eliminate uncertainty in the process system engineering community. A data-driven robust optimization (DDRO) methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. A hybrid model of extraction–exhausting steam turbine is developed, and its coefficients are considered as uncertain parameters. A deterministic mixed integer linear programming model of the steam system is formulated based on the model of the components to minimize the operating cost of the ethylene plant. The uncertain parameter set of the proposed model is derived from the historical data, and the Dirichlet process mixture model is employed to capture the features for the construction of the uncertainty set. In combination with the derived uncertainty set, a data-driven conic quadratic mixed-integer programming model is reformulated for the optimization of the steam system under uncertainty. An actual case study is utilized to validate the performance of the proposed DDRO method.

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.