复合Poisson 模型带比例与固定交易费用的最优分红与注资

研究了复合Poisson 模型带比例与固定费用的最优分红与注资问题. 每次分红与注资时, 存在比例及固定的交易费用. 通过控制分红与注资的时刻以及分红及注资量,实现破产前分红减注资的折现期望的最大化. 由于存在固定交易费用, 问题为一个脉冲控制问题. 根据问题的参数不同, 问题的解可分为两大类. 一类解为只进行最优分红不需要注资, 而另一类情况需要注资. 需要注资时, 最优注资策略由最优注资上界以及最优注资下界描述. 当赤字小于最优注资下界的绝对值时, 进行注资. 最后, 在理赔为指数分布时明确地给出了两类共七种最优策略以及值函数的形式. 从而彻底地解决了该问题.     

A single-period inventory placement problem for a supply chain with the expected profit objective

Consider the expected profit maximizing inventory placement problem in an N-stage, supply chain facing a stochastic demand for a single planning period for a specialty item with a very short selling season. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy customer demand. Stocking decisions are made before demand occurs. Because of delays, only a known fraction of demand at a stage will wait for shipments. Unsatisfied demand is lost. The revenue, salvage value, ordering, shipping, processing, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. After characterizing an optimal solution, we propose an algorithm for its computation. For the zero fixed cost case, the computations can be done on a spreadsheet given normal demands. For the nonnegative fixed cost case, we develop an effective branch and bound algorithm.     

Growth Optimal Portfolio Selection Under Proportional Transaction Costs with Obligatory Diversification

A continuous time long run growth optimal or optimal logarithmic utility portfolio with proportional transaction costs consisting of a fixed proportional cost and a cost proportional to the volume of transaction is considered. The asset prices are modeled as exponent of diffusion with jumps whose parameters depend on a finite state Markov process of economic factors. An obligatory portfolio diversification is introduced, accordingly to which it is required to invest at least a fixed small portion of our wealth in each asset.     

Optimal dividend payout for classical risk model with risk constraint

In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramér-Lundberg risk model subject to both proportional and fixed transaction costs.We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b.Given fixed level b,we derive a integro-differential equation satisfied by the value function.By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed.Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T.Also,numerical examples are presented to illustrate our results.     

考虑顾客退货和固定成本的联合补货与定价策略

为了吸引更多顾客,许多电子商务零售商允许顾客在一定时间内退货,导致其利润明显减少。同时,在补货时不仅产生依赖补货量的变动成本,而且会产生与补货量无关的固定成本。基于此,以最大化电子商务零售商的利润为目标,建立考虑顾客退货和固定成本的联合补货与定价模型,其中顾客的退货量与满足的需求呈正比。在一般需求情形下,部分刻画多期问题的最优策略;在特殊需求情形下,证明(s,S,p)策略对单期问题最优,并对多期问题的最优策略进行严格刻画。根据已有刻画为多期问题构造启发式策略。数值结果表明启发式策略近似最优;当初始库存水平足够高/低时,最优补货水平和定价随退货率与固定成本单调变化。关键词:联合补货与定价模型;顾客退货;固定成本;随机动态规划;最优策略     

Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs

We consider two linear project time–cost tradeoff problems with multiple milestones. Unless a milestone is completed on time, penalty costs for tardiness may be imposed. However, these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs. Our model describes these penalty costs as the total weighted number of tardy milestone. The first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs, while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs. We develop a linear programming formulation for the case with a fixed number of milestones. For the case with an arbitrary number of milestones, we show that under completely ordered jobs, the first problem is NP-hard in the ordinary sense while the second problem is polynomially solvable.     

