考虑多重覆盖的应急设施多级协同布局鲁棒优化

应急设施的合理布局是灾后实现物资高效、公平和稳定供应的重要保障.针对突发自然灾害的不确定性,研究基于多重覆盖的应急设施多级协同布局鲁棒优化问题.首先,提出多级设施选址下的多重覆盖水平函数,以最小覆盖水平和期望总成本最优为目标,建立应急设施多级协同选址双目标优化模型;其次,应用基数不确定集和p-鲁棒方法构建两类鲁棒优化模型,分别研究场景内不确定需求和随机场景对设施布局的影响;最后,以湖南省救灾备荒种子储备库选址为例进行实证分析,验证所提出优化模型的有效性.研究结果表明:多级协同布局相比传统布局方案更具优势;鲁棒优化模型能够有效应对不确定情形和随机场景下的物资需求;决策者的风险偏好程度和预算水平对设施协同布局有重要影响,需对二者进行综合权衡.     

需求不确定的设施选址与多阶段生产鲁棒模型研究

选址决策是长期的战略性问题,在选址问题中考虑不确定性因素至关重要。假设需求取值于有界的对称区间,在设施选址与多阶段生产问题中提出一种新的鲁棒性方法,通过调节不确定预算,来权衡解的鲁棒性与系统成本之间的关系。该鲁棒性问题不仅能够转化成线性规划,而且可以计算出设施的最低服务水平。最后,通过随机生成数值算例,得出不同鲁棒性水平下拓扑结构截然不同的设施网络,并分析了服务水平与成本之间的权衡关系,同时对需求的不确定水平作了敏感性分析。     

Incorporating uncertainty in optimal decision making: Integrating mixed integer programming and simulation to solve combinatorial problems

We introduce a novel methodology that integrates optimization and simulation techniques to obtain estimated global optimal solutions to combinatorial problems with uncertainty such as those of facility location, facility layout, and scheduling. We develop a generalized mixed integer programming (MIP) formulation that allows iterative interaction with a simulation model by taking into account the impact of uncertainty on the objective function value of previous solutions. Our approach is generalized, efficient, incorporates the impact of uncertainty of system parameters on performance and can easily be incorporated into a variety of applications. For illustration, we apply this new solution methodology to the NP-hard multi-period multi-product facility location problem (MPP-FLP). Our results show that, for this problem, our iterative procedure yields up to 9.4% improvement in facility location-related costs over deterministic optimization and that these cost savings increase as the variability in demand and supply uncertainty are increased.     

A continuous approach to considering uncertainty in facility design

This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs on a continuous scale by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm meta-heuristic with a flexible bay construct of the departments and total facility area. It is shown that depending on the attitude of the decision-maker towards uncertainty, the optimal design can change significantly. Furthermore, designs can be optimized directly for robustness over a range of uncertainty that is pre-specified by the user. This formulation offers a computationally tractable and intuitively appealing alternative to previous stochastic layout formulations that are based on discrete scenario probabilities.     

Hydroelastic optimization of a keel fin of a sailing boat: a multidisciplinary robust formulation for ship design

The paper presents a formulation for multidisciplinary design optimization of vessels, subject to uncertain operating conditions. The formulation couples the multidisciplinary design analysis with the Bayesian approach to decision problems affected by uncertainty. In the present context, the design specifications are no longer given in terms of a single operating design point, but in terms of probability density function of the operating scenario. The optimal configuration is that which maximizes the performance expectation over the uncertain parameters variation. In this sense, the optimal solution is “robust” within the stochastic scenario assumed. Theoretical and numerical issues are addressed and numerical results in the hydroelastic optimization of a keel fin of a sailing yacht are presented.     

Robust supply chain design under uncertain demand in agile manufacturing

This paper considers a supply chain design problem for a new market opportunity with uncertain demand in an agile manufacturing setting. We consider the integrated optimization of logistics and production costs associated with the supply chain members. These problems routinely occur in a wide variety of industries including semiconductor manufacturing, multi-tier automotive supply chains, and consumer appliances to name a few. There are two types of decision variables: binary variables for selection of companies to form the supply chain and continuous variables associated with production planning. A scenario approach is used to handle the uncertainty of demand. The formulation is a robust optimization model with three components in the objective function: expected total costs, cost variability due to demand uncertainty, and expected penalty for demand unmet at the end of the planning horizon. The increase of computational time with the numbers of echelons and members per echelon necessitates a heuristic. A heuristic based on a k-shortest path algorithm is developed by using a surrogate distance to denote the effectiveness of each member in the supply chain. The heuristic can find an optimal solution very quickly in some small- and medium-size cases. For large problems, a “good” solution with a small gap relative to our lower bound is obtained in a short computational time.     

