Determining Optimum Fertilizer Combinations Through Goal Programming with Penalty Functions: An Application to Sugar Beet production in Spain

A goal programming model was used to analyse optimum fertilizer combinations. Under this approach, the fertilizer requirements, instead of being fixed values as in traditional linear programming, are considered targets which may or may not be achieved. A penalty system coupled to the goal programming model makes the specified lower and upper levels of nutrients more flexible and realistic. A simple example is used to expound the model, and then applied to real data to give optimum combinations of fertilizers for sugar beet in Western Andalusia (Spain).     

A Dynamic Programming Approach to the Three-machine Scheduling Problem

The three-machine scheduling problem, in which a number of jobsare to be sequenced for processing in the same order on eachof three machines so that the total elapsed time to completethe work is minimized, is formulated as a dynamic program. Aprocedure is developed which reduces the problem to one of evaluatinga subset of the total possible sequences. Some illustrativeexamples are given and the efficiency of the procedure discussedover a number of problems.     

关于线性二层规划分枝定界方法的探讨

对求解线性二层规划的分枝定界方法进行了探讨.给出的一个例子表明,目前的分枝定界方法不能很好地解决上层带有任意线性形式约束的线性二层规划问题,进而在线性二层规划新定义的基础上提出了求解线性二层规划的扩展分枝定界方法.算例表明扩展分枝定界方法可以有效解决原分枝定界方法的不足.     

混合模式下U型装配线平衡问题的目标规划求解

装配线平衡对于提高装配效率和降低装配成本都有重要意义。为了满足顾客需求的多样化和减少成本，通常采用混合模式的装配线。本文针对混合模式下U型装配线平衡问题，提出一个目标规划法以求解该问题，量化示例表明所提方法是有效的。     

基于便利收益视角的投机与大宗商品价格波动分析——以天然橡胶为例

从便利收益视角来分析投机与大宗商品价格波动的关系,首先导出了基于IGARCH模型的动态便利收益近似计算式,并据此来判断投机行为是否引起价格与供需基本面的脱离;然后构建了包含动态便利收益的投机套利模型来度量投机行为对价格的影响强度.最后对天然橡胶市场的投机情况进行了实证分析.结果表明,总体上看,短期价格对投机者的预期反应敏感,使市场产生"自我实现的预言"效应;投机行为引起天然橡胶价格与供需基本面脱离,起到了推涨助跌的作用,加剧天然橡胶价格波动.     

An Optimum Solution for One-Dimensional Slitting Problems: A Dynamic Programming Approach

One-dimensional slitting problems are often encountered in textile, paper or sheet-metal industries where a roll of this product needs to be divided into various narrower-width rolls. The rolls are slit into pieces such that the total value of the sale is maximized depending on the width and the number of defects in the sheet. As the width of a piece increases, the value of the piece increases also, but on the other hand, the number of defects in the piece increases as well, causing reduction in its value. Based on these constraints, a dynamic programming formulation is framed so as to maximize the total value of the sale. Computational complexity with a numerical example is discussed to demonstrate how the procedure works.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .     

The Scheduling of Continuous Flow Prodcution: A Separable Programming Approach

Zero-one integer programming formulations have been described in the literature to solve a wide range of problems in areas as diverse as capital budgeting, allocation, machine sequencing, etc., but as yet large-scale realistic problems can be very expensive to compute using the standard branch-and-bound extensions to linear programming packages. Many authors, noting that there are many situations in which low-cost approximate solutions may be very acceptable, suggest the use of approximating methods, such as the corresponding linear programme or "effective gradients". This paper describes a complex production scheduling problem for which a near-optimal solution is obtained using a separable programming algorithm.By utilizing the special features of separable programming, the model is able to include considerations of setup times in the optimization. Computational experience suggests that the method is a considerable improvement on heuristic attempts, giving improvements in throughput of approximately 30 per cent.     

A Simulation Approach to Cost Estimation in the Project Contracting Industry

In the project contracting industry (particularly in Third World and developing economies) one of the basic requirements for a company to produce a bid is an accurate estimate of the overall costs. A typical contract will involve several hundred quotes from different suppliers, and some of the figures will be inherently more risky than others.This paper looks at the effect of component price uncertainties on the overall cost of a project and develops a company-based simulation model to evaluate this. The basic data is derived from the individual expertise existing within the company, and this is statistically tested for consistency.The application of the simulation model is demonstrated, and it is also used to test some simple hypotheses about the existing modus operandi.     

A Practical Application of Linear Programming in the Mining Industry

The paper describes the application of linear programming to the allocation of coking coals from twenty-eight collieries to seven central washeries and blending plants in one N.C.B. area. The problem, which is of the simplex type, is reduced to the transportation form. Some details are given of the production method, implementation of the linear programming model and the follow-up.     

A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem

We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme. Research supported in part by NSF grant numbers CCR–9901822 and DMS–0317323. Work done as part of the first authors Ph.D. dissertation at RPI.     

A Branch-and-Bound Approach for Solving a Class of Generalized Semi-infinite Programming Problems

A nonconvex generalized semi-infinite programming problem is considered, involving parametric max-functions in both the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality relation, conditions are described ensuring the uniform boundedness of the optimal sets of the dual problems w.r.t. the parameter. Finally a branch-and-bound approach is suggested transforming the problem of finding an approximate global minimum of the original nonconvex optimization problem into the solution of a finite number of convex problems.     

Productivity Bargaining: A Case Study in the Steel Industry

Journal of the Operational Research Society -