Stochastic models for strategic resource allocation in nonprofit foreclosed housing acquisitions

Increased rates of mortgage foreclosures in the U.S. have had devastating social and economic impacts during and after the 2008 financial crisis. As part of the response to this problem, nonprofit organizations such as community development corporations (CDCs) have been trying to mitigate the negative impacts of mortgage foreclosures by acquiring and redeveloping foreclosed properties. We consider the strategic resource allocation decisions for these organizations which involve budget allocations to different neighborhoods under cost and return uncertainty. Based on interactions with a CDC, we develop stochastic integer programming based frameworks for this decision problem, and assess the practical value of the models by using real-world data. Both policy-related and computational analyses are performed, and several insights such as the trade-offs between different objectives, and the efficiency of different solution approaches are presented.     

自然科学基金资助计划和支出预算的平衡

在政府推进部门预算制度和财政拨款管理制度改革的大环境下,国家自然科学基金逐渐采用预算管理制度,因此需要平衡资助计划和支出预算．本文在建立科学基金计划和预算的协调模型中,提出计划批准对年度支出敏感度的概念,设计了对经费使用的计划和支出纵横两维拨付的动态监控方法．并且通过模型的计算,可以快速给出综合考虑资助计划发展和使用经费有效两个方面因素的多种方案,供决策者参考．     

Periodic maintenance and repair rate control in stochastic manufacturing systems

In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.Research of this author was supported in part by the University of Georgia.Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.     

大型交通规划模型及其性质

本文提出了一个大型交通规则的模型，并研究了该模型中约束矩阵中基的性质．     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.     

Weber problems with mixed distances and regional demand

We consider a location problem where the distribution of the existing facilities is described by a probability distribution and the transportation cost is given by a combination of transportation cost in a network and continuous distance. The motivation is that in many cases transportation cost is partly given by the cost of travel in a transportation network whereas the access to the network and the travel from the exit of the network to the new facility is given by a continuous distance.      

A stochastic manpower planning model under varying class sizes

Solution related to different types of manpower planning problems arising in different industries and organizations are very much helpful for proper planning and implementation of different objectives. Previously those type of problems are mostly solved under the deterministic set up. Gradually several scientists have developed different types of stochastic models appropriate for solving such types of problems. The present study is an attempt to develop a stochastic manpower planning model under the set up where the classes are of varying sizes and promotion occurs only on the basis of seniority. The work of second author was supported by a research fellowship from Council of Scientific and Industrial Research (Sanction No. 9/28(611)/2003-EMR-I), India.     

Dynamic evolution of economically preferred facilities

In a sustained development scenario, it is often the case that an investment is to be made over time in facilities that generate benefits. The benefits result from joint synergies between the facilities expressed as positive utilities specific to some subsets of facilities. As incremental budgets to finance fixed facility costs become available over time, additional facilities can be opened. The question is which facilities should be opened in order to guarantee that the overall benefit return over time is on the highest possible trajectory. This problem is common in situations such as ramping up a communication or transportation network where the facilities are hubs or service stations, or when introducing new technologies such as alternative fuels for cars and the facilities are fueling stations, or when expanding the production capacity with new machines, or when facilities are functions in a developing organization that is forced to make choices of where to invest limited funding.     

Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning

In this paper, we propose a modification of Benson’s algorithm for solving multiobjective linear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson’s original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of -nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjective linear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method.