A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty

A multi-period stochastic model and an algorithmic approach to location of prison facilities under uncertainty are presented and applied to the Chilean prison system. The problem consists of finding locations and sizes of a preset number of new jails and determining where and when to increase the capacity of both new and existing facilities over a time horizon, while minimizing the expected costs of the prison system. Constraints include maximum inmate transfer distances, upper and lower bounds for facility capacities, and scheduling of facility openings and expansion, among others. The uncertainty lies in the future demand for capacity, because of the long time horizon under study and because of the changes in criminal laws, which could strongly modify the historical tendencies of penal population growth. Uncertainty comes from the effects of penal reform in the capacity demand. It is represented in the model through probabilistic scenarios, and the large-scale model is solved via a heuristic mixture of branch-and-fix coordination and branch-and-bound schemes to satisfy the constraints in all scenarios, the so-called branch-and-cluster coordination scheme. We discuss computational experience and compare the results obtained for the minimum expected cost and average scenario strategies. Our results demonstrate that the minimum expected cost solution leads to better solutions than does the average scenario approach. Additionally, the results show that the stochastic algorithmic approach that we propose outperforms the plain use of a state-of-the-art optimization engine, at least for the three versions of the real-life case that have been tested by us.     

Facility location dynamics: An overview of classifications and applications

In order to modify the current facility or develop a new facility, the dynamics of facility location problems (FLPs) ought to be taken into account so as to efficiently deal with changing parameters such as market demand, internal and external factors, and populations. Since FLPs have a strategic or long-term essence, the inherited uncertainty of future parameters must be incorporated in relevant models, so these models can be considered applicable and ready to implement. Furthermore, due to largely capital outlaid, location or relocation of facilities is basically considered as a long-term planning. Hence, regarding the way in which relevant criteria will change over time, decision makers not only are concerned about the operability and profitability of facilities for an extended period, but also seek to robust locations fitting well with variable demands. Concerning this fact, a trade-off should be set between benefits brought by facility location changes and costs incurred by possible modifications. This review reports on literature pointing out some aspects and characteristics of the dynamics of FLPs. In fact, this paper aims not only to review most variants of these problems, but also to provide a broad overview of their mathematical formulations as well as case studies that have been studied by the literature. Finally, based on classified research works and available gaps in the literature, some possible research trends will be pointed out.     

Fix-and-Relax-Coordination for a multi-period location–allocation problem under uncertainty

A multi-period discrete facility location problem is introduced for a risk neutral strategy with uncertainty in the costs and some of the requirements along the planning horizon. A compact 0–1 formulation for the Deterministic Equivalent Model of the problem under two alternative strategies for the location decisions is presented. Furthermore, a new algorithmic matheuristic, Fix-and-Relax-Coordination, is introduced. This solution scheme is based on a specialization of the Branch-and-Fix Coordination methodology, which exploits the Nonanticipativity Constraints and uses the Twin Node Family concept. The results of an extensive computational experience allow to compare the alternative modeling strategies and assess the effectiveness of the proposed approach versus the plain use of a state-of-the-art MIP solver.     

电商集群的流量预测与不确定性区间估计

流量预测对智能容量规划和任务调度具有重要意义,然而大规模电商集群的流量会出现各种不确定的突发事件,如线上促销活动、用户聚集请求等。这些不确定性事件会导致时间序列中出现很 多突发脉冲,从而给流量预测带来巨大挑战。同时,容量预测应当对不确定性具有鲁棒性,即能很好地应对未来可能出现的情况,保证集群稳定性,而并非严格地根据预测值进行容量收缩。针对大规模分布式电商集群的流量场景以及动态容量规划的需求,该文提出了包含不确定性估计的流量实时预测框架。该框架基于多变量的长短期记忆网络自动编码器和贝叶斯理论,在进行流量确定性预测的同时能够给出准确的不确定性区间估计。     

Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like models

Companies frequently decide on the location and design for new facilities in a sequential way. However, for a fixed number of new facilities, the company might be able to improve its profit by taking its decisions for all the facilities simultaneously. In this paper we compare three different strategies: simultaneous location and independent design of two facilities in the plane, the same with equal designs, and the sequential approach of determining each facility in turn. The basic model is profit maximization for the chain, taking market share, location costs and design costs into account. The market share captured by each facility depends on the distance to the customers (location) and its quality (design), through a probabilistic Huff-like model. Recent research on this type of models was aimed at finding global optima for a single new facility, holding quality fixed or variable, but no exact algorithm has been proposed to find optimal solutions for more than one facility. We develop such an exact interval branch-and-bound algorithm to solve both simultaneous location and design two-facility problems. Then, we present computational results and exhibit the differences in locations and qualities of the optimal solutions one may obtain by the sequential and simultaneous approaches.     

Dynamic location problem under uncertainty with a regret‐based measure of robustness

In this paper, we present a dynamic uncapacitated facility location problem that considers uncertainty in fixed and assignment costs as well as in the sets of potential facility locations and possible customers. Uncertainty is represented via a set of scenarios. Our aim is to minimize the expected total cost, explicitly considering regret. Regret is understood as a measure, for each scenario, of the loss incurred for not choosing that scenario's optimal solution if that scenario indeed occurred. We guarantee that the regret for each scenario is always upper bounded. We present a mixed integer programming model for the problem and we propose a solution approach based on Lagrangean relaxation integrating a local neighborhood search and a subgradient algorithm to update Lagrangean multipliers. The problem and the solutions obtained are first analyzed through the use of illustrative examples. Computational results over sets of randomly generated test problems are also provided.     

