不同风险偏好下虚拟企业风险规划研究

针对虚拟企业风险规划问题,在分析其各种风险具有随机性的特点的基础上,运用随机规划理论,分别建立风险规划的期望值模型和机会约束规划模型来描述决策者在不同风险偏好下的决策行为。针对所建立的模型,分别设计了基于蒙特卡罗模拟的粒子群优化算法、遗传算法和蚁群算法对其进行求解。仿真分析表明期望值模型较好地描述了风险中性决策者的决策行为,机会约束规划模型随着其偏好系数取值的不同描述了不同风险偏好(风险厌恶、风险中性、风险爱好)决策者的决策行为。通过对三种算法仿真结果的比较分析,表明基于蒙特卡罗模拟的粒子群优化算法在寻优能力、稳定性和收敛速度等方面优于其余两种算法,是解决此类风险规划问题的有效手段。     

基于模糊需求的多产品供应商选择的多目标规划模型

由决策于环境的不确定性,供应商选择问题存在大量的模糊信息,传统的确定性规划模型已经不能够很好地处理此类问题。本文基于模糊需求量信息,对于多产品供应商问题建立了模糊多目标规划模型。同时考虑到各目标及约束的重要性程度不同的影响,通过引进适当的权重对多目标规划模型进行求解。文中结合实际算例验证模型的可行性和有效性。     

均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

针对均衡约束数学规划模型难以满足约束规范及难于求解的问题,基于Mond和Weir提出的标准非线性规划的对偶形式,利用其S稳定性,建立了均衡约束数学规划问题的一类广义Mond-Weir型对偶,从而为求解均衡约束优化问题提供了一种新的方法.在Hanson-Mond广义凸性条件下,利用次线性函数,分别提出了弱对偶性、强对偶性和严格逆对偶性定理,并给出了相应证明.该对偶化方法的推广为研究均衡约束数学规划问题的解提供了理论依据.     

多目标规划的光滑同伦方法

本文给出了求解多目标规划的一种连续同伦方法 .首先 ,运用光滑熵函数将多目标多约束的问题化为单目标单约束的问题 ,然后构造了求解单目标问题的同伦方法 ,并证明了其大范围收敛性 .     

基于模糊——随机规划的WEEE回收物流网络优化研究

针对废旧电子电气设备(WEEE)绿色回收问题,根据实际需求刻画其回收物流网络结构;在模型构建中.考虑参数为随机和模糊共存的情况,提出应用随机机会约束规划和模糊机会约束规划相结合的方法来建模;设模型参数是相互独立的,合理利用转换定理将不确定规划转变为常规数学规划,并借助LINGO软件求解最优方案.     

普遍型模糊随机规划

本文提出了一种求解多目标模糊随机规划问题的普遍方法。这种方法在同一个理论框架内处理约束与目标中的随机性和模糊性,因此它具有相当的普遍性。确定性规划,模糊规划和随机规划都可看成是它的特例。     

油田高含水期稳产措施配置多层目标规划

措施规划对于延长油田稳产年限 ,提高采油速度及提高最终采收率是十分必要的 .有些学者建立了油田稳产措施规划的整体或区块规划模型 ,但没有考虑实际油田生产各生产层系的地质特性和所采取措施的差别 .本文针对油田开发实际中存在多层现象 ,以区块的各个生产层为基础 ,建立了油田措施的多层目标规划模型 ,并采用合理的算法进行求解 .应用结果表明 ,多层目标规划使措施配置更精细 ,更能反映生产实际 ,是解决油田措施配置问题的一项有力工具     

一家跨国公司生产分配规划问题的研究

基于香港一家时装制造公司的实际背景,对有关生产分配规划的问题进行了研究,建立了一个多目标规划模型,运用了禁忌搜索算法求解此模型,仿真结果显示出算法的有效性。     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

卫星数传接收规划模型与算法研究

作为对地观测卫星任务执行的两个重要阶段之一,数传接收的规划任务是一个具有多时间窗口、多优化目标和多资源约束的NP-Hard优化问题。中继星的引入为数据全天候近实时传输提供可能,同时也为数传规划提出新的问题。本文主要完成两项工作:第一,建立风险控制的卫星数传接收规划模型;第二,阐述基于遗传禁忌的模型求解方法,进一步采用分布式并行求解策略,改善了求解算法的收敛速度和鲁棒性。最后,通过STK提供基础仿真数据,验证了本文规划模型和求解算法的有效性。     

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

A hybrid technique using constraint programming and linear programming is applied to the problem of scheduling with earliness and tardiness costs. The linear model maintains a set of relaxed optimal start times which are used to guide the constraint programming search heuristic. In addition, the constraint programming problem model employs the strong constraint propagation techniques responsible for many of the advances in constraint programming for scheduling in the past few years. Empirical results validate our approach and show, in particular, that creating and solving a subproblem containing only the activities with direct impact on the cost function and then using this solution in the main search, significantly increases the number of problems that can be solved to optimality while significantly decreasing the search time.     

Scheduling jobs with time-resource tradeoff via nonlinear programming

We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The objective is to find a resource allocation and a schedule that minimizes the makespan. We explicitly allow for succinctly encodable time-resource tradeoff functions, which calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, with performance bound (3+ε) for any ε>0. Our approach relies on a fully polynomial time approximation scheme to solve the nonlinear mathematical programming relaxation. We also derive lower bounds for the approximation.     

