Planning production using mathematical programming: The case of a woodturning company

Herein we present a case of production planning in a woodturning company. The company wishes to plan the turning of various types of products of different radii in a set of parallel machines (lathes) and with the following principal conditions: for each type of product there is a minimum production lot size; some lathes cannot manufacture every type of product; the production capacity of a lathe depends on the lathe itself and the type of product to be manufactured; the products are classified into families according to radius; and there is an intra-family setup time (for manufacturing different products that have the same radius) and an inter-family setup time (for consecutively manufacturing products that have different radii), which is longer; part of the production can be subcontracted; each type of product can be manufactured on different lathes and/or subcontracted; and the operators can work overtime, during which additional time they can simultaneously operate multiple lathes. The goal is to meet the demand at minimum cost, which includes the cost of any overtime plus that of any subcontracting. The problem was modelled and solved by mixed-integer linear programming (MILP). The company considers the results to be satisfactory.     

大型关系数据库Oracle教学模式的改进

本文就大型关系数据库Oracle的教学,结合实践提出了精选内容、强化实验和依托工程实践开展教学的思路,并就具体的实现方法进行了探讨,以期为课程教学提供一个值得借鉴的教学模式。     

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

This study applies a genetic algorithm embedded with mathematical programming techniques to solve a synchronized and integrated two-level lot sizing and scheduling problem motivated by a real-world problem that arises in soft drink production. The problem considers a production process compounded by raw material preparation/storage and soft drink bottling. The lot sizing and scheduling decisions should be made simultaneously for raw material preparation/storage in tanks and soft drink bottling in several production lines minimizing inventory, shortage and setup costs. The literature provides mixed-integer programming models for this problem, as well as solution methods based on evolutionary algorithms and relax-and-fix approaches. The method applied by this paper uses a new approach which combines a genetic algorithm (GA) with mathematical programming techniques. The GA deals with sequencing decisions for production lots, so that an exact method can solve a simplified linear programming model, responsible for lot sizing decisions. The computational results show that this evolutionary/mathematical programming approach outperforms the literature methods in terms of production costs and run times when applied to a set of real-world problem instances provided by a soft drink company.     

Solving dynamic stochastic economic models by mathematical programming decomposition methods

Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracy.     

A portable implementation of a modular multiprocessing database programming language

This paper introduces the database programming language RAPP, which is an integration of the data type relation and relational algebraic operations with the modular multiprocessing language Pascal Plus. A portable version of the RAPP compiler has been implemented and is described.     

A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions

This work presents a hybrid fuzzy-goal multi-objective programming scheme for topological optimization of continuum structures, in which both static and dynamic loadings are considered. The proposed methodology fortopological optimization first employs a fuzzy-goal programming scheme at the top level for multi-objective problems with static and dynamic objectives. For the static objective with multi-stiffness cases in the fuzzy-goal formulation, a hybrid approach, involving a hierarchical sequence approach or a hierarchical sequence approach coupled with a compromise programming method, is especially suggested for the statically loaded multi-stiffness structure at the sublevel. Concerning dynamic optimization problems of freevibration cases, nonstructural mass, oscillation of the objective function, and repeated eigenvalues are also discussed. Solid Isotropic Material with Penalization density–stiffness interpolation scheme is used to indicate the dependence ofmaterial modulus upon regularized element densities. The globally convergent version of the method of moving asymptotes and the sequential linear programming method areboth employed as optimizers. Several applications have been applied to demonstrate the validation of the presented methodologies.     

An application of mathematical programming concepts to behavioural research design

More and more frequently, human factors specialists are being asked to design behavioural research and evaluation techniques that will be applied many times to many different systems, and not always by behavioural scientists. One way to meet the repeatability requirement is to base evaluation technique design on the concepts of mathematical optimisation (eg, linear programming). This paper presents a general model for the application of mathematical programming concepts to behavioural research design, and an example of the use of this approach to design a simulator certification programme for the Strategic Air Command (SAC).     

Computer-aided derivation of the optimal mathematical models to study gear-pair dynamic by using genetic programming

A general problem is addressed to perform optimal identification of the dynamic system automatically, by using genetic programming algorithm (Koza 1992). The main objective of this approach is to derive optimal mathematical model (reliable and accurate) and determine optimal parameter values for generated mathematical model on the basis of measured dynamic response for selected structure that behaves dynamically. A gear-pair dynamic is studied as an example.     

A DSS for production planning focused on customer service and technological aspects

Production planning and control in manufacturing systems cover several aspects, at different hierarchical levels, including decisions on production and inventory quantities, resource acquisition, production allocation and sequencing. We consider a problem that is typical of companies that manufacture products in production plants placed in different production areas worldwide. A solution framework for the production allocation and balancing problems based on mathematical programming is proposed. Its computational efficiency is improved using techniques from constraint programming, in order to make it possible to solve real world instances of the problems. An industrial test case is used as a benchmark to prove the effectiveness of the proposed approach.     

Online hierarchical scheduling: An approach using mathematical programming

This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize the makespan, i.e., the maximum load of all machines. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both the algorithm and the lower bound are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m=4 and 5, respectively.     