Uncertain aggregate production planning

Based on uncertainty theory, multiproduct aggregate production planning model is presented, where the market demand, production cost, subcontracting cost, etc., are all characterized as uncertain variables. The objective is to maximize the belief degree of obtaining the profit more than the predetermined profit over the whole planning horizon. When these uncertain variables are linear, the objective function and constraints can be converted into crisp equivalents, the model is a nonlinear programming, then can be solved by traditional methods. An example is given to illustrate the model and the converting method.     

Local search heuristics for the mobile facility location problem

In the mobile facility location problem (MFLP), one seeks to relocate (or move) a set of existing facilities and assign clients to these facilities so that the sum of facility movement costs and the client travel costs (each to its assigned facility) is minimized. This paper studies formulations and develops local search heuristics for the MFLP. First, we develop an integer programming (IP) formulation for the MFLP by observing that for a given set of facility destinations the problem may be decomposed into two polynomially solvable subproblems. This IP formulation is quite compact in terms of the number of nonzero coefficients in the constraint matrix and the number of integer variables; and allows for the solution of large-scale MFLP instances. Using the decomposition observation, we propose two local search neighborhoods for the MFLP. We report on extensive computational tests of the new IP formulation and local search heuristics on a large range of instances. These tests demonstrate that the proposed formulation and local search heuristics significantly outperform the existing formulation and a previously developed local search heuristic for the problem.     

Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning

Planning infrastructure networks such as roads, pipelines, waterways, power lines and telecommunication systems, require estimations on the future demand as well as other uncertain factors such as operating costs, degradation rates, or the like. When trying to construct infrastructure that is either optimal from a social welfare or profit perspective (depending on a public or private sector focus), typically researchers treat the uncertainties in the problem by using robust optimization methods. The goal of robust optimization is to find optimal solutions that are relatively insensitive to uncertain factors. This paper presents an efficient and tractable approach for finding robust optimum solutions to linear and, more importantly, quadratic programming problems with interval uncertainty using a worst case analysis. For linear, mixed-integer linear, and mixed-integer problems with quadratic objective and constraint functions, our robust formulations have the same complexity and tractability as their deterministic counterparts. Numerous examples with differing difficulties and complexities, especially with selected ones on network planning/operations problems, have been tested to demonstrate the viability of the proposed approach. The results show that the computational effort of the proposed approach, in terms of the number of function calls, for the robust problems is comparable to or even better than that of deterministic problems in some cases.     

碳税影响下再制造物流网络鲁棒优化模型

为了解决不确定环境下低碳再制造物流网络设计的问题,在政府征收企业碳税的情况下,综合考虑网络中再制造产品需求量和废旧产品质量的不确定性以及设施选址和节点间运输路线的决策问题,采用鲁棒优化方法,以碳税成本和物流成本之和最小化为目标,建立了再制造物流网络鲁棒混合线性规划模型。通过案例验证了鲁棒模型的可行性,就税率和不确定参数的变化进行分析,表明鲁棒模型的决策具有实用性和有效性。     

Scalable approach to uncertainty quantification and robust design of interconnected dynamical systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks.     

The general optimal market area model with uncertain and nonstationary demand

Facility location problems involve determining the number of facilities to open, the location of facilities, and the market area that each facility will serve. While the environment is seldom stable, algorithms for solving models that incorporate change and uncertainty are rare and limited in scope. Consequently, the common approach in practice is to use algorithms for static models with perhaps some scenario analysis to accommodate change and uncertainty. We introduce an analytically tractable model that includes dynamic and uncertain demand. By studying how the model can be solved by solving a related model with stationary demand, we are able to derive guidelines on how to apply static analysis tools to problems with dynamic demand. While the analysis is contingent upon the underlying model, evidence on the model's robustness suggests that the results represent plausible guidelines for problems that extend well beyond the model.     

The robust vehicle routing problem with time windows

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.     

Non-probabilistic robust optimization approach for flood control system design

Flood risk management in floodplain systems is a long-standing problem in water resources management. Soft strategies such as land cover change are used to mitigate damages due to flooding. In this approach one chooses the best combination of land covers such that flood damage and the investment costs are minimized. Because of the uncertain nature of the problem, former studies addressed this problem by stochastic programming models which are found to be computationally expensive. In this work, a novel non-probabilistic robust counterpart approach is proposed in which the uncertainty of the rainfall events requires a new formulation and solution algorithms. Non-probabilistic methods, developed in the field of robust optimization were shown to have advantages over classical stochastic methods in several aspects such as: tractability, non-necessity of full probabilistic information, and the ability to integrate correlation of uncertain variables without adding complexity. However, unlike former studies in the field of robust optimization, the resulting optimization model in the flood risk management problem is nonlinear and discontinuous and leads to an intractable robust counterpart model. In this work, a novel iterative linearization scheme is proposed to effectively solve nonlinear robust counterpart models. This work demonstrates the tractability and applicability of non-probabilistic robust optimization to nonlinear problems similar to the flood risk management problem. The results show considerable promise of the robust counterpart approach in terms of showing the tradeoff between flood risk and cost in an efficient manner.