A comprehensive reverse supply chain model using an interactive fuzzy approach – A case study on the Vietnamese electronics industry

Reverse supply chains (RSCs) have gained much attention from governments, companies and scholars due to increasing levels of environmental concern, resource depletion and regulation. In Europe and other developed countries, RSCs have been imposed by regulation so that manufacturers take greater responsibility for their end-of-life products. In developing countries like Vietnam, this situation is much more complicated since there are many destinations for end-of-life products other than the take-back systems of their manufacturers. Consequently, product flow quantities to RSC facilities in Vietnam, as well as other parameters, are vague and uncertain. To help electronics companies set up more effective RSCs, this study employs a fuzzy approach to account for such uncertain parameters. Furthermore, risk factors are integrated into the proposed model to make it more comprehensive. The solution approach gives much greater flexibility for decision-makers to obtain a satisfactory solution.     

A Tabu-Search Hyperheuristic for Timetabling and Rostering

Hyperheuristics can be defined to be heuristics which choose between heuristics in order to solve a given optimisation problem. The main motivation behind the development of such approaches is the goal of developing automated scheduling methods which are not restricted to one problem. In this paper we report the investigation of a hyperheuristic approach and evaluate it on various instances of two distinct timetabling and rostering problems. In the framework of our hyperheuristic approach, heuristics compete using rules based on the principles of reinforcement learning. A tabu list of heuristics is also maintained which prevents certain heuristics from being chosen at certain times during the search. We demonstrate that this tabu-search hyperheuristic is an easily re-usable method which can produce solutions of at least acceptable quality across a variety of problems and instances. In effect the proposed method is capable of producing solutions that are competitive with those obtained using state-of-the-art problem-specific techniques for the problems studied here, but is fundamentally more general than those techniques.     

A Foreign Exchange Allocation Algorithm for the Acquisition of Key Spare Parts and Supplies in a Developing Country

Most developing countries are severely constrained by the size of their foreign exchange reserve necessary for the purchase on the international market of certain key items to be employed in their industries, including the export sectors that are responsible for generating the foreign exchange in the first place. The scarcity of this foreign exchange creates enormous problems for these countries. To cope with this dilemma, certain countries resort to all kinds of gambles and approaches that may not be defensible. A rational basis for the allocation of this scarce resource is described in this article. It consists primarily of two components. The first part deals with an optimal strategy for the identification of key items through a criticality assignment routine. The second relates to the algorithm for allocating foreign exchange to a pool of critical items to maximize the returns from such an allocation. The case study is Guyana, a developing country in South America.     

A tabu-search heuristic for the flexible-resource flow shop scheduling problem

This paper presents a tabu-search heuristic for the flexible-resource flow shop scheduling (FRFS) problem [7]. The FRFS problem generalizes the classic flow shop scheduling problem by allowing job-operation processing times to depend on the amount of resource assigned to an operation; the objective is to determine simultaneously the job sequence, resource-allocation policy, and operation start times that optimize system performance. The tabu-search heuristic (TSH) employs a nested-search strategy based on a decomposition of the FRFS problem into these three components. We discuss computational experience with the THS procedure on more than 1600 test problems. The results show that TSH is effective in obtaining near-optimal solutions to the FRFS test problems. In particular, TSH generates optimal solutions for more than 70% of the test problems for which optimal solutions are known; overall, these solutions are within 0.3% of optimality on the average, and within 2.5% of optimality in the worst case.This research was supported in part by National Science Foundation grant SES90-22940.     

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline-based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration of flexible beams with attached tip bodies. The identification problem is formulated as a least-squares fit to data subject to the system dynamics given by a coupled system of ordinary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite-dimensional Hilbert space. Projecting the AEE into splinebased subspaces leads naturally to a sequence of approximating finite-dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.     

Interval length imbedding for nonlinear two-point boundary-value problems

In problems of optimal sequential estimation, in the study of fluid and electrolyte systems, in nonlinear mechanics, and throughout applied mathematics we are confronted with solving nonlinear two-point boundary-value problems. A new approach is provided which seems especially useful when solutions are desired for a variety of interval lengths.     

