The Computation of Shadow Prices in Linear Programming

The purpose of this paper is to demonstrate that when degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables do not necessarily correspond to shadow prices. In such instances, major commercial L.P. packages (such as IBM's MPS and MPSX) may provide misleading information about the shadow prices. It will be shown how the actual values of the shadow prices may be determined, and the nature of the relationship between shadow prices and dual variables will be discussed.     

A Production Planning and Stock Control Problem in the Textile Industry

This paper describes the techniques used in an enquiry into production planning and stock holding problems encountered by one of our member firms.The investigation of the problem falls into three parts:

1. i)
   The analysis of demand.
    
2. ii)
   The determination of optimum stock levels.
    
3. iii)
   The solution of the allocation problem which arises if the capacity available for the production of stock lines is not equal to the amount required to bring stocks back to the optimum levels. This problem has not been fully investigated, but a proposed method of solution is given in an appendix.
    

     

An Analogue Equipment for Use in Production Planning

Many planning problems may be more efficiently resolved by an interaction of man and machine than by either alone. This paper considers an analogue equipment built to assist the production planning of a small number of products which share common labour and machine resources. It deals with up to four products and six production periods at a time. The stock levels which would result at the end of each period with a given forecast demand pattern and a given labour pattern are shown on an array of current meters. This rapid display of the stock position enables the operator to assess many more production plans in a given time than previous manual methods could allow. It also permits rapid modifications to be made to a plan with knowledge of the likely consequences. This is a simple and effective approach to a problem which is difficult to treat analytically.     

基于投入产出线性规划模型的燃料乙醇影子价格研究

影子价格能够反映资源的稀缺性及对国民经济的贡献程度.应用投入产出与线性规划相结合的分析方法,构建了投入产出线性规划模型,并基于笔者编制的2005年燃料乙醇投入产出表,针对燃料乙醇制造业部门的不同发展速度,运用投入产出线性规划模型对燃料乙醇的影子价格进行了具体测算.     

考虑生产计划的多周期切割问题优化研究

切割生产广泛存在于工业企业,是原材料加工的重要环节。已有文献主要关注单周期切割问题,但是切割计划也是生产计划的一部分,切割计划和生产计划应该协调优化,达到全局最优。本文研究考虑生产计划的多周期切割问题,目标是最小化运营成本,包括准备成本、切割成本、库存成本以及母材消耗成本。首先建立混合整数规划模型;提出动态规划启发式算法;最后对算例在多种情境下测试,分析成本因子变化对最优结果的影响。算法结果与CPLEX最优结果比较,平均误差为1.85%,表明算法是有效的。     

A Note on the Application of Dynamic Correction to the Optimization of a Multiperiod Resource Allocation Problem

In this note, Luss's approach to optimization of a multiperiod resource allocation problem is employed to include carry-over effects of the controllable variable on future periods and also to include the carry-over effect from previous periods.     

油田开发措施配置的最优控制建模及求解

为了解决油田开发后期各种措施的规划问题,本文提出了一个最优控制数学模型,并讨论了其求解方法,将其应用于油田后期的开发措施配置,并通过油田实例应用证明了这一方法的实用性.     

Linear Formulation of a Distributed Boundary Control Problem

In this paper, we consider a distributed boundary control problem governed by an elliptic partial differential equation with state constraints and a minimax objective function. The continuous optimal control problem, discretized with the finite element method, is numerically approximated by a family of linear programming problems. Application to an optimal configuration problem is discussed.     

多周期Probit模型中MLE的存在性

本文我们讨论了多周期Probit模型中MLE的存在性问题,给出了当协方差阵已知时,参数的MLE存在的充要条件;当协方差阵未知但具有序列结构时,参数的MLE存在的一个必要条件和一个充分条件.     

Fuzzy Multi-fractional Programming for Land Use Planning in Agricultural Production System

In this paper, we present a multi-objective linear fractional programming (MOLFP) approach for multi-objective linear fuzzy goal programming (MOLFGP) problem. Here, we consider a problem in which a set of pair of goals are optimized in ratio rather than optimizing them individually. In particular, we consider the optimization of profit to cash expenditure and crop production in various seasons to land utilization as a fractional objectives and used remaining goals in its original form. Further, the goals set in agricultural production planning are conflicting in nature; thus we use the concept of conflict and nonconflict between goals for computation of appropriate aspiration level. The method is illustrated on a problem of agricultural production system for comparison with Biswas and Pal [1] method to show its suitability.     

关于资源影子价格不唯一问题的讨论

本讨论了资源的影子价格不唯一时,对影子价格的应用所产生的影响,及如何判断资源的影子价格是否唯一,如何解决这种不唯一性带来的问题,以避免决策的失误。     

Dynamic Programming Formulation of the Redundancy Allocation Problem

Dynamic programming formulation for obtaining the optimum number of redundancies at each stage in a system is explained in detail. It is also emphasized and illustrated by examples, that the ‘summation’ form of functional equations, as suggested in the paper, provide a faster solution to an otherwise computationally voluminous method.     

Probabilistic Formulation of the Emergency Service Location Problem

The problem of locating emergency service facilities is studied under the assumption that the locations of incidents (accidents, fires, or customers) are random variables. The probability distribution for rectilinear travel time between a new facility location and the random location of the incident P _i is developed for the case of P _i being uniformly distributed over a rectangular region. The location problem is considered in a discrete space. A deterministic formulation is obtained and recognized to be a set cover problem. Probabilistic variation of the central facility location problem is also presented.An example and some computational experience are provided to emphasize the impact of the probabilistic formulation on the location decision.     

Primal and Dual Variational Formulation of a Frictional Contact Problem

Mediterranean Journal of Mathematics - This paper represents a continuation of Barboteu et al. (Analysis of a contact problem with unilateral constraint and slip-dependent friction, Math...     

关于Veldsman的一个问题

Veldsman,S. gives next open problem: if σ is superprime radical and M_n(R) the full matrix ring of type n×n over the ring R. what is the redation between σ(M_n(R)) and M_n(σ(R))? This problem is answerd in this paper.