Fuzzy chance-constrained programming model for a multi-echelon reverse logistics network for household appliances

Efficient planning and design of an appropriate reverse logistics network is crucial to the economical collection and disposal of scrapped household appliances and electrical products. Such systems are commonly modelled as mixed-integer programs, whose solutions will determine the location of individual facilities that optimize material flow. One of the major drawbacks of current models is that they do not adequately address the important issue of uncertainty in demand and supply. Another deficiency in current models is that they are restricted to a two-echelon system. This study addresses these deficiencies by embodying such uncertainties in the model using the technique of fuzzy-chance constrained programming, and by extending the model to a three-echelon system. A heuristic in the form of a hybrid genetic algorithm is then employed to generate low-cost solutions. The overall objective is to find economical solutions to the general problem of determining the volume of appliances to be moved between the three echelons of customer base to collection sites, collection sites to disposal centres and disposal centre to landfill centre/remanufacturing centre; and to the problems of positioning the disposal centres and the landfill centre/remanufacturing centres within the problem domain. A case example in China is presented and the quality and robustness of the solutions are explored through sensitivity analysis.     

Application of fuzzy optimization to a supply chain network design: A case study of an edible vegetable oils manufacturer

This study applies fuzzy sets to integrate the supply chain network of an edible vegetable oils manufacturer. The proposed fuzzy multi-objective linear programming model attempts to simultaneously minimize the total transportation costs. The first part of the total transportation costs is between suppliers and silos; and rest one is between manufacturer and warehouses. The approach incorporates all operating realities and actual flow patterns at production/distribution network with reference to demands of warehouses, capacities of tin and pet packaging lines. The model has been formulated as a multi objective linear programming model where data are modeled by triangular fuzzy numbers. Finally, the developed fuzzy model is applied for the case study, compiled the results and discussed.     

Bag rationalisation for a food manufacturer

A food manufacturer has decided to rationalise the types of bags used to pack their products with a view to achieving economies of scale and improved efficiency. Under the new regime, the name and characteristics of the product are to be printed on the bag during packaging, with the bag colour as a secondary distinctive feature. There are several ways of describing the director's conflicting objectives of minimising both cost and customer colour conflicts. We model the problem in two ways: as a Zero-One Integer Programme, and as a variant of a classical Graph Colouring Problem. Problem-specific observations, and data pre-processing, enable us to decompose the originally intractable problem, and to solve it using commercial integer programming software. Our solution compares favourably with that from a heuristic for graph colouring and our recommended allocation of eight colours was accepted for implementation.     

Integrated service network design for a cross-docking supply chain network

This paper considers an integrated service network design problem for a given set of freight demands that is concerned with integration of locating cross-docking (CD) centers and allocating vehicles for the associated direct (transportation) services from origin node to a CD center or from a CD center to the destination node. For the vehicle allocation, direct services (sub-routes) should be determined for the given freight demands, and then the vehicle allocation has to be made in consideration of routing for the associated direct service fulfillment subject to vehicle capacity and service time restriction. The problem is modeled as a path-based formulation for which a tabu-search-based solution algorithm is proposed. To guarantee the performance of the proposed solution algorithm, strong valid inequalities are derived based on the polyhedral characteristics of the problem domain and an efficient separation heuristic is derived for identifying any violated valid inequalities. Computational experiments are performed to test the performance of the proposed solution algorithm and also that of a valid-inequality separation algorithm, which finds that the solution algorithm works quite well and the separation algorithm provides strengthened lower bounds. Its immediate application may be made to strategic (integrated) service network designs and to tactical service network planning for the CD network.     

End-to-end availability-dependent pricing of network services

We discuss how a new pricing scheme can be integrated within a communication network. The pricing scheme is based on the availability of end-to-end communications, and is an alternative to congestion pricing, which is not applicable when communication capacity is higher than demand (as happens in most communication backbone networks). We also investigate how, based on this scheme, an optimization algorithm for updating the network topology can be applied. The network update problem is modeled as a combinatorial optimization problem, which is approximately solved using a Genetic Algorithm. The good results obtained in a case study show that the method is robust and can be applied even when end-to-end availability measures can only be computed approximately (in this case, using a Monte Carlo method). This research is part of the PAIR associated research project, supported by the INRIA, France, and has also received the support of ECOS-Sud, under Action U03E02. The participation of Pablo Rodríguez was supported by the French Embassy in Uruguay as part of the French Ministère des Affaires étrangères scientific cooperation program; and by the “Programa de Jóvenes Investigadores” of CSIC, UDELAR, Uruguay.     

Least-cost network topology design for a new service

We describe an implementation of the tabu search metaheuristic that effectively finds a low-cost topology for a communications network to provide a centralized new service. Our results are compared to those of a greedy algorithm which applies corresponding decision rules, but without the guidance of the tabu search framework. These problems are difficult computationally, representing integer programs that can involve as many as 10,000 integer variables and 2000 constraints in practical applications. The tabu search results approach succeeded in obtaining significant improvements over the greedy approach, yielding optimal solutions to problems small enough to allow independent verification of optimality status and, more generally, yielding both absolute and percentage cost improvements that did not deteriorate with increasing problem size.This research was partially supported by the Air Force Office of Scientific Research and the Office of Naval Research Contract No. F49629-90-C-0033.     