ON AXISYMMETRIC TRAVELING WAVES AND RADIAL SOLUTIONS OF SEMI‐LINEAR ELLIPTIC EQUATIONS

ABSTRACT. Combining analytical techniques from perturbation methods and dynamical systems theory, we present an elementaryapproach to the detailed construction of axisymmetric diffusive interfaces in semi‐linear elliptic equations. Solutions of the resulting non‐autonomous radial differential equations can be expressed in terms of a slowlyvarying phase plane system. Special analytical results for the phase plane system are used to produce closed‐form solutions for the asymptotic forms of the curved front solutions. These axisym‐metric solutions are fundamental examples of more general curved fronts that arise in a wide variety of scientific fields, and we extensivelydiscuss a number of them, with a particular emphasis on connections to geometric models for the motion of interfaces. Related classical results for traveling waves in one‐dimensional problems are also reviewed briefly. Manyof the results contained in this article are known, and in presenting known results, it is intended that this article be expositoryin nature, providing elementarydemonstrations of some of the central dynamical phenomena and mathematical techniques. It is hoped that the article serves as one possible avenue of entree to the literature on radiallysymmetric solutions of semilinear elliptic problems, especiallyto those articles in which more advanced mathematical theoryis developed.     

Decision resource management and practical intervention in conflicts — a model and its implications

One of the major problems for O.R. lies in providing decision-making assistance in complex conflicts. Too often in the past the approach has been concentrated on providing technical solutions to well-defined hypothetical problems, rather than on attempting to tackle the decision-makers' real problems of trying to make sense of the complex situations in which they find themselves. The paper is intended to contribute towards practical understanding by outlining a theory which explains the ways in which decision-makers' views of the environment are affected by conflicts, particularly under conditions of crisis.The theory attempts to integrate a series of pragmatic hypotheses derived from International Relations, by extending concepts originating in cognitive psychology. The theory's crucial concept is that of “resources” treated by the authors as the number of units of information processed over a given time period. By considering the impact of resources on the conscious analysis of problems a set of postulates is arrived at, which are applicable to a wide variety of decision-making situations.In particular the principle of “inappropriate resource saving” is proposed which suggests that resource considerations imply that unsuitable oversimplistic approaches are likely to dominate decision-making in precisely the situations where the necessity of a complex sophisticated approach is greatest.Finally the implications of the theory for decision-making in general, and for understanding other parties in conflicts, in particular, are discussed. The importance is stressed of; forward contingency planning (putting time in the bank), conscious resource management, and forming multiple models of complex situations.     

Super-selection rules modulating complexity: an overview

Complex systems comprising a large number of elements are potentially capable of finding themselves in a huge variety of states arising by combining the states of their parts. If such a combinatorial explosion were indeed materializing, the observed behavior would resemble to random noise. It is therefore essential that physically relevant complex systems be capable of developing mechanisms for selecting a meaningful subset of states out of the large set of a priori available states. In this communication some generic mechanisms for reducing complexity are analyzed and illustrated on case studies.     

Using components of mathematical ability for initial development and identification of mathematically promising students

Kruteskii's work on the mathematical abilities of school children is a seminal work on the nature of mathematical ability. However, the task of developing methods for the practical application of his work is still a significant problem in mathematics education. The authors have developed a practical application of Kruteskii's approach to the important problem of initially developing components of mathematical ability in student and thereafter identifying mathematically promising students. Examples of problems that were designed to develop ability to generalize, flexibility and reversibility of mental processes are presented. A practical guide for determining the level of development of components of mathematical abilities in individual students, in terms of specified observables, is presented as a set of structured reference tables. The authors set out a practical application protocol that combines use of the tables and sets of specially developed problems for initial development of mathematical abilities prior to identification of mathematically promising students in the general classroom. A significant motivation for this work is the desire to avoid time-consuming and resource intensive practices such as interviews and summer schools which therefore have been used successfully because these practices are now out of reach for all but very wealthy countries or highly ideologically driven systems. On the other hand, special examinations heavily depend on the level of preparedness of the students for the particular examination, and therefore some students with high abilities but with fewer opportunities to prepare could be overlooked.     

