Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study

In this paper, we deal with actual problems on production and work force assignment in a housing material manufacturer and a subcontract firm. We formulate two kinds of two-level programming problems: one is a profit maximization problem of both the housing material manufacturer and the subcontract firm, and the other is a profitability maximization problem of them. Applying the interactive fuzzy programming for two-level linear and linear fractional programming problems, we derive satisfactory solutions to the problems. After comparing the two problems, we discuss the results of the applications and examine actual planning of the production and the work force assignment of the two firms to be implemented.     

A stochastic approach to a case study for product recovery network design

Uncertainty is one of the characteristics of product recovery networks. In particular the strategic design of their logistic infrastructure has to take uncertain information into account. In this paper we present a stochastic programming based approach by which a deterministic location model for product recovery network design may be extended to explicitly account for the uncertainties. Such a stochastic model seeks a solution which is appropriately balanced between some alternative scenarios identified by field experts. We apply the stochastic models to a representative real case study on recycling sand from demolition waste in The Netherlands. The interpretation of the results is meant to give more insight into decision-making under uncertainty for reverse logistics.     

Determining optimal resource recycling boundary at regional level: A case study on Tokyo Metropolitan Area in Japan

Conventionally, material inputs to industries come from either natural resources or intermediate products. With the increasing attention on greening the industrial process, municipal solid waste (MSW) can be separated and utilized as inputs to large-scale industries. As such, waste flows need to be managed to meet the requirements of industries by considering both quality and scale. Small scales of municipal recycling centers (MRCs) for pre-treating recyclable wastes often lead to higher pre-treatment cost and lower recycling efficiencies. Theoretically, appropriate facility scale and recycling boundary should be based upon a balanced consideration between economies of scale and transportation costs. However, only a few empirical studies on recycling boundaries have been conducted. Existing modeling studies are mostly case studies for planning purposes and do not theoretically examine the mechanisms and factors that determine recycling boundary. Under such a circumstance, this paper fills such a gap by quantitatively seeking the determinants for recycling boundaries and the related mechanism. An optimization model applying on the recycling of waste plastics is developed and tested in the Tokyo Metropolitan Region (TMR) in Japan. The results indicate two determinants for recycling boundary at the regional level: spatial density of separated wastes and the ratio of unit transportation cost to unit treatment cost. Separated wastes that are collected in low spatial density and have a low ratio of unit transportation cost to unit treatment cost should be better recycled in a large region. The finding implies that regional recycling networks should have multiple layers designed for different types of wastes due to the differences in their spatial density, unit transportation cost and unit treatment cost.     

Algorithms for network piecewise-linear programs: A comparative study

Piecewise-Linear Programming (PLP) is an important area of Mathematical Programming and concerns the minimisation of a convex separable piecewise-linear objective function, subject to linear constraints. In this paper a subarea of PLP called Network Piecewise-Linear Programming (NPLP) is explored. The paper presents four specialised algorithms for NPLP: (Strongly Feasible) Primal Simplex, Dual Method, Out-of-Kilter and (Strongly Polynomial) Cost-Scaling and their relative efficiency is studied. A statistically designed experiment is used to perform a computational comparison of the algorithms. The response variable observed in the experiment is the CPU time to solve randomly generated network piecewise-linear problems classified according to problem class (Transportation, Transshipment and Circulation), problem size, extent of capacitation, and number of breakpoints per arc. Results and conclusions on performance of the algorithms are reported.     

Analytic network process in supplier selection: A case study in an electronic firm

Supplier selection, which is the first step of the activities in the product realization process starting from the purchasing of material till to the end of delivering the products, is evaluated as a critical factor for the companies desiring to be successful in nowadays competition conditions. With the scope of this paper, supplier selection was considered as a multi criteria decision problem. A model aiming the usage of analytic network process (ANP) in supplier selection is developed owning to the evaluation of the relations between supplier selection criterias in a feedback systematic. The proposed model is implemented in a company of electronic.     

