公交车调度问题的数学模型

对 2 0 0 1年全国大学生数学建模竞赛的 B题——公交车调度问题进行了分析 ,建立了调度的目标规划模型及 0— 1规划模型 .在假设各站上、下车人数服从均匀分布的条件下 ,通过对模型的求解 ,求出了公交公司的最小运行车辆数 5 2辆 ,并给出了发车时刻表 ,其中上行方向运行 2 2 5班次 ,下行方向运行 2 2 0班次 .该模型简单 ,求解容易 ,能较好地考虑各方利益     

Integrated Production and Distribution Planning for Södra Cell AB

In this paper we consider integrated planning of transportation of raw material, production and distribution of products of the supply chain at Södra Cell AB, a major European pulp mill company. The strategic planning period is one year. Decisions included in the planning are transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customer via terminals or directly and selection of potential orders and their levels at customers. Distribution is carried out by three different transportation modes; vessels, trains and trucks. We propose a mathematical model for the entire supply chain which includes a large number of continuous variables and a set of binary variables to reflect decisions about product mix and order selection at customers. Five different alternatives regarding production mix in a case study carried out at Södra Cell are analyzed and evaluated. Each alternative describes which products will be produced at which pulp mills.     

Water resources planning based on complex system dynamics: A case study of Tianjin city

A complex system dynamic (SD) model focusing on water resources, termed as TianjinSD, is developed for the integrated and scientific management of the water resources of Tianjin, which contains information feedback that governs interactions in the system and is capable of synthesizing component-level knowledge into system behavior simulation at an integrated level, thus presenting reasonable predictive results for policy-making on water resources allocation and management. As for the Tianjin city, interactions among 96 components for 12 years are explored and four planning alternatives are chosen, one of which is based on the conventional mode assuming that the existing pattern of human activities will be prevailed, while the others are alternative planning designs based on the interaction of local authorities and planning researchers. Optimal mode is therefore obtained according to different scenarios when compared the simulation results for evaluation of different decisions and dynamic consequences.     

关于圆形和方形城市工作区道路交通面积的解析与比较

对于城市规划来讲，事先预测其工作区内所需道路面积，以尽量避免实际交通网络中发生拥挤阻塞，具有重要意义，在本文，我们通过考虑一个城市通勤高峰时期的车辆交通情况，并通过利用走行中的车辆占用道路面积这一概念，基于一个相对现实的模型，从理论上对圆形方形城市工作区推导了所需的道路面积，并将两者加以比较，以发现与其交通网络结构相关的工作区的相对有效形状。     

Economic evaluation for the optimal introduction of flexible manufacturing technology under rivalry

Unless procedures for the economic evaluation of flexible manufacturing technology are revamped, much of U.S. industry could repeat the experience of American automobile and steel companies from the recent past. The dynamic character of flexible manufacturing technology in terms of associated developments in microelectronics, a trend toward equipment modularity, and the increasing diversity of relevant markets make flexible manufacturing especially vulnerable to the weaknesses of conventional procedures for the justification of capital expenditures. Building on the work of V. Smith, M.I. Kamien and N.L. Schwartz, this paper presents optimization models from which economically reasonable plans can be derived for the implementation of flexible manufacturing technology. Although the assumptions of these models are not focused on the situation of a specific plant, model implications and the overall perspectives here on the economic evaluation of flexible system options should provide general guidance for manufacturing planners.     

Local characterization of invariant sets of an autonomous differential inclusion

Summary An application in robotics motivates us to characterize the evolution of a subset in state space due to a compact neighborhood of an arbitrary dynamical system—an instance of a differential inclusion. Earlier results of Blagodat·skikh and Filippov (1986) and Butkovskii (1982) characterize the boundary of theattainable set and theforward projection operator of a state. Our first result is a local characterization of the boundary of the forward projection ofa compact regular subset of the state space. Let the collection of states such that the differential inclusion contains an equilibrium point be called asingular invariant set. We show that the fields at the boundary of the forward projection of a singular invariant set are degenerate under some regularity assumptions when the state-wise boundary of the differential inclusion is smooth. Consider instead those differential inclusions such that the state-wise boundary of the problem is a regular convex polytope—a piecewise smooth boundary rather than smooth. Our second result gives conditions for theuniqueness andexistence of the boundary of the forward projection of a singular invariant set. They characterize the bundle of unstable and stable manifolds of such a differential inclusion.     

Multi-product production planning: A goal programming approach

Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.     

Domestic crude oil resource appraisal

This paper endeavours to estimate the cummulative level of discovery and production of crude oil in the United States where the importance of price and technological change is considered. Two separate functional specifications for the cumulative level are hypothesized and estimated. The results suggest that between 170 and 180 billion barrels will be ultimately recoverable of which 117 billion barrels have been produced through the end of 1989.     

Decision support for the career field selection process at the US Air Force Academy

Each year, the US Air Force Academy graduates nearly 1000 young men and women. To support the decision of which cadets will be classified into which career fields, we describe a linear programming formulation with appealing computational properties that enable it as the core of a decision support tool. We explore methods for measuring and balancing cadets' class standing, Air Force career field requirements, and cadets' career field preferences in the context of this model. Our computational experiments demonstrate the improvement of this method over previous classification approaches, yielding more than 10% increase in the number of cadets assigned to their top career field choice and yielding nearly a 100% reduction in the number of cadets not receiving any of their career field choices. We also explore alternative methods for measuring cadets' career field preferences and demonstrate the positive effect of the new measurement scheme on the overall classification. Because of the short running time of this model, it will serve as a flexible, real-time component of the Academy's classification process.     

Walking an unknown street with bounded detour

A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + π times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.