Methods for optimum and near optimum disassembly sequencing

This paper considers disassembly sequencing problems subjected to sequence dependent disassembly costs. In practice, the methods for dealing with such problems rely mainly on metaheuristic and heuristic methods, which intrinsically generate suboptimum solutions. Exact methods are NP-hard and therefore unsuitable to most of the practical problems. Nevertheless, it is useful to have exact methods available that can be applied in order to check, at least medium sized problems, to what extent the heuristically obtained solutions deviate from the optimum solution. The existing exact approaches, which are based on integer linear programming (ILP), become unmanageable, even for the cases of modest product complexity. To alleviate this problem to some extent, the iterative method that has been proposed by Lambert (2006) is applied here. This method is based on repeatedly solving a binary integer linear programming (BILP) problem instead of an ILP problem. The method appears to converge sufficiently quickly to be valuable for dealing with medium sized problems. We then use the iterative method for the validation of a new heuristic method that is also proposed in this paper. Finally, both the heuristic and the iterative BILP methods are implemented on a cellphone from practice consisting of 25 components that are represented, according to a set of precedence relationships, via a disassembly precedence graph.     

Production outsourcing: A linear programming model for the Theory-Of-Constraints

This paper presents an analysis of the outsourcing problem. Pertinent variables are identified and the relationships between them are defined. We formulate the outsourcing problem as a Linear-Programming (LP) problem and identify an analytical solution. We proceed with an example examining three decision models: standard cost accounting, standard Theory-Of-Constraints (TOC) and our own solution. The model enables managers to determine which products to manufacture and which to outsource. The solution of the LP formulation enables managers to apply the model by computing an operational ratio, without having to solve a linear programming problem. The final model is simpler to apply and requires the computation of fewer variables than other prevalent models.     

基于SAND列式的桁架结构优化问题序列线性规划算法

该文提出了一种基于协同分析和设计列式(即SAND 列式,Simultaneous Analysis and Design)和序列线性规划(Sequential Linear Programming)技术的桁架结构优化新方法。与传统列式下将隐式响应函数(如位移、应力等)于设计变量(如杆件截面积等)处作线性展开的做法不同,以桁架结构为例,该文在SAND 列式下,采用杆件截面积和结构节点位移同时作为设计/分析变量,仅对杆件协调条件这一显式双线性函数予以线性近似并构造LP子问题。通过求解一系列LP子问题,可以得到优化问题的近似最优解。与传统优化列式下的SLP 方法相比,该文方法不仅设计变量运动极限的选取相对容易,而且线性近似的误差可以精确估计。数值算例表明,采用该文算法可以快速、稳定地得到优化问题的近似最优解。     

Limit analysis of FRP strengthened masonry arches via nonlinear and linear programming

The collapse load of masonry arches strengthened with FRP materials is determined. The arch is made of quadrangular blocks and the nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated at the interface between the blocks. Two methods are used to solve the problem. In the first method, a nonlinear programming problem (NLP) is formulated and is solved by using the successive quadratic programming algorithm (SQP) and combinatorial analysis. This method finds the optimal solution in the analysed cases. In the second method, a linear programming problem (LP) is formulated and is solved with classical techniques. LP approximates the optimal solution to any desired degree of accuracy. Although the number of variables of LP is much larger than that of NLP, LP process time can result much lower than NLP process time. Numerical examples are provided in order to show the advantages of the two methods and the effectiveness of FRP strengthening for different arch geometries.     

A Branch-and-price algorithm for placement routing for a multi-head beam-type component placement tool

We develop a branch-and-price procedure for a placement routing problem for a multi-head beam-type component placement tool. The problem is modelled as an integer programming model with a huge number of variables, each of which corresponds to a placement route. Its linear programming relaxation is solved by a column generation method. For the column generation subproblem to determine the columns to be added, we develop a dynamic programming procedure. We also propose an effective branching rule to partition the current solution space to eliminate the current fractional solution. Through experiments using real tool data, we observe that the LP relaxation solution value is noticeably close to an integer optimal solution value and hence the integer program formulation and the column generation approach are effective.     

Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning

We present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer programming (MIP) model and a linear programming (LP) model are used to find an optimal set of beam angles and their corresponding fluence maps. The MIP model is solved using the branch-and-bound method while the LP model is solved using the interior point method. In order to reduce the computational burden for solving the optimization models, we introduce iterative beam angle elimination algorithms in which an insignificant beam angle is eliminated in each iteration. Other techniques are also explored including feasible set reduction for LP and data reduction. Experiments are made to show the computational advantage of the iterative methods for optimizing angles using real patient cases.     

机械蒸气再压缩系统再生高浓度溶液的性能研究

机械蒸气再压缩(MVR)系统是一种高效的蒸发系统,本文通过模拟与实验的方法对MVR系统再生高浓度CaCl2溶液的性能进行研究,分析了蒸发压力、入口溶液质量浓度等输入参数对MVR系统再生性能的影响.研究结果表明:蒸发压力通过吸气密度影响再生速率,蒸发压力越大,再生速率越大,系统能耗越大;入口CaCl2溶液质量浓度为0.3...     

Material requirements planning with flexible bills-of-material

In conventional Material Requirements Planning (MRP), a Bills-of-Materials (BOM) for products is fixed. If time or quantity as stated in the Master Production Schedule (MPS) is not flexible for the final product, flexible BOM may be introduced to compensate for the inflexibility in the MPS. This paper addresses situations where a flexible BOM could be used to deal with unexpected shortages when using MRP to plan for requirements of dependent demand items. The requirements stated in the MPS are met in a timely manner by allowing the substitution of items for one another in the case of a shortage. A linear programming (LP) formulation is provided to help deal, if possible, with a shortage using the flexibility in the BOM. The LP model identifies a ‘mix’ of lower-level items that satisfy both the reality of shortages and ensure as small a deviation from the default BOM as possible. A detailed example in the food production environment is presented to explain how the flexible BOM concept may be applied.     

Scheduling parallel processors: An integer linear programming based heuristic for minimizing setup time

The problem of scheduling parallel processors in a make-to-stock environment with sequence setup costs is considered. A new algorithm which formulates a series of 0-1 integer sub problems is proposed and contrasted with an earlier formulation (Dearing and Henderson 1982,1984). Parallels between the sub problem formulations and generalized networks are discussed. The efficiency and quality of the solutions provided were tested using previously published data for a loom assignment problem. The heuristic solution was evaluated against the optimal integer linear programming (ILP) solution, and a rounded linear program (LP) approximation to the optimal solution for several sample problems. Results indicate that the heuristic is efficient, provides near optimal solutions to production planning problems and requires significantly less computing capability than previously reported LP, TLP approaches.     

A simple model for the study of the tolerance of interfacial crack under thermal load

Thermal stresses due to a mismatch between material properties may induce failure of a bonded interface. A simple model for linear dissimilar elastic bonded solids containing an interfacial Zener–Stroh crack under a uniform temperature shift is proposed. Its solution is derived. This result may provide some information about the interface defect tolerant size, which is mainly responsible for triggering interface failures under thermal load. Thus, it can be used to assess the interface integrity and reliability under thermal load. On the other hand, the practical interface crack problem in this study provides another background (mechanism) for the Zener–Stroh crack model.     

Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing

The shortest route representation of the dynamic multi-item multi-level capacitated lotsizing problem is appealing due to the tight bound provided by its Linear Programming (LP) relaxation. However, it suffers from two main drawbacks: Firstly, even solving the LP relaxation of problem instances with up to 16 time periods and 40 items with standard mathematical programming software might require a prohibitive amount of computer time. Secondly, the quadratic growth of the number of variables with the number of periods restricts the solution of problem instances with many periods. Both drawbacks will be addressed in this paper by proposing reformulations of the original shortest route model. Especially we will introduce a model formulation which allows theuser to find a tradeoff between model size and tightness of the lower bound obtained by the LP relaxation by specifying the number oflook ahead periods . Furthermore, we will provide an iterative procedure for determining those look ahead periods which result in the tightest LP relaxation. Theoretical insights as well as computational results are provided, too.     

