Robust,multi-objective optimization for the military medical evacuation location-allocation problem

Determining where to locate mobile aeromedical staging facilities (MASFs) as well as identifying how many aeromedical helicopters to allocate to each MASF, commonly referred to as the medical evacuation (MEDEVAC) location-allocation problem, is vital to the success of a deployed MEDEVAC system. Within this research, we develop an integer mathematical programming formulation to determine the location and allocation of MEDEVAC assets over the phases of a military deployment to support operations ranging from peacekeeping through combat to post-combat resolution. Our model seeks to address the multi-objective problem of maximizing the expected demand coverage as a measure of solution effectiveness, minimizing the maximum number of located MASFs in any deployment phase as a measure of solution efficiency, and minimizing the total number of MASF relocations throughout the deployment as a measure of solution robustness. This research makes two contributions. First, it formulates a representative mathematical programming formulation and identifies an accompanying solution methodology (i.e., the ε-constraint Method) to assess and recommend improvements to deployed military MEDEVAC systems designed to provide large-scale emergency medical response for contingency operations that range in casualty-inducing intensity (i.e., demand) over the phases of a deployment. Second, the research illustrates the application of the model for a realistic, synthetically generated medical planning scenario in southern Azerbaijan. Comparisons are made between the model’s (multi-phase) optimal solution and the phase-specific optimal solutions that disregard concerns of transitions between phases. The results highlight the conflicting nature between the objectives and illustrate the trade-offs between objectives as restrictions applied to the second and third objectives are respectively tightened or relaxed.     

VMI环境下的库存与发货模型研究

供应商管理库存(VMI)是供应链上库存管理的一种新思想,本文分析了三个有代表性的VMI环境下的库存与发货管理模型,这三个模型分别采用了基于时间的整合发货策略、基于数量的整合发货策略,以及基于时间和数量的混合发货策略。本文就每一个模型计算出了最优参数值,并比较了三种策略的利弊,分析了每一种策略的适用环境。     

An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations

This paper addresses the resource-constrained project scheduling problem with uncertain activity durations. An adaptive robust optimization model is proposed to derive the resource allocation decisions that minimize the worst-case makespan, under general polyhedral uncertainty sets. The properties of the model are analyzed, assuming that the activity durations are subject to interval uncertainty where the level of robustness is controlled by a protection factor related to the risk aversion of the decision maker. A general decomposition approach is proposed to solve the robust counterpart of the resource-constrained project scheduling problem, further tailored to address the uncertainty set with the protection factor. An extensive computational study is presented on benchmark instances adapted from the PSPLIB.     

On greedy and strategic evaders in sequential interdiction settings with incomplete information

We consider a class of sequential network interdiction problem settings where the interdictor has incomplete initial information about the network while the evader has complete knowledge of the network including its structure and arc costs. In each decision epoch, the interdictor can block (for the duration of the epoch) at most k arcs known to him/her. By observing the evader’s actions, the interdictor learns about the network structure and costs and thus, can adjust his/her actions in subsequent decision epochs. It is known from the literature that if the evader is greedy (i.e., the shortest available path is used in each decision epochs), then under some assumptions the greedy interdiction policies that block k-most vital arcs in each epoch are efficient and have a finite regret. In this paper, we consider the evader’s perspective and explore deterministic “strategic” evasion policies under the assumption that the interdictor is greedy. We first study the theoretical computational complexity of the evader’s problem. Then we derive basic constructive properties of optimal evasion policies for two decision epochs when the interdictor has no initial information about the network structure. These properties are then exploited for the design of a heuristic algorithm for a strategic evader in a general setting with an arbitrary time horizon and any initial information available to the interdictor. Our computational experiments demonstrate that the proposed heuristic outperforms the greedy evasion policy on several classes of synthetic network instances under either perfect or noisy information feedback. Finally, some interesting insights from our theoretical and computational results conclude the paper.     