A branch and bound algorithm for disassembly scheduling with assembly product structure

This paper considers a production planning problem in disassembly systems, which is the problem of determining the quantity and timing of disassembling end-of-use/life products in order to satisfy the demand of their parts or components over a planning horizon. The case of single product type without parts commonality is considered for the objective of minimizing the sum of setup and inventory holding costs. To show the complexity of the problem, we prove that the problem is NP-hard. Then, after deriving the properties of optimal solutions, a branch and bound algorithm is suggested that incorporates the Lagrangean relaxation-based upper and lower bounds. Computational experiments are performed on a number of randomly generated problems and the test results indicate that the branch and bound algorithm can give optimal solutions up to moderate-sized problems in a reasonable computation time. A Lagrangean heuristic for a viable alternative for large-sized problems is also suggested and compared with the existing heuristics to show its effectiveness.     

O.R. Applications in Industry and Problems of Industrialisation of a Developing Economy with Special Reference to India

The paper has two distinct parts. The first part reviews industrial applications of O.R. in developing countries in general and India in particular. Based on the analysis, the paper suggests concrete steps for further use of operational research in industry.The second part of the paper deals critically with the problems of industrialisation leading to a specific industrial structure in the economy of a developing country. Analysing various relevant criteria for industrialisation of developing economies the paper outlines a methodology suitable for modelling the problem. It then attempts to identify the prerequisites for successful use of O.R. in the multicriteria problem of industrialisation. The paper also discusses the role that national and international agencies can play in bringing about more meaningful applications of O.R. in developing economies.     

Dynamic fleet management as a logistics queueing network

This paper introduces a new framework for modeling and solving dynamic fleet management problems, which we call the Logistics Queueing Network (LQN). A variety of problems in logistics involve the combined problem of moving freight from origin to destination while simultaneously managing the capacity required to move this freight. Standard formulations for real-world problems usually lead to intractably large linear programs. The LQN approach can take into account more real-world detail and is considerably faster than classical LP formulations. The solutions generated using the LQN approach are shown to be within a few percentage points of the LP optimal solutions depending on the size of the capacity fleets.     

How to divide the indivisible

A novel approach to the fair division problem is proposed, which is based on the concept of a priori estimates and ideas of dynamical systems theory. For several problems on the division of a resource with discrete components, this approach leads to explicit constructive solutions in cases for which even the existence of solutions has not been previously known.

     

The Bangladesh grain model

Determining the “optimal” number, size, location and design of grain storage facilities in a developing country is a complex problem with significant health, social, political, demographic and financial implications. Formulating and “solving” such a problem requires the consideration not only of average measures of demand (e.g. minimum per capita requirements), supply and costs, but of population movements, rationing systems, developments in domestic production due to new methods and fertilizers, severe limitations in foreign currency, the infra-structure of the transportation system, improvements in vermin control and many other factors which are most often of but minor importance in corresponding logistic studies in more developed countries. Furthermore, in comparison to more developed countries, there is a dearth of reasonably detailed and accurate historical data to say nothing of relevant prognoses.The following case study describes how such a nationwide logistics problem was tackled in Bangladesh. Although it leads up to a discussion of a solution procedure based upon the solution of rather large-scale mixed integer programming problems, the article is primarily intended for a target audience of OR practioners, economic planners and decision makers involved in operational planning for developing countries.     

