校车安排问题

探讨如何安排校车运行使得教师和工作人员尽量满意的问题.首先建立动态规划模型和选址规划模型,求出合理站点位置及其总距离.然后用归一法定义满意度与距离的函数关系,考虑各区域人数,建立选址规划模型.得到合理站点位置和总满意度.之后建立双目标非线性规划模型,利用量纲分析法给出权重,以此求出合理乘车位置和满意度.最后对问题进行推...     

A Dynamic Supplier Selection and Inventory Management Model for a Serial Supply Chain with a Novel Supplier Price Break Scheme and Flexible Time Periods

A new supplier price break and discount scheme taking into account order frequency and lead time is introduced and incorporated into an integrated inventory planning model for a serial supply chain that minimizes the overall incurred cost including procurement, inventory holding, production, and transportation. A mixed-integer linear programming (MILP) formulation is presented addressing this multi-period, multi-supplier, and multi-stage problem with predetermined time-varying demand for the case of a single product. Then, the length of the time period is considered as a variable. A new MILP formulation is derived when each period of the model is split into multiple sub-periods, and under certain conditions, it is proved that the optimal solution and objective value of the original model form a feasible solution and an upper bound for the derived model. In a numerical example, three scenarios of the derived model are solved where the number of sub-period is set to 2, 3, and 4. The results further show the decrease of the optimal objective value as the length of the time period is shortened. Sufficient evidence demonstrates that the length of the time period has a significant influence on supplier selection, lot sizing allocation, and inventory planning decisions. This poses the necessity of the selection of appropriate length of a time period, considering the trade-off between model complexity and cost savings.     

Assortment planning for vertically differentiated products under a consider-then-choose model

Consider-then-choose models, borne out by empirical literature in marketing and psychology, note that customers follow a two-stage procedure to choose among alternatives. In this paper, we consider the assortment optimization problem of a retailer who manages a category of vertically differentiated products under customers’ consider-then-choose behavior. We characterize some structural results of the optimal assortment and find that the problem can be solved as the shortest path problem. Also, we develop an efficient algorithm to identify an optimal assortment.     

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.     

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

1.ExtendedEntropyModelEntropymodelsarewidelyusedasaforecastingtechniqueinregionalplanning,see11]and[7].Theydescribeinacertainwaythemostprobablespatialinteractionandcanbeusedtoestimateorigin-destinationtripmatrices.Butthemodelsaretoosimple,soitisdifficulttomeetpracticalrequirements.HallefjordandJo..stenl2]putforwardthegeneralizationofthestandardentropymodels.Onthebasisofthisandaccordingtothedemandofthepredictionofthetripamountfortransportationplanning,wearriveatthefollowing:wherep,μandnarepo…     

Derivative evaluation and computational experience with large bilevel mathematical programs

A bilevel program is a mathematical program involving functions defined implicitly as solutions to another mathematical program. We discuss a method for extracting derivative information on the implicit function, which is especially efficient when the lower-level problem has simple bounds on the variables and/or many inactive constraints. Computational experience on problems with up to 230 variables and 30 constraints is presented.Computational support from Robert Bivins and Myron Stein is gratefully acknowledged. We have also appreciated comments from Jon Bard and an anonymous referee. This work was supported in part by the US Department of Energy through the Los Alamos National Laboratory.     

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．     

Dynamic motion planning in low obstacle density environments

A fundamental task for an autonomous robot is to plan its own motions. Exact approaches to the solution of this motion planning problem suffer from high worst-case running times. The weak and realistic low obstacle density (L.O.D.) assumption results in linear complexity in the number of obstacles of the free space (Van der Stappen et al., 1997). In this paper we address the dynamic version of the motion planning problem in which a robot moves among polygonal obstacles which move along polylines. The obstacles are assumed to move along constant complexity polylines, and to respect the low density property at any given time. We will show that in this situation a cell decomposition of the free space of size O(n²(n) log² n) can be computed in O(n²(n) log² n) time. The dynamic motion planning problem is then solved in O(n²(n) log³ n) time. We also show that these results are close to optimal.     

On solving stochastic production planning problems via scenario modelling

Summary Linear Porgramming models for stochastic planning problems and a methodology for solving them are proposed. A production planning problem with uncertainty in demand is used as a test case, but the methodology presented here is applicable to other types of problems as well. In these models, uncertainty in demand is characterized via scenarios. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield an implementable non-anticipative policy. Such an approach makes it possible to model correlated and nonstationary demand as well as a variety of recourse decision types. For computational purposes, two alternative representations are proposed. A compact approach that is suitable for the Simplex method and a splitting variable approach that is suitable for the Interior Point Methods. A crash procedure that generates an advanced starting solution for the Simplex method is developed. Computational results are reported with both the representations. Although some of the models presented here are very large (over 25000 constraints and 75000 variables), our computational experience with these problems is quite encouraging.     

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.