A DYNAMIC PROGRAMMING MODEL FOR OPTIMAL ALLOCATION OF DECISION TIME

Recurrent decision making by a lower-level manager can be viewed as a sequential decision process in which time and uncertainty are limiting factors. Under these conditions, the manager must determine how to best utilize his decision making time consistent with his own particular set of decision values. A dynamic programming model was devised to determine the optimal (consistent) allocation of decision time among five different types of problems for a sequence of simulated recurrent decision situations. Fifty-one lower-level managers were interviewed about their use of decision time and decision procedures. The model was validated by comparing model assumptions and results with the findings from the interviews. The model was used to determine the effects of variations in the levels of time available and uncertainty upon the optimal allocation of decision time.     

Stochastic Optimization for Natural Disaster Asset Prepositioning

A key strategic issue in pre‐disaster planning for humanitarian logistics is the pre‐establishment of adequate capacity and resources that enable efficient relief operations. This paper develops a two‐stage stochastic optimization model to guide the allocation of budget to acquire and position relief assets, decisions that typically need to be made well in advance before a disaster strikes. The optimization focuses on minimizing the expected number of casualties, so our model includes first‐stage decisions to represent the expansion of resources such as warehouses, medical facilities with personnel, ramp spaces, and shelters. Second‐stage decisions concern the logistics of the problem, where allocated resources and contracted transportation assets are deployed to rescue critical population (in need of emergency evacuation), deliver required commodities to stay‐back population, and transport the transfer population displaced by the disaster. Because of the uncertainty of the event's location and severity, these and other parameters are represented as scenarios. Computational results on notional test cases provide guidance on budget allocation and prove the potential benefit of using stochastic optimization.     

应急救援物资紧缺的两级配送路径选择研究

针对应急救援物资紧缺难以满足所有需求的情形,以单个需求点最大缺货量最小、车辆运输费用最小为双目标,建立从配送中心到分发点再到需求点的两级配送路径选择模型,设计复杂性为O(n3)的近似算法GA进行求解,证明算法近似比的上下界并讨论影响因素,用数值验证算法GA的近似比接近于1,表明算法GA具有较好的性能。最后以雅安灾区配送实例验证模型和算法的有效性。     

碳交易政策下多式联运路径选择问题的鲁棒优化研究

针对碳交易政策下的多式联运路径选择问题,考虑运输时间和单位运费率不确定且其概率分布未知的情况,引入鲁棒优化建模方法对其进行研究。首先利用box不确定集合刻画分布未知的运输时间和运费率,然后在碳交易政策下确定模型的基础上,构建鲁棒性可调节的多式联运路径选择模型,并通过对偶转化得到相对易求解的鲁棒等价模型。实例分析表明,鲁棒模型能较好地处理参数概率分布未知的多式联运路径选择问题,方便决策者根据偏好调整不确定预算水平进行决策。运输时间和单位运费率的不确定性都会影响多式联运路径决策,但是作用机理有所不同。将上述碳交易政策下的模型拓展到其他低碳政策,结果表明多种低碳政策的组合能更好实现多式联运减排。     

Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis

We derive the analogue of the classic Arrow–Pratt approximation of the certainty equivalent under model uncertainty as described by the smooth model of decision making under ambiguity of Klibanoff, Marinacci, and Mukerji (2005). We study its scope by deriving a tractable mean‐variance model adjusted for ambiguity and solving the corresponding portfolio allocation problem. In the problem with a risk‐free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher ambiguity aversion only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In particular, a positive alpha corresponds to a long position in the ambiguous asset, a negative alpha corresponds to a short position in the ambiguous asset, and greater ambiguity aversion reduces optimal exposure to ambiguity. The analytical tractability of the enhanced Arrow–Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of model uncertainty on equilibrium asset prices.     

Optimal dispatching control of an AGV in a JIT production system

This paper deals with an FMS (Flexible Manufacturing System) in a JIT (Just-In-Time) production system. The FMS consists of m workstations, one dispatching station and a single AGV (Automated Guided Vehicle). Each workstation has an input buffer of limited capacity and its processing times are distributed stochastically. When the processing of a new component starts at the workstation, a withdrawal Kanban attached to it is sent to the dispatching station. The AGV chooses one from workstations whose withdrawal Kanbans are accumulated at the dispatching station, and conveys a component with a withdrawal Kanban from the dispatching station to the workstation. The main purpose of this paper is to find an optimal dispatching policy of the AGV that maximizes the long-run expected average reward per unit time. The problem is formulated as a semi-Markov decision process and an optimal dispatching policy is computed. Numerical experiments are performed to make several comparisons.     