A remark on a regularity assumption for the mathematical programming problem in Banach spaces

This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces.     

Integrated production and material handling scheduling using mathematical programming and constraint programming

In this article, we propose an integrated formulation of the combined production and material handling scheduling problems. Traditionally, scheduling problems consider the production machines as the only constraining resource. This is however no longer true as material handling vehicles are becoming more and more valuable resources requiring important investments. Their operations should be optimized and above all synchronized with machine operations. In the problem addressed in this paper, a job shop context is considered. Machines and vehicles are both considered as constraining resources. The integrated scheduling problem is formulated as a mathematical programming model and as a constraint programming model which are compared for optimally solving a series of test problems. A commercial software (ILOG OPLStudio) was used for modeling and testing both models.     

Necessary optimality conditions for a special class of bilevel programming problems with unique lower level solution

We consider a bilevel programming problem in Banach spaces whose lower level solution is unique for any choice of the upper level variable. A condition is presented which ensures that the lower level solution mapping is directionally differentiable, and a formula is constructed which can be used to compute this directional derivative. Afterwards, we apply these results in order to obtain first-order necessary optimality conditions for the bilevel programming problem. It is shown that these optimality conditions imply that a certain mathematical program with complementarity constraints in Banach spaces has the optimal solution zero. We state the weak and strong stationarity conditions of this problem as well as corresponding constraint qualifications in order to derive applicable necessary optimality conditions for the original bilevel programming problem. Finally, we use the theory to state new necessary optimality conditions for certain classes of semidefinite bilevel programming problems and present an example in terms of bilevel optimal control.     

Four-Day Workweek Scheduling with Two or Three Consecutive Days Off

A four-day workweek days-off scheduling problem is considered. Out of the three days off per week for each employee, either two or three days must be consecutive. An optimization algorithm is presented which starts by utilizing the problem's special structure to determine the minimum workforce size. Subsequently, workers are assigned to different days-off work patterns in order to minimize either the total number or the total cost of the workforce. Different procedures must be followed in assigning days-off patterns, depending on the characteristics of labor demands. In some cases, optimum days-off assignments are determined without requiring mathematical programming. In other cases, a workforce size constraint is added to the integer programming model, greatly improving computational performance.     

A constraint programming approach for a batch processing problem with non-identical job sizes

This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several jobs simultaneously and the objective is to minimize the maximal lateness. The constraint programming formulation proposed relies on the decomposition of the problem into finding an assignment of the jobs to the batches, and then minimizing the lateness of the batches on a single machine. This formulation is enhanced by a new optimization constraint which is based on a relaxed problem and applies cost-based domain filtering techniques. Experimental results demonstrate the efficiency of cost-based domain filtering techniques. Comparisons to other exact approaches clearly show the benefits of the proposed approach: it can optimally solve problems that are one order of magnitude greater than those solved by a mathematical formulation or by a branch-and-price.     

Posynomial geometric programming with interval exponents and coefficients

Geometric programming provides a powerful tool for solving nonlinear problems where nonlinear relations can be well presented by an exponential or power function. In the real world, many applications of geometric programming are engineering design problems in which some of the problem parameters are estimates of actual values. This paper develops a solution method when the exponents in the objective function, the cost and the constraint coefficients, and the right-hand sides are imprecise and represented as interval data. Since the parameters of the problem are imprecise, the objective value should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the objective values. Based on the duality theorem and by applying a variable separation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level geometric programs. Solving the pair of geometric programs produces the interval of the objective value. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering optimization areas.     

Interactions between nonlinear programming and modeling systems

Modeling systems are very important for bringing mathematical programming software to nonexpert users, but few nonlinear programming algorithms are today linked to a modeling system. The paper discussed the advantages of linking modeling systems with nonlinear programming. Traditional algorithms can be linked using black-box function and derivatives evaluation routines for local optimization. Methods for generating this information are discussed. More sophisticated algorithms can get access to almost any type of information: interval evaluations and constraint restructuring for detailed preprocessing, second order information for sequential quadratic programming and interior point methods, and monotonicity and convex relaxations for global optimization. Some of the sophisticated information is available today; the rest can be generated on demand.     

A (0–1) goal programming model for scheduling the tour of a marketing executive

This paper addresses the problem of scheduling the tour of a marketing executive (ME) of a large electronics manufacturing company in India. In this problem, the ME has to visit a number of customers in a given planning period. The scheduling problem taken up in this study is different from the various personnel scheduling problems addressed in the literature. This type of personnel scheduling problem can be observed in many other situations such as periodical visits of inspection officers, tour of politicians during election campaigns, tour of mobile courts, schedule of mobile stalls in various areas, etc. In this paper the tour scheduling problem of the ME is modeled using (0–1) goal programming (GP). The (0–1) GP model for the data provided by the company for 1 month has 802 constraints and 1167 binary variables. The model is solved using LINDO software package. The model takes less than a minute (on a 1.50 MHz Pentium machine with 128 MB RAM) to get a solution of the non-preemptive version and about 6 days for the preemptive version. The main contribution is in problem definition and development of the mathematical model for scheduling the tour.