Branch-and-price for staff rostering: An efficient implementation using generic programming and nested column generation

We present a novel generic programming implementation of a column-generation algorithm for the generalized staff rostering problem. The problem is represented as a generalized set partitioning model, which is able to capture commonly occurring problem characteristics given in the literature. Columns of the set partitioning problem are generated dynamically by solving a pricing subproblem, and constraint branching in a branch-and-bound framework is used to enforce integrality. The pricing problem is formulated as a novel three-stage nested shortest path problem with resource constraints that exploits the inherent problem structure. A very efficient implementation of this pricing problem is achieved by using generic programming principles in which careful use of the C++ pre-processor allows the generator to be customized for the target problem at compile-time. As well as decreasing run times, this new approach creates a more flexible modeling framework that is well suited to handling the variety of problems found in staff rostering. Comparison with a more-standard run-time customization approach shows that speedups of around a factor of 20 are achieved using our new approach. The adaption to a new problem is simple and the implementation is automatically adjusted internally according to the new definition. We present results for three practical rostering problems. The approach captures all features of each problem and is able to provide high-quality solutions in less than 15 minutes. In two of the three instances, the optimal solution is found within this time frame.     

Calculation of probability density functions for nonlinear vibration systems

Technical systems are subjected to a variety of excitations that cannot generally be described in deterministic ways. Random excitations such as road roughness, wind gusts or loads on marine structures are commonly described by stochastic differential equations (SDEs). Given a set of SDEs, the main task is in finding probability density functions (PDFs), which yield statistical information about the system states. Monte-Carlo simulations represent a general way of generating PDFs, however, reliable integration methods can be time-consuming for complex systems. An alternative way of finding PDFs lies in the analysis of the Fokker-Planck equation, a partial differential equation of the PDF. Linear problems under Gaussian excitation can be solved analytically, which is the case only for a small class of nonlinear problems. As a result, there are a number of methods of approximating PDFs for general problems. Most of these are restricted to comparably low dimensions, such as d=4 ("curse of dimensionality"), limiting the relevance to technical applications. This paper presents solutions to problems of dimensions up to d=10, applying a Galerkin-method that expands approximate solutions into orthogonal polynomials. Problems include polynomial nonlinearities in damping and restoring terms, such as classical Duffing-elements, as well as other types of nonlinearities, demonstrated on a typical problem in vehicle dynamics. All results are compared with results from Monte-Carlo simulations or exact solutions, where available. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A review of TSP based approaches for flowshop scheduling

Contemporary flowshops that are variants of the classical flowshop frequently pose challenging scheduling problems. Such flowshops include no-wait, blocking, and robotic flowshops. These may sometimes be modeled as traveling salesman problems (TSP) and then solved using efficient algorithms available for the TSP. Encountered in auto, electronic, chemical, steel and even modern service industries, such problems are reviewed in this paper. We show that the TSP based approach is quite effective over a broad range. It tackles no-wait flowshops, blocking flowshops, group scheduling of parts in a flowshop using a generalized extension of the TSP, lot streaming and scheduling problems, and as recently done, scheduling of parts and robot movements in automated production cells. In this review paper, we describe several well-documented applications of no-wait and blocking scheduling models and illustrate some ways in which the increasingly used modern manufacturing systems such as robotic cells may be modeled as TSP. We also review the computational complexity of a wide variety of flowshop models. Finally, we suggest some fruitful directions for future research.     

Mobile and immobile gaseous transport: Embedded analytical solutions to finite volume methods

The motivation is driven by deposition processes based on chemical vapor problems. The underlying model problem is based on coupled transport–reaction equations with mobile and immobile areas. We deal with systems of ordinary and partial differential equations. Such equation systems are delicate to solve and we introduce a novel solver method, that takes into account ways to solve analytically parts of the transport and reaction equations. The main idea is to embed the analytical and semianalytical solutions, which can then be explicitly given to standard numerical schemes of higher order. The numerical scheme is based on flux‐based characteristic methods, which is a finite volume method. Such a method is an attractive alternative to the standard numerical schemes, which fully discretize the full equations. We instead reduce the computational time while embedding fast computable analytical parts. Here, we can accelerate the solver process, with a priori explicitly given solutions. We will focus on the derivation of the analytical solutions for general and special solutions of the characteristic methods that are embedded into a finite volume method. In the numerical examples, we illustrate the higher‐order method for different benchmark problems. Finally, the method is verified with realistic results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2.