An inventory control policy for liquefied natural gas as a transportation fuel

In this paper, we study a novel stochastic inventory management problem that arises in storage and refueling facilities for Liquefied Natural Gas (LNG) as a transportation fuel. In this inventory problem, the physio-chemical properties of LNG play a key role in the design of inventory policies. These properties are: (1) LNG suffers from both quantity decay and quality deterioration and (2) the quality of on-hand LNG can be upgraded by mixing it with higher-quality LNG. Given that LNG quality can be upgraded, an inventory control policy for this problem needs to consider the removal of LNG as a decision variable. We model and solve the problem by means of a Markov Decision Process (MDP) and study the structural characteristics of the optimal policy. The insights obtained in the analysis of the optimal policy are translated into a simple, though effective, inventory control policy in which actions (i.e., replenishment and/or removal) are driven by both the quality and the quantity of the inventories. We assess the performance of our policy by means of a numerical study and show that it performs close to optimal in many numerical instances. The main conclusion of our study is that it is important to take quality into consideration when design inventory control policies for LNG, and that the most effective way to cope with quality issues in an LNG inventory system involves both the removal and the replenishment of inventories.     

Scheduling dedicated jobs with variative processing times

We consider the following optimization problem. There is a set of \(n\) dedicated jobs that are to be processed on \(m\) parallel machines. The job set is partitioned into subsets and jobs of each subset have a common due date. Processing times of jobs are interconnected and they are the subject of the decision making. The goal is to choose a processing time for each job in a feasible way and to construct a schedule that minimizes the maximum lateness. We show that the problem is NP-hard even if \(m=1\) and that it is NP-hard in the strong sense if \(m\) is a variable. We prove that there is no approximate polynomial algorithm with guaranteed approximation ratio less than 2. We propose an integer linear formulation for the problem and perform experiments. The experiments show that the solutions obtained with CPLEX within the limit of 5 min are on average about 5 % from the optimum value for instances with up to 150 jobs, 16 subsets and 11 machines. Most instances were solved to optimality and the average CPLEX running time was 32 s for these instances.     

Risk of Extreme Events in Multiobjective Decision Trees Part 2. Rare Events

Earlier work with decision trees identified nonseparability as an obstacle to minimizing the conditional expected value, a measure of the risk of extreme events, by the well-known method of averaging out and folding back. This second of two companion papers addresses the conditional expected value that is defined as the expected outcome assuming that a random variable is observed only in the upper 100 (1 −α) percent of potential outcomes, where α is a cumulative probability preselected by the decision maker. An approach is proposed to overcome the need to evaluate all policies in order to identify the optimal policy. The approach is based in part on approximating the conditional expected value by using statistics of extremes. An existing convenient approximation of the conditional expected value is shown to be separable into two constituent elements of risk and can thus be optimized, along with other objectives including the unconditional expected value of the outcome, in a multiobjective decision tree. An example of sequential decision making for remediation or environmental contamination is provided. The importance of the results for risk analyis beyond the minimization of conditional expected values is pointed out.     

基于收益管理的海运集装箱舱位分配与路径选择优化模型

文章应用收益管理的方法对不确定环境下海运集装箱的舱位分配问题进行了定量研究.首先针对海运收益管理的应用特征,建立了考虑空箱调运和路径选择的集装箱多航段能力分配模型,然后考虑需求的不确定性,应用稳健优化方法对此模型进行求解.最后,通过数值仿真得到了优化的舱位分配方案,比较发现稳健优化模型取得了较确定性规划模型更好的收益.显示了模型和方法对于集装箱海运企业的收益管理问题具有应用价值.     

多车型确定性动态车辆调配问题

详细地描述了多车型确定性动态车辆调配问题.建立了问题的线性规划模型,鉴于线性模型的缺点,构造一个线性函数来近似目标函数中未来时段部分,从而建立起问题的时空分解模型,把问题从时间和空间上分解为多个单时段单节点问题,并根据单时段单节点问题的特点设计简单的排序求解方法.最后给出了问题的完整求解过程,从而使问题能够得到有效解决.     