A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling

Due to the implementation of government legislation, social responsibility, environmental concern, economic benefits and customer awareness the industries are under a great pressure not only to provide environmentally friendly products but also to take back the product after its use. The issue in reverse logistics is to take back the used products, either under warranty or at the end of use or at the end of lease, so that the products or its parts are appropriately disposed, recycled, reused or remanufactured. In order to overcome this issue, it is necessary to setup a logistics network for arising goods flow from end users to manufacturers. In this study, the optimum usage of secondary lead recovered from the spent lead–acid batteries for producing new battery is presented. The disposal in surface or sewage water or land of liquid content of the lead–acid batteries is strictly restricted. Because of the need for environmental protection and the lack of considerable lead resources, the spent batteries treatment and lead recovery are becoming crucial now-a-days. The objective of this paper is to develop a multi echelon, multi period, multi product closed loop supply chain network model for product returns and the decisions are made regarding material procurement, production, distribution, recycling and disposal. The proposed heuristics based genetic algorithm (GA) is applied as a solution methodology to solve mixed integer linear programming model (MILP). Finally the computational results obtained through GA are compared with the solutions obtained by GAMS optimization software. The solution reveals that the proposed methodology performs very well in terms of both quality of solutions obtained and computational time.     

Core instances for testing: A case study

Data generation for computational testing of optimization algorithms is a key topic in experimental algorithmics. Recently, concern has arisen that many published computational experiments are inadequate with respect to the way test instances are generated. In this paper we suggest a new research direction that might be useful to cope with the possible limitations of data generation. The basic idea is to select a finite set of instances which ‘represent’ the whole set of instances. We propose a measure of the representativeness of an instance, which we call ε-representativeness: for a minimization problem, an instance x_ε is ε-representative of another instance x if a (1 + ε)-approximate solution to x can be obtained by solving x_ε. Focusing on a strongly NP-hard single machine scheduling problem, we show how to map the infinite set of all instances into a finite set of ε-representative core instances. We propose to use this finite set of ε-representative core instances to test heuristics.     

A minimalist two-level foundation for constructive mathematics

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin.One level is given by an intensional type theory, called Minimal type theory. This theory extends a previous version with collections.The other level is given by an extensional set theory that is interpreted in the first one by means of a quotient model.This two-level theory has two main features: it is minimal among the most relevant foundations for constructive mathematics; it is constructive thanks to the way the extensional level is linked to the intensional one which fulfills the “proofs-as-programs” paradigm and acts as a programming language.     

System dynamics modelling of mixed recycling mode based on contract: a case study of online and offline recycling of E-waste in China

ABSTRACT

As the pace of global sustainable economic development accelerates, increasing attention has been brought to the reutilization of waste electronic resources (E-waste). As the leading manufacturer and consumer of electronic products, China has now become the largest producer of E-waste around the world. Considering the current state of recycling mode in China, Huawei Technologies Co. Ltd. (Huawei) took the lead in implementing a blended operation model of manufacturer-led recycling model (offline recycling, OffR) and retailer-led recycling model (online recycling, OnR). In order for the improvement of recycling efficiency for Huawei and other telecommunication companies, this paper constructs a closed-loop network model of mixed recycling (MR) between manufacturers and retailers based on contract, where manufacturers and retailers jointly recycle E-waste for the provision of E-waste to manufacturers for remanufacturing. In this paper, the MR model is compared against the OffR model and OnR model to evaluate the recycling allocation mechanism run by both manufacturer and retailer and then a contract-based, closed-loop network model of mixed recycling between manufacturers and retailers is developed on the basis of obtaining the optimal MR model. By means of simulation analysis, the optimal recycling allocation ratio between manufacturer and retailer is determined. The results obtained from this study are expected to help manufacturers and retailers with effective negotiation and cooperation, so as to improve the efficiency of E-waste recycling while promoting sustainable development and reducing the economic losses caused by price competition to the minimum. This research contributes to not only the waste management studies but also the recycling of E-waste in China and other countries.     