Unit commitment ? a fuzzy mixed integer Linear Programming solution

Unit commitment (UC) of a large system is a complex puzzle with integer/continuous variables and numerous inter-temporal constraints. After deregulation, price offers submitted by GenCos are predominantly in the form of linear price quantity (PQ) pairs. A fuzzy UC formulation that uses price offers modeled as PQ pairs. This fuzzy linear optimisation formulation of UC is solved using a mixed integer linear programming (MILP) routine. In this formulation, start up cost is modelled using linear variables. The fuzzy formulation provides modeling flexibility, relaxation in constraint enforcement and allows the method to seek a practical solution. The use of MILP technique makes the proposed solution method rigorous and fast. The method is tested on a 24 h, 104-generator system demonstrating its speed and robustness gained by using the LP technique. A five-generator system is additionally used to create a see-through example demonstrating advantages of using the fuzzy optimisation model.     

Limit analysis of masonry arches with finite compressive strength and externally bonded reinforcement

The collapse load of masonry arches with limited compressive strength and externally bonded reinforcement, such as FRP, is evaluated by solving the minimization problem obtained by applying the upper bound theorem of limit analysis. The arch is composed of a finite number of blocks. The nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated in the interface between two adjacent blocks. The crushing in the collapse mechanism is schematised by the interpenetration of the blocks with the formation of hinges at internal or boundary points of the interface. The minimization problem is solved with linear optimization, taking advantages of the robust algorithms offered by linear programming (LP). The optimal solution of the linear programming problem approximates the exact solution to any degree of accuracy. The dual of the minimization problem is also formulated and is solved in order to present the statics (thrust curve, locus of feasible internal reactions, etc.) of the reinforced arch as a consequence of the kinematical assumptions used in the primal minimization problem. Numerical examples are presented in order to show the effectiveness of the proposed method. Finally, it is shown that the results provided by the proposed LP are in good agreement with an experiment on a FRP-strengthened arch characterized by crushing failure of the masonry.     

Limit analysis of masonry arches with finite compressive strength and externally bonded reinforcement

The collapse load of masonry arches with limited compressive strength and externally bonded reinforcement, such as FRP, is evaluated by solving the minimization problem obtained by applying the upper bound theorem of limit analysis. The arch is composed of a finite number of blocks. The nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated in the interface between two adjacent blocks. The crushing in the collapse mechanism is schematised by the interpenetration of the blocks with the formation of hinges at internal or boundary points of the interface. The minimization problem is solved with linear optimization, taking advantages of the robust algorithms offered by linear programming (LP). The optimal solution of the linear programming problem approximates the exact solution to any degree of accuracy. The dual of the minimization problem is also formulated and is solved in order to present the statics (thrust curve, locus of feasible internal reactions, etc.) of the reinforced arch as a consequence of the kinematical assumptions used in the primal minimization problem. Numerical examples are presented in order to show the effectiveness of the proposed method. Finally, it is shown that the results provided by the proposed LP are in good agreement with an experiment on a FRP-strengthened arch characterized by crushing failure of the masonry.     

Application of multiple assessment items optimization method to determining the repair ranking of existing reinforced concrete bridge system

Abstract

The D. (Degree) E. (Extent) R. (Relevancy) evaluation method is widely used to assess the damage states of existing reinforced concrete (RC) bridges in Taiwan. The present study is first to distinguish between relevancy (R^a, a = 1.5, 2) and non‐relevancy (R^a, a= 1) for the repair ranking of the existing RC bridge system to be assessed. The multiple assessment items optimization method was mainly applied to seek the optimum repair ranking. The five existing RC bridges, i.e. Chi‐jou, Lan‐yang, Dah‐jea, Dah‐duh and Dah‐an in Taiwan are chosen as practical examples. The results show that when each bridge is judged to be non‐relevant by the system, the repair ranking predicted by the D.E.R. evaluation method is correct. Nevertheless, when the bridge system has one or more one important bridge, the repair ranking predicted by the D.E.R. evaluation method is not accurate. The proposed method may be remedied the defect of the D.E.R. evaluation method to predict the repair rankings of existing RC bridge system.     