考虑产品变质的VMI混合补货发货策略及优化仿真

本文研究了“产品可变质”情况下的VMI库存补货与装运调度问题,并建立了Poisson需求过程下的VMI混合补货发货模型,根据此模型通过简单的规划求解即可得到使长期平均成本最小的最佳混合策略组合。由于模型推演过程中涉及到对补货周期内期望发货次数的近似估计,因而模型解是拟最优的。算例和模型仿真显示,模型结果与仿真结果十分相近,从而模型有效性得以确认。     

LOT-SIZING IN CAPACITATED MULTI-STAGE SERIAL SYSTEMS

The lot-sizing problem in capacitated multi-stage systems with a serial product structure is addressed. This is a complex optimization problem that is part of the decision set in material requirements planning (MRP) systems. The mathematical model that describes the problem uses the concept of echelon stock and includes lead times. Setup times are taken into account, which implies that the problem of finding a feasible solution is NP-Complete. This paper proposes a heuristic method that provides a production plan in order to minimize inventory, production, and setup costs. The heuristic starts from a solution for the uncapacitated problem, which is given by the sequential application of the Wagner-Whitin algorithm. Feasibility is then attempted by shifting production amounts between periods. Computational tests conducted in 1,800 instances with up to 40 components and 18 periods have shown that feasible solutions were obtained in 83.7% of the instances. For the infeasible instances, on average, the heuristic is able to find solutions with very low capacity excess. The solutions' quality is evaluated through a lower bound provided by Lagrangean relaxation and on average the gap is less than 10%.     

Production quantity allocation for order fulfilment in the supply chain: a neural network based approach

In the current global business environment, it is very important to know how to allocate products from the producer to buyers (or distributors). If products are not appropriately distributed due to absence of an effective allocation policy, the producer and buyers cannot expect to increase customer satisfaction and financial profit. Sometimes some buyers can order more than the actual demand due to inappropriately forecasting customer orders. This is the big obstacle to the effective allocation of products. If the producer can become aware of buyers’ actual demands, it is possible to realise high-level order fulfilment through the effective allocation of products. In this study, new allocation policies are proposed considering buyers’ demands. The back propagation algorithm, one of the learning algorithms in neural network theory, is used to recognise actual demands from the previous buyers’ orders. After excluding surplus demands included in buyers’ demands, products are allocated to buyers according to one of the existing allocation policies depending on the company's decision. In the numerical examples, new allocation policies reducing buyers’ surplus demands outperform previous allocation policies with respect to average amount of backorder.     

A Multivariate Methodology for Simultaneously Capturing and Clustering Judgment Policies

This paper presents a new linear model methodology for clustering judges with homogeneous decision policies and differentiating dimensions which distinguish judgment policies. This linear policy capturing model based on canonical correlation analysis is compared to the standard model based on regression analysis and hierarchical agglomerative clustering. Potential advantages of the new methodology include simultaneous instead of sequential consideration of information in the dependent and independent variable sets, decreased interpretational difficulty in the presence of multicollinearity and/or suppressor/moderator variables, and a more clearly defined solution structure allowing assessment of a judge's relationship to all of the derived, ideal policy types. An application to capturing policies of information systems recruiters responsible for hiring entry-level personnel is used to compare and contrast the two techniques.     

Risk‐Based Sampling: I Don't Want to Weight in Vain

Recently, there has been considerable interest in developing risk‐based sampling for food safety and animal and plant health for efficient allocation of inspection and surveillance resources. The problem of risk‐based sampling allocation presents a challenge similar to financial portfolio analysis. Markowitz (1952) laid the foundation for modern portfolio theory based on mean‐variance optimization. However, a persistent challenge in implementing portfolio optimization is the problem of estimation error, leading to false “optimal” portfolios and unstable asset weights. In some cases, portfolio diversification based on simple heuristics (e.g., equal allocation) has better out‐of‐sample performance than complex portfolio optimization methods due to estimation uncertainty. Even for portfolios with a modest number of assets, the estimation window required for true optimization may imply an implausibly long stationary period. The implications for risk‐based sampling are illustrated by a simple simulation model of lot inspection for a small, heterogeneous group of producers.