Multi-choice multi-objective mathematical programming model for integrated production planning: a case study

This article develops a multi-choice multi-objective linear programming model in order to solve an integrated production planning problem of a steel plant. The aim of the integrated production planning problem is to integrate the planning sub-functions into a single planning operation. The sub-functions are formulated by considering the capacity of different units of the plant, cost of raw materials from various territories, demands of customers in different geographical locations, time constraint for delivery the products, production cost and production rate at different stages of production process. Departure cost is also considered in the formulation of mathematical programming model. Some of the parameters are decided from a set of possible choices, therefore such parameters are considered as multi-choice type. Multi-choice mathematical programming problem cannot be solved directly. Therefore an equivalent multi-objective mathematical programming model is established in order to find the optimal solution of the problem. Computation of the mathematical programming model is performed with the practical production data of a plant to study the methodology.     

一种支持数据库物理设计的方法和工具

关系数据库的逻辑设计．由于其实现独立于现实世界，已成功地形式化了．而关系数据库的物理设计，由于其实现依赖于具体实现细节．很难用形式化加以描述．本文介绍一种在物理设计中融进需求分析的方法来驱动关系数据库的物理设计．     

Oracle数据库系统优化的研究

随着网络应用的普及,系统数据的存放地——数据库的数据量也急剧膨胀。计算机应用系统被广泛应用在社会的各行业、各部门。如何提高海量数据库系统的性能变得尤为重要,本文通过理论和实验研究,对Oracle海量数据库的优化作了一些研究和探索,说明海量数据库系统性能优化的重要性及Oracle海量数据库系统优化可以通过应用系统本身的调整来提高系统的性能。     

数据库开发中面向对象编程思想

关系数据库在业界深远的影响。但随着软件的设计越来越复杂,当前以数据库设计为中心的数据库应用系统的开发已经难以适应需求,设计出来的系统难以维护和升级。基于面向对象的分析和设计的特点正好可以解决这方面的问题。本文将面向对象的思想如何与传统的数据库开发结合起来,可以思路更清晰的来分析和设计相关领域的应用系统。     

gBoost: a mathematical programming approach to graph classification and regression

Graph mining methods enumerate frequently appearing subgraph patterns, which can be used as features for subsequent classification or regression. However, frequent patterns are not necessarily informative for the given learning problem. We propose a mathematical programming boosting method (gBoost) that progressively collects informative patterns. Compared to AdaBoost, gBoost can build the prediction rule with fewer iterations. To apply the boosting method to graph data, a branch-and-bound pattern search algorithm is developed based on the DFS code tree. The constructed search space is reused in later iterations to minimize the computation time. Our method can learn more efficiently than the simpler method based on frequent substructure mining, because the output labels are used as an extra information source for pruning the search space. Furthermore, by engineering the mathematical program, a wide range of machine learning problems can be solved without modifying the pattern search algorithm.     

A dynamic programming algorithm for the Knapsack Problem with Setup

The Knapsack Problem with Setup (KPS) is a generalization of the classical Knapsack problem (KP), where items are divided into families. An individual item can be selected only if a setup is incurred for the family to which it belongs. This paper provides a dynamic programming (DP) algorithm for the KPS that produces optimal solutions in pseudo-polynomial time. In order to reduce the storage requirements of the algorithm, we adopt a new technique that consists in converting a KPS solution to an integer index. Computational experiments on randomly generated test problems show the efficiency of the DP algorithm compared to the ILOG׳s commercial product CPLEX 12.5.     

Economic calibrated models for water allocation in agricultural production: A review

There is a growing need to assess the effects of policies and global changes on both water resources and agriculture. Agricultural programming models are adequate to study this topic as their functional forms and calibration capacities make them suitable to represent real agricultural production systems and explicit the link between water and production. We present a review of the research on agricultural economic programming models that represent water demand and allocation among farming activities for different problem settings. The different types of models are discussed and particularly the integration of water into the production function so as to reflect the agronomic response of yields to varying levels of water. Uncertainty and risk integration as well as spatial and temporal scale issues are reviewed as they are determining to model results in a science support to policy perspective. A research agenda for future research in this field is provided.     

A long range production/resource planning system using linear programming

In January 1985, a project was initiated to optimize and update the entire Production Planning function, including long-range and short-range scheduling, Material Requirements Planning, and a Production/Resource Planning System for the Molding and Assembly area. This paper addresses the latter.

The Molding and Assembly area at Johnson Wax molds and assembles caps and their components for our products. We were looking for a long range strategic plan for the area. The natural solution was optimization in the form of linear programming.

The models were set up on Control Data's Cybernet Computer using PDS/Magen (for matrix generation) and APEX IV (for problem solving). This was accessed from an IBM-XT via a modem. (The models have since been moved to our inhouse IBM 3083 Mainframe and use Haverly Systems' OMNI and MPSX-370.) The project involved gathering information on the Molding and Assembly area, developing and testing a prototype, developing the data base and data tables for all caps concerned, expanding the prototype and developing the program to handle all caps, preparing output reports (using FOCUS Information Management System), and final implementation.     

线性规划技术在石油化工行业的应用--生产计划优化的历史、现状

详细论述了线性规划技术(LP)在世界石油化工行业应用技术的开发和应用历史，着重阐述了LP在石化行业生产计划优化方面应用的主要关键技术的起源、开发历史和应用状态；详细论述了目前LP的主要应用技术以及相关的工艺模型技术在石化生产计划优化领域应用的最新应用，并以实例说明了应用LP技术可能获得的实际经济效益；论述了国内LP应用技术的近10年来的应用状态。