Computing statistics for Hamiltonian systems: A case study

We present the results of a set of numerical experiments designed to investigate the appropriateness of various integration schemes for molecular dynamics simulations. In particular, we wish to identify which numerical methods, when applied to an ergodic Hamiltonian system, sample the state-space in an unbiased manner. We do this by describing two Hamiltonian system for which we can analytically compute some of the important statistical features of its trajectories, and then applying various numerical integration schemes to them. We can then compare the results from the numerical simulation against the exact results for the system and see how closely they agree. The statistic we study is the empirical distribution of particle velocity over long trajectories of the systems. We apply four methods: one symplectic method (Störmer–Verlet) and three energy-conserving step-and-project methods. The symplectic method performs better on both test problems, accurately computing empirical distributions for all step-lengths consistent with stability. Depending on the test system and the method, the step-and-project methods are either no longer ergodic for any step length (thus giving the wrong empirical distribution) or give the correct distribution only in the limit of step-size going to zero.     

A case study on the shareholder network effect of stock market data: An SARMA approach

One of the key research problems in financial markets is the investigation of inter-stock dependence. A good understanding in this regard is crucial for portfolio optimization. To this end, various econometric models have been proposed. Most of them assume that the random noise associated with each subject is independent. However, dependence might still exist within this random noise. Ignoring this valuable information might lead to biased estimations and inaccurate predictions. In this article, we study a spatial autoregressive moving average model with exogenous covariates. Spatial dependence from both response and random noise is considered simultaneously. A quasi-maximum likelihood estimator is developed, and the estimated parameters are shown to be consistent and asymptotically normal. We then conduct an extensive analysis of the proposed method by applying it to the Chinese stock market data.

     

Effects of product postponement on the distribution network: a case study

This case study is based on a supply network analysis conducted at 3M Company, a large multi-national company headquartered in Maplewood, Minnesota. The company has developed product colouring technology that enables product postponement. This study focuses on the development of a discrete-event simulation model and inventory management equations to accurately portray the behaviour of the proposed distribution network that supports product postponement capability. The paper describes, in detail, the modelling process in the context of this actual case study. In this study, it is shown that properly devised product postponement strategy allows for best-in-class delivery within a specified lead-time. The reasons for choosing this inventory management practice are discussed. The benefits and drawbacks of product postponement are reviewed in general terms. Simulation as a tool for analysing supply networks is developed and evaluated for its ability to support a data-driven decision process.     

A global optimization approach for the linear two-level program

Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.The paper was completed while this author was visiting the Department of Mathematics of Linköping University.     

A quasiconcave minimization method for solving linear two-level programs

In this paper the linear two-level problem is considered. The problem is reformulated to an equivalent quasiconcave minimization problem, via a reverse convex transformation. A branch and bound algorithm is developed which takes the specific structure into account and combines an outer approximation technique with a subdivision procedure.     

A two-level additive Schwarz preconditioner for nonconforming plate elements

Summary. A two-level additive Schwarz preconditioner is developed for the systems resulting from the discretizations of the plate bending problem by the Morley finite element, the Fraeijs de Veubeke finite element, the Zienkiewicz finite element and the Adini finite element. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of a generous overlap. Received February 1, 1994 / Revised version received October 24, 1994     

A greedy algorithm for the two-level nested logit model

We consider the assortment optimization problem under the classical two-level nested logit model. We establish a necessary and sufficient condition for the optimal assortment and develop a simple and fast greedy algorithm that iteratively removes at most one product from each nest to compute an optimal solution.     

Structuring decision problems: A case study and reflections for practitioners

This article reviews several approaches to problem structuring and, in particular, the three-step structuring process for decision analysis proposed by von Winterfeldt and Edwards: (1) identifying the problem; (2) selecting an appropriate analytical approach; (3) developing the a detailed analytic structure. This three-step process is re-examined in the context of a decision analysis of alternative policies to reduce electromagnetic field exposure from electric power lines. This decision analysis was conducted for a public health organization funded by the California Public Utilities Commission and it was scrutinized throughout by interested stakeholders. As a result a significant effort went into structuring this problem appropriately, with some successes and some missteps. The article extracts lessons from this experience, updating existing guidance on structuring problems for decision analysis, and concluding with some general insights for problem structuring.     

A robust two-level domain decomposition preconditioner for systems of PDEs

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.