Mathematical analysis applied to school attendance areas

The objective of this paper is to develop a generalized mathematical model of pupil assignment within school districts. This model can then be used to examine various policies of student integration. Proposed bussing schemes, school location policies, educational parks, attendance boundaries, etc., can be tested for cost, travel time or other measures of efficiency. Extension to other areas of educational planning is feasible.

Mathematical programming techniques are used to assign resources (say school children) to facilities (say schools) subject to restrictions on facilities (say capacity limits) and resources (say a maximum travel time or a desirable range of school “mixtures”) so that a measure of performance, the “objective function” (say total cost or total time of travel) is optimized. The model is intended to allow examination of a wide range of objective functions and system constraints.     

A linear programming solution to the faculty assignment problem

This paper investigates the problem of assigning faculty to courses at a university. A program is developed which is both efficient in that integer programming is not required, and effective, in that it facilitates interaction by administration in determining the optimal solution. The results of some empirical tests are also reported.     

Improving fuel utilization in steel mill operations using linear programming

This paper describes the use of linear programming to improve the fuel utilisation at a major Midwestern steel mill. In particular, linear programming is used to determine an efficient fuel allocation plan for this steel mill, which reduces the total fuel costs for the steel mill operations. The efficient fuel allocation plan that is developed utilises two externally purchased fuels: natural gas and fuel oil, and two gases: blast furnace gas and coke plant gas, which are internally generated as natural by-products of the production process. Test results from the application of the linear programming model are presented and discussed, and indicate that considerable cost savings can be achieved by utilizing a fuel allocation plan which more effectively utilizes the by-product gases which are produced within the steel making process.     

A mixed-integer linear programming decision model for aquaculture

This paper presents a mathematical model for use in aquaculture, the rearing of aquatic animals in a controlled environment. The model addresses the real-world strategic planning requirements of an emerging technology as well as the short- and long-term production scheduling requirements of a mature aquaculture facility. A solution procedure for large-scale problems is described and tested, and an illustrative application is presented.     

Generating search directions in multiobjective linear programming using the analytic hierarchy process

The algorithm presented in this paper describes an interactive approach for generating search directions in multiobjective linear programming problems (MOLP). The approach is based on using the AHP to assign priorities to vertices adjacent to those that are in the basis, as generated by the simplex method. Using these priorities, an approximate gradient is found that is used to weigh the objective functions during the next iteration. The novel feature of the algorithm is that the decision-maker (DM) is not required to provide interactive inputs to implicit preference questions concerning his objectives, but instead considers explicit evaluation of adjacent possible improvements to generate the next step in his most preferred direction.     

A linear programming model of housing market equilibrium

This paper reviews Wheaton's assertion that the Herbert-Stevens Linear Programming Model produces solutions which do not meet Alonso's criteria for market equilibrium. It demonstrates that, although Wheaton's criticism is valid in general, under certain conditions an alternative specification of the objective function coefficients and the dual variables in the linear program produces a model whose solutions satisfy Alonso's criteria. Finally, this paper shows that the NBER model is an application in which a linear programming problem computes market equilibria.     

A note on distribution analysis in a linear programming model

A linear programming model is used to examine the correspondence between population projections for the provinces and projections for production sectors in Sweden. Furthermore the model is used for analyzing the conflict between the two objectives – regional equality in per capita income and minimal investment requirements. The calculations of the model show that it is possible simultaneously to attain the production targets for the sectors and the population targets for the provinces. The cost in terms of investment resources for a reduction of the difference in regional income is comparatively modest at the beginning of the equalization process bu the cost increases sharply as the equalization process proceeds. Finally a comparison is made with an extended dynamized version of the model also including transportation costs.     

线性规划数学模型的一种新解法

总结了线性规划问题数学模型各种解法的优势和局限性 ,结合具体实例给出一种适用性强、便于理解和记忆的新解法———新两阶段法的解题思想和步骤     

Discussion of dynamic programming and linear programming approaches to stochastic control and optimal stopping in continuous time

This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary differential equation, variational or quasi-variational inequality depending on the type of problem; the solution provides the value of the problem as a function of the initial position (the value function). The other method recasts the problems as linear programs over a space of feasible measures. Both approaches use Dynkin’s formula in essential but different ways. The aim of this paper is to present the main ideas underlying these approaches with only passing attention paid to the important and necessary technical details.     

Analyses of the solution to a linear fractional functionals programming

Summary In this paper the effect of changing one constant of the Linear Fractional Functionals Programming problem has been discussed under the condition that the optimal basis for the original problem remains unaffected. In the changed form the optimal solution and new value of the objective functions are obtained.     

A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy

Decisions in Economics and Finance - We develop a new methodology to retrieve risk neutral probabilities (equivalent martingale measure) with maximum entropy from quoted option prices. We assume...     

A note on spatial and temporal price and allocation modeling: Quadratic programming or linear complementary programming?

This paper presents a clarification of the specific conditions under which the linear complementary programming (LCP) formulation, instead of the quadratic programming (QP) formulation, is applicable in such areas as spatial and temporal price and allocation modeling. An important condition for the use of the LCP formulation is that the coefficient matrix of the demand and/or supply functions is asymmetric. Dynamic formulations can be treated as a LCP but it is demonstrated that the problem can be reformulated in a standard QP format.     

山区变电站竖向设计初探

文章阐述了变电站总图设计中竖向设计的4种形式和影响变电站竖向设计的因素,并通过实例分析指出适宜山区变电站采取的竖向布置形式。     

山区变电站竖向设计初探

文章阐述了变电站总图设计中竖向设计的4种形式和影响变电站竖向设计的因素,并通过实例分析指出适宜山区变电站采取的竖向布置形式.     

A goal programming approach to public investment decisions: A case study of rural roads in Indonesia

The development planner must often face complex problems with multiple, conflicting objectives. Goal programming provides a general methodology for solving such problems. The tool is applied here to aid in the selection of rural road projects in the Indonesian Rural Works Program. Selection criteria are formalized into a set of nineteen goals which form the basis for a goal programming model. Changes in priority levels of goals and weights are used to analyze the respective effects upon the spatial distribution of investments. The approach is applicable to a wide range of problems and a variety of sensitivity analyses. Despite clear advantages, several drawbacks must be noted. First, the application of the methodology, given its degree of sophistication, is limited to a central decision making unit which has access to appropriate software. Second, the technique assumes that the planner has the ability to formulate alternative actions and consequences in a quantifiable expression.     

A stochastic characterization of Loewner optimality design criterion in linear models

In this paper we present a new stochastic characterization of the Loewner optimality design criterion. The result is obtained by proving a generalization to the well known corollary of Anderson's theorem. Certain connections between the Loewner optimality and the stochastic distance optimality design criterion are showed. We also present applications and generalizations of the main result. Received: 9 August 2000