MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

两台恒速机上的MapReduce排序算法研究

研究源自于MapReduce系统的一类排序问题。给定两台恒速机和一组按列表到达的工件，每个工件包含两类任务：Map Task和Reduce Task。假设Map任务和Reduce任务都是不可中断的，Map任务可以并行处理，即可以任意分割成若干小的任务并在两台机器上同时处理，而Reduce任务只可以在单台机器上处理。一旦工件到达，必须为其指派机器和开工时间，目标是使得最后完工时间最小。对LSc算法的竞争比进行了分析，得到其一般情形下的竞争比当$s\geq（1+\sqrt{5}）/2$时为$1+1/s$，否则为$1+s/（s+1）$。而当每个工件$J_j$都满足其Map任务总长大于等于Reduce任务总长时，其竞争比当$s\geq（1+\sqrt{3}）/2$时不超过$1+1/（2s）$，否则为不超过$1+s/（2s+1）$。     

Mathematical models for job-shop scheduling problems with routing and process plan flexibility

As a result of rapid developments in production technologies in recent years, flexible job-shop scheduling problems have become increasingly significant. This paper deals with two NP-hard optimization problems: flexible job-shop scheduling problems (FJSPs) that encompass routing and sequencing sub-problems, and the FJSPs with process plan flexibility (FJSP-PPFs) that additionally include the process plan selection sub-problem. The study is carried out in two steps. In the first step, a mixed-integer linear programming model (MILP-1) is developed for FJSPs and compared to an alternative model in the literature (Model F) in terms of computational efficiency. In the second step, one other mixed-integer linear programming model, a modification of MILP-1, for the FJSP-PPFs is presented along with its computational results on hypothetically generated test problems.     

110警车配置及巡逻方案

针对110警车调度问题,引入了图论中的最短路算法以及计算几何的相关理论,建立了车辆调配模型、巡逻路线模型以及基于模糊数学的评价指标模型.另外,用C++编写了一个可视化的软件,不仅实现了手动描点,自动求出覆盖线段集合的功能,同时利用计算机模拟警车的巡逻路线,最后通过计算机检验得到结果,其合理性和实用性都令人满意.针对问题一,通过人机结合,配置17辆警车就能实现D1的目标,很好地兼顾了警车巡逻的运行成本,减少公安部门车辆和人员等的投入.针对问题二,采用模糊数学相关理论使评价指标实现了从定性到定量的转变.针对问题三和六,在D1的基础上,兼顾了巡逻效果的显著性,采用最少被巡逻道路优先的贪心算法建立了动态巡逻模型,得到了合理的巡逻方案.在此方案中,我们动用了30辆警车完成了问题一的目标.另外还额外考虑了案发事件概率不均匀分布的情况,建立了改进模型.针对问题四,在完成问题三指标的基础上,为了尽可能提高巡逻车辆的隐蔽性和增强巡逻效果,采用轮盘赌算法来引入随机性.针对问题五,采用最远距离道路优先贪心策略,使模型尽可能满足条件D1,D2.针对问题七,提出了一些额外因素及其解决方案,进一步完善了模型,使模型更贴近现实.     

Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

We study bicriteria problems of minimizing maximum tardiness and total due date assignment cost in various scheduling environments. We assume that each job can be assigned a different due date without any restriction, and that each due date assignment cost is a non-decreasing function of the quoted due date. We settle the complexity of most of the problems studied by either proving that they are NP-hard or finding a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.     

New Bundle Methods for Solving Lagrangian Relaxation Dual Problems

Bundle methods have been used frequently to solve nonsmooth optimization problems. In these methods, subgradient directions from past iterations are accumulated in a bundle, and a trial direction is obtained by performing quadratic programming based on the information contained in the bundle. A line search is then performed along the trial direction, generating a serious step if the function value is improved by or a null step otherwise. Bundle methods have been used to maximize the nonsmooth dual function in Lagrangian relaxation for integer optimization problems, where the subgradients are obtained by minimizing the performance index of the relaxed problem. This paper improves bundle methods by making good use of near-minimum solutions that are obtained while solving the relaxed problem. The bundle information is thus enriched, leading to better search directions and less number of null steps. Furthermore, a simplified bundle method is developed, where a fuzzy rule is used to combine linearly directions from near-minimum solutions, replacing quadratic programming and line search. When the simplified bundle method is specialized to an important class of problems where the relaxed problem can be solved by using dynamic programming, fuzzy dynamic programming is developed to obtain efficiently near-optimal solutions and their weights for the linear combination. This method is then applied to job shop scheduling problems, leading to better performance than previously reported in the literature.     

An approximation algorithm for the generalized assignment problem

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep _ij and incurs a cost ofc _ij ; each machinei is available forT _i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T _i time units.We also extend this result to a variant of the problem where, instead of a fixed processing timep _ij , there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T. Research partially supported by an NSF PYI award CCR-89-96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.Research supported in part by a Packard Fellowship, a Sloan Fellowship, an NSF PYI award, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.     

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.     

A dynamic production planning and scheduling algorithm for two products processed on one line

This paper presents a dynamic production planning and scheduling algorithm for two products processed on one line over a fixed time horizon. Production rates are assumed fixed, and restrictions are placed or inventory levels and production run lengths. The resulting problem is a nonlinear binary program, which is solved using an implicit enumeration strategy. The algorithm focuses on the run changeover period while developing tighter bounds on the length of the upcoming run to improve computational efficiency. About 99% pf 297 randomly generated problems with varying demand patterns are solved in less than 15 seconds of CPU time on a CDC Cyber 172 Computer. A mixed integer programming formulation of the generalized multi-product case under no-backlogging of demand is also given.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.