Sequence Independent Lifting in Mixed Integer Programming

We investigate lifting, i.e., the process of taking a valid inequality for a polyhedron and extending it to a valid inequality in a higher dimensional space. Lifting is usually applied sequentially, that is, variables in a set are lifted one after the other. This may be computationally unattractive since it involves the solution of an optimization problem to compute a lifting coefficient for each variable. To relieve this computational burden, we study sequence independent lifting, which only involves the solution of one optimization problem. We show that if a certain lifting function is superadditive, then the lifting coefficients are independent of the lifting sequence. We introduce the idea of valid superadditive lifting functions to obtain good aproximations to maximum lifting. We apply these results to strengthen Balas' lifting theorem for cover inequalities and to produce lifted flow cover inequalities for a single node flow problem.     

改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型,针对不确定环境下的投资组合问题,把证券的收益率、风险损失率和流动性用区间数描述,建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次,为求解该模型,提出了改进的区间可接受度确定性转换方法,通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后,通过数值实验将提出的方法与传统方法进行比较,结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。     

Bi-objective multi-resource scheduling problem for emergency relief operations

Abstract

Resource scheduling for emergency relief operations is complex as it has many constraints. However, an effective allocation and sequencing of resources are crucial for the minimization of the completion times in emergency relief operations. Despite the importance of such decisions, only a few mathematical models of emergency relief operations have been studied. This article presents a bi-objective mixed integer programming (MIP) that helps to minimize both the total weighted time of completion of the demand points and the makespan of the total emergency relief operation. A two-phase method is developed to solve the bi-objective MIP problem. Additionally, a case study of hospital network in the Melbourne metropolitan area is used to evaluate the model. The results indicate that the model can successfully support the decisions required in the optimal resource scheduling of emergency relief operations.     

考虑最坏中断损失下的P-中位设施选址问题的模型与算法研究

蓄意突袭以及恐怖袭击会造成设施服务的突然中断成为网络系统的主要危害之一,因此网络设施选址决策应该同时考虑正常和紧急状态下系统的运作成本.本文研究考虑最坏中断损失下的网络设施选址问题,建立了该问题的双层规划模型,上层规划涉及设施选址决策,下层规划研究确定设施位置后,设施中断产生最大损失的问题.本文运用基于拉格朗日松弛的混合遗传算法来求解该双层规划问题.将European150数据集作为研究对象,对比研究了本文研究问题与传统的P-中位选址问题的结果,分析不同选址策略下网络系统的效率被中断影响的程度是不同的.最后通过改变一些关键参数,比如常规运作权重、设施数量、中断设施数量,对相关结果进行了分析.     

Supply chain configuration for diffusion of new products: An integrated optimization approach

We develop an integrated/hybrid optimization model for configuring new products’ supply chains while explicitly considering the impact of demand dynamics during new products’ diffusion. The hybrid model simultaneously determines optimal production/sales plan and supply chain configuration. The production and sales plan provides decisions on the optimal timing to launch a new product, as well as the production and sales quantity in each planning period. The supply chain configuration provides optimal selection of options and safety stock level kept at each supply chain function. Extensive computational experiments on randomly generated testbed problems indicate that the hybrid modeling and solution approach significantly outperforms non-hybrid alternative modeling and solution approaches under various diffusion and supply chain topologies. We provide insights on optimal production/sales plan and supply chain configuration for new products during their diffusion process. Also, managerial implications relevant to effectiveness of the hybrid approach are discussed.     

现货价格和需求关联时期权组合合约模式下采购风险管理策略

在现货价格和客户端需求关联的情形下,本文引用期权组合合约建立现货市场供应量有限时的两阶段采购风险管理模型,以期最大化零售商的期望收益。文中先用逆向归纳法列出零售商第二阶段的最优策略,采用标准扰动定理得出有效合约应满足的最优性条件,并将原模型转化为单调的最短路径问题,应用动态规划求解最优的采购策略。最后用算例分析了现货价格与需求的相关系数及现货市场的供应量对最优策略的影响,发现当供应量一定时,各有效合约的最优预订量及有效合约的总预订量都随着相关系数的增大而提高,并且有效合约受相关系数的影响大小取决于合约的灵活性;并且,当相关系数一定时,有效合约的总预订量及执行价格最低的有效合约的最优预订量都随着供应量的增加而单调减少。     

资产负债管理多阶段模型及应用

本文根据我国实际情况,考虑未来各种经济因素的不确定性,建立了资产负债管理问题多阶段随机优化模型.对基金公司的多阶段资产配置问题、个人财务计划问题、银行资产负债管理问题以及养老金问题进行研究,针对每一个具体问题对目标函数和约束条件进行了调整和改进.对未来不确定的经济因素采用向量自回归方法进行预测,得到了最优资产配置,使得与负债选择和投资者财富相联系的资产投资决策通过多期随机规划达到最优.     

动态联盟中伙伴选择问题的区间规划模型及其求解

伙伴选择和风险管理是动态联盟中的重要决策问题,当考虑失败风险时,失败概率无法给出精确值,因此,考虑采用不确定性规划描述此类问题.提出动态联盟中伙伴选择问题的区间规划模型,模型中用区间数表示联盟伙伴的失败概率.为了求解该模型,引入序关系,并利用Nakahara和Ishibuchi的定理,将区间规划模型转化为等价的清晰双目标模型.设计带自适应适值函数的遗传算法,求出问题的全部非劣解.经过对多个问题的仿真,证明了算法的有效性.     

The wireless network jamming problem

In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the wireless network jamming problem. We develop several mathematical programming formulations based on covering the communication nodes and limiting the connectivity index of the nodes. Two case studies are presented comparing the formulations with the addition of various percentile constraints. Finally, directions of further research are addressed.     

Robust portfolio planning in the presence of market anomalies

In this study, a short-term portfolio modeling formulation is developed using existing anomalies as a single determinant for daily Istanbul Stock Exchange National 100 Composite Index (ISE) and US dollars (USD) returns in a Robust optimization (RO) framework. Using anomalies in planning within an RO framework establishes a balance between risk seeking and risk averse behaviors, as generating profit from anomalies is risky and RO enables to settle down the extreme risk seeking behavior. Applications of the model using various data sets result in real profit generation such that terminal wealth figures increase considerably more than Wholesale Price Index (WPI). This study demonstrates that RO is a viable approach to make use of anomaly information for short-term profits.