有交易成本的利率期限结构的分析

本文利用无套利均衡方法对存在着交易费，赋税，以及买卖差价等交易成本的债券市场进行分析．用数学方法严格地证明了一个基本结论：在有交易成本的债券市场上，弱无套利性与相容期限结构的存在性是等价的．     

Analysis of some greedy algorithms for the single-sink fixed-charge transportation problem

The single-sink fixed-charge transportation problem (SSFCTP) consists of finding a minimum cost flow from a number of nodes to a single sink. Beside a cost proportional to the amount shipped, the flow cost encompass a fixed charge. The SSFCTP is an important subproblem of the well-known fixed-charge transportation problem. Nevertheless, just a few methods for solving this problem have been proposed in the literature. In this paper, some greedy heuristic solutions methods for the SSFCTP are investigated. It is shown that two greedy approaches for the SSFCTP known from the literature can be arbitrarily bad, whereas an approximation algorithm proposed in the literature for the binary min-knapsack problem has a guaranteed worst case bound if adapted accordingly to the case of the SSFCTP.     

Maximizing the Growth Rate of a Portfolio with Fixed and Proportional Transaction Costs

In this paper a portfolio optimization problem with transaction costs is studied. Transactions of assets are formulated as an impulsive control, which does not allow continuous transactions. The introduction of fixed rate costs has the effect of preventing continuous transactions. The objective of this paper is studying the problem of maximizing the growth rate of expected log utility. A quasi-variational inequality (QVI) of "ergodic type" is derived from the optimization problem. To solve the inequality, we use a perturbation method, where we obtain a necessary estimate of solutions of non-ergodic type QVIs by using a stochastic representation of the solutions.     

A simple algorithm for the source-induced fixed-charge transportation problem

The fixed-charge problem is a non-linear programming problem of practical interest in business and industry. The source-induced fixed-charge transportation problem (SIFCTP) is a variation of the regular fixed-charge transportation problem (FCTP) in which a fixed cost is incurred for every supply point that is used in the solution, along with a variable cost that is proportional to the amount shipped. This problem is significantly different from the widely studied FCTP, where a fixed cost is incurred upon activation of a route. The introduction of the fixed costs in addition to variable costs results in the objective function being a step function. Therefore, fixed-charge problems are usually solved using sophisticated analytical or computer software. This paper deviates from that approach. It presents a computationally simple algorithm for the solution of source-induced fixed-charge problems. The results of empirical tests of the effectiveness of the proposed algorithm are presented.     

Spatial behaviour of solutions of the dual‐phase‐lag heat equation

In this paper we study the spatial behaviour of solutions of some problems for the dual‐phase‐lag heat equation on a semi‐infinite cylinder. The theory of dual‐phase‐lag heat conduction leads to a hyperbolic partial differential equation with a third derivative with respect to time. First, we investigate the spatial evolution of solutions of an initial boundary‐value problem with zero boundary conditions on the lateral surface of the cylinder. Under a boundedness restriction on the initial data, an energy estimate is obtained. An upper bound for the amplitude term in this estimate in terms of the initial and boundary data is also established. For the case of zero initial conditions, a more explicit estimate is obtained which shows that solutions decay exponentially along certain spatial‐time lines. A class of non‐standard problems is also considered for which the temperature and its first two time derivatives at a fixed time T are assumed proportional to their initial values. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal Dividend Payments in a Dual Risk Model with both Fixed and Proportional Costs

In this paper, we study the optimal dividend problem in a dual risk model, which might be appropriate for companies that have fixed expenses and occasional profits. Assuming that dividend payments are subject to both proportional and fixed transaction costs, our object is to maximize the expected present value of dividend payments until ruin, which is defined as the first time the company's surplus becomes negative. This optimization problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality (QVI), we obtain the analytical solutions of the value function and its corresponding optimal dividend strategy when jump sizes are exponentially distributed.     

Cooperative games in facility location situations with regional fixed costs

A continuous single-facility location problem, where the fixed cost (or installation cost) depends on the region where the new facility is located, is studied by mean of cooperative Game Theory tools. Core solutions are proposed for the total cost allocation problem. Sufficient conditions in order to have a nonempty core are given, then the Weber problem with regional fixed costs is studied.     