Evaluation of stress intensity factors by the R-functions method

An attempt has been made to apply the novel R-functions method (RFM) to the linear elastic fracture mechanics (LEFM) problems. Essential feature of this method consists in a conversion of logical operations performed on sets (relevant to the sub-domains) into algebraic operations performed on elementary functions. The RFM is an analytical-numerical approach to the solution of the boundary value problems involving arbitrary domains that may be concave or/and multiconnected. The solution constructed by the R-functions method is realized in two phases. In the first one an analytical formula for the so-called general structure of solution (GSS) is designed in such a way that it satisfies the prescribed boundary conditions while a certain number of functions remains undetermined. In the second step a suitable numerical procedure is employed to evaluate these functions in order to satisfy the governing equation of the problem considered. The method was proved to be effective in elasticity problems, especially when fully computerized through the use of symbolic programming. The paper gives:

u

some basic information about the R-functions method,

formulation of the RFM designed for applications to the LEFM problems,

general structure of the solution for 2D cracked bodies with relevant types of singularity and boundary conditions taken into account,

an outline of the numerical approach and some illustrative examples.

The present work may be considered as an encouraging first step, but further significant effort is required before the R-functions method of treating the problems of fracture mechanics becomes a useful and efficient mathematical tool.     

Deconvolution of kinetic decays and fitting of multiple exponential decay curves by the linear prediction method

A method based on linear prediction (LP) theory is employed in analyzing multiple exponential decay signals. A generalized LP method is also proposed to determine true system response in deconvolution problems when the convoluted signals have a decay time comparable to the duration of excitation pulse. These LP methods linearize the least-squares fit and require no prior knowledge of the exact number of the decaying exponents.     

Scenario-based approach for flexible resource loading under uncertainty

Order acceptance decisions in manufacture-to-order environments are often made based on incomplete or uncertain information. To quote reliable due dates in order processing, manage resource capacity adequately and take into account uncertainty, the paper presents and analyses models and tools for more robust resource loading. We refer to the problem as flexible resource loading under uncertainty. We propose a scenario-based solution approach that can deal with a wide range of uncertainty types. The approach is based on an MILP to find a plan with minimum expected costs over all relevant scenarios. To solve this MILP, we propose an exact branch-and-price algorithm. Further, we propose a much faster improvement heuristic based on an LP (linear programming) approximation. A disadvantage of the scenario-based MILP, is that a large number of scenarios may make the model intractable. We therefore propose an approximate approach that uses the aforementioned solution techniques and only a sample of all scenarios. Computational experiments show that, especially for instances with sufficient slack, solutions obtained with deterministic techniques that only use the expected scenario can be significantly improved with respect to their expected costs (i.e. robustness). We also show that for large instances, our heuristics outperform the exact approach given a maximum computation time as a stopping criterion. Moreover, it turns out that using a small sample of selected scenarios generally yields better results than using all scenarios.     

A multiple-scale Trefftz method for an incomplete Cauchy problem of biharmonic equation

In this paper we numerically solve both the direct and the inverse Cauchy problems of biharmonic equation by using a multiple-scale Trefftz method (TM). The approximate solution is expressed to be a linear combination of T-complete bases, and the unknown coefficients are determined to satisfy the boundary conditions, by solving a resultant linear equations system. We introduce a better multiple-scale in the T-complete bases by using the concept of equilibrated norm of the coefficient matrix, such that the explicit formulas of these multiple scales can be derived. The condition number of the coefficient matrix can be significantly reduced upon using these better scales; hence, the present multiple-scale Trefftz method (MSTM) can effectively solve the inverse Cauchy problem without needing of the overspecified data, which is an incomplete Cauchy problem. Numerical examples reveal the efficiency that the new method can provide a highly accurate numerical solution even the problem domain might have a corner singularity, and the given boundary data are subjected to a large random noise.