Encapsulation of air vessel design in a neural network

The trial and error process of calculating the characteristics of an air vessel suitable to protect a rising main against the effects of hydraulic transients has proved to be cumbersome for the design engineer. The own experience and sets of charts, which can be found in the literature, can provide some help. The aim of this paper is to present a neural network allowing instantaneous and direct calculation of air and vessel volumes from the system parameters. This neural network has been implemented in the hydraulic transient simulation package DYAGATS.     

Reallocation of paths of ABR services in a multistage interconnection network (MIN)-type ATM switch network

In this paper, we develop algorithms for reallocating paths of available bit rate (ABR) services in an asynchronous transfer mode (ATM) switch network. ATM traffic control for fair share bandwidth allocation is usually performed under the assumption that paths of all services in a switch network are fixed. However, each connection may have multiple paths from an ingress queue to an egress queue since most ATM switch networks have the structure of the multistage interconnection network of switch elements. Therefore, paths already established for ABR connections may have to be changed to enhance throughput of the switch, if the ATM switch has the capability of adjusting paths of ABR connections while they are being served. We present three algorithms, in which throughput for ABR connections is estimated to decide whether or not paths of the connections should be changed. These algorithms are compared with an existing traffic management algorithm through simulation experiments. Results of the experiments show that the suggested algorithms give higher throughput in terms of the number of transmitted ABR cells without increasing the delay time of ABR services as well as quality of service (QoS) guaranteed services or decreasing the number of transmitted cells of QoS guaranteed services.     

General network design: A unified view of combined location and network design problems

This paper presents a unified framework for the general network design problem which encompasses several classical problems involving combined location and network design decisions. In some of these problems the service demand relates users and facilities, whereas in other cases the service demand relates pairs of users between them, and facilities are used to consolidate and re-route flows between users. Problems of this type arise in the design of transportation and telecommunication systems and include well-known problems such as location-network design problems, hub location problems, extensive facility location problems, tree-star location problems and cycle-star location problems, among others. Relevant modeling aspects, alternative formulations and possible algorithmic strategies are presented and analyzed.     

Iterative improvement methods for a multiperiod network design problem

We address an important problem in telecommunications planning: the multiperiod network expansion problem. Our aim is to show that it can be efficiently solved using a new local search approach. To achieve our goal, we first show how to adapt the problem's formulation to meet our local search program's requirements. We then describe GLIT (Generic Local Improvement Template), a new, generic auto-calibrating local search algorithm; the different neighbouring strategies that we designed specifically for this problem; as well as a Genetic algorithm for this problem. We compare and discuss the performance of these algorithms using extensive computational tests on a large range of instances with up to 7500 arcs. These experiments show that GLIT clearly outperforms competitive approaches, especially when it is coupled with Genetic algorithms. We also show that the hybrid algorithms Genetic/Tabu, Genetic/Simulated Annealing, and finally Genetic/GLIT all outperform both pure Genetic and pure local search algorithms.     

Consolidation of customer orders into truckloads at a large manufacturer

We describe the development and operation of an interactive system based on a mathematical optimisation model which is used by a major US manufacturer to consolidate customer orders into truckloads. Dozens of users employ the system daily for planning delivery of orders from manufacturing plants to customers by truckload carriers, saving numerous hours of the users' time and reducing transportation costs.     

The multi-layered network design problem

We address the problem of designing a network built on several layers. This problem occurs in practical applications but has not been studied extensively from the point of view of global optimisation, since the problem of designing a single-layered network is complex. An example of an application is the design of a virtual network (Internet Protocol) built on a sparse optical transport network.     

Multi-period reverse logistics network design

The configuration of the reverse logistics network is a complex problem comprising the determination of the optimal sites and capacities of collection centers, inspection centers, remanufacturing facilities, and/or recycling plants. In this paper, we propose a profit maximization modeling framework for reverse logistics network design problems. We present a mixed-integer linear programming formulation that is flexible to incorporate most of the reverse network structures plausible in practice. In order to consider the possibility of making future adjustments in the network configuration to allow gradual changes in the network structure and in the capacities of the facilities, we consider a multi-period setting. We propose a multi-commodity formulation and use a reverse bill of materials in order to capture component commonality among different products and to have the flexibility to incorporate all plausible means in tackling product returns. The proposed general framework is justified by a case study in the context of reverse logistics network design for washing machines and tumble dryers in Germany. We conduct extensive parametric and scenario analysis to illustrate the potential benefits of using a dynamic model as opposed to its static counterpart, and also to derive a number of managerial insights.     

The hierarchical network design problem

In this paper the authors introduce the hierarchical network design