Solving the capacitated lot-sizing problem with backorder consideration

In this research, we formulate and solve a type of the capacitated lot-sizing problem. We present a general model for the lot-sizing problem with backorder options, that can take into consideration various types of production capacities such as regular time, overtime and subcontracting. The objective is to determine lot sizes that will minimize the sum of setup costs, holding cost, backorder cost, regular time production costs, and overtime production costs, subject to resource constraints. Most existing formulations for the problem consider the special case of the problem where a single source of production capacity is considered. However, allowing for the use of alternate capacities such as overtime is quite common in many manufacturing settings. Hence, we provide a formulation that includes consideration of multiple sources of production capacity. We develop a heuristic based on the special structure of fixed charge transportation problem. The performance of our algorithm is evaluated by comparing the heuristic solution value to lower bound value. Extensive computational results are presented.     

A simulated annealing algorithm with the random compound move for the sequential partitioning problem of directed acyclic graphs

In this paper, we present an approach for finding a minimum cost partition of the nodes of a directed acyclic graph into subsets of a given size, subject to the constraint that the precedence relationships among the elements are satisfied, based on the concept of simulated annealing. Simulated annealing is generally applicable, and can be used to obtain solutions arbitrarily close to an optimum. However, the standard simulated annealing approach with a conventional neighbourhood structure does not yield good solutions for this problem, since this is a multiple partitioning problem and the number of subsets is not fixed. For this problem, we develop an effective neighbourhood structure and a new acceptance criterion. We also assess the effectiveness of the developed algorithm. The results show that this proposed algorithm outperforms, in terms of solution quality, any other algorithm using tabu search. The computational time of the procedure is proportional to the number of nodes in the graph.     

ℓ1-Minimization with Magnitude Constraints in the Frequency Domain

In this paper, we study the -optimal control problem with additional constraints on the magnitude of the closed-loop frequency response. In particular, we study the case of magnitude constraints at fixed frequency points (a finite number of such constraints can be used to approximate an -norm constraint). In previous work, we have shown that the primal-dual formulation for this problem has no duality gap and both primal and dual problems are equivalent to convex, possibly infinite-dimensional, optimization problems with LMI constraints. Here, we study the effect of approximating the convex magnitude constraints with a finite number of linear constraints and provide a bound on the accuracy of the approximation. The resulting problems are linear programs. In the one-block case, both primal and dual programs are semi-infinite dimensional. The optimal cost can be approximated, arbitrarily well from above and within any predefined accuracy from below, by the solutions of finite-dimensional linear programs. In the multiblock case, the approximate LP problem (as well as the exact LMI problem) is infinite-dimensional in both the variables and the constraints. We show that the standard finite-dimensional approximation method, based on approximating the dual linear programming problem by sequences of finite-support problems, may fail to converge to the optimal cost of the infinite-dimensional problem.     

Optimal impulse control of a portfolio with a fixed transaction cost

The aim of this work is to investigate a portfolio optimization problem in presence of fixed transaction costs. We consider an economy with two assets: one risky, modeled by a geometric Brownian motion, and one risk-free which grows at a certain fixed rate. The agent is fully described by his/her utility function and the objective is to maximize the expected utility from the liquidation of wealth at a terminal date. We deal with different forms of utility functions (power, logarithmic and exponential utility), describing in each case how the fixed transaction costs influence the agent’s behavior. We show when it is optimal to recalibrate his/her portfolio and which are the best adjusted portfolios. We also analyze how the optimal strategy is influenced by the risk-aversion, as well as other model parameters.     

自由作业环境下的供应链排序问题

本文研究自由作业环境下的供应链排序问题,研究供应链的上游如何安排工件在自由作业机器上加工,把加工完毕的工件分批发送给下游,使得生产排序费用和发送费用总和最少.这里,生产排序费用是用工件送到时间的函数来表示;发送费用是由发送的固定费用和与运输路径有关的变化费用所组成.本文研究以工件最大送到时间为生产排序费用的自由作业供应链排序问题,在指出问题的NP困难性后,用动态规划算法构造多项式时间近似算法,并分析算法的性能比.本文最后还对特殊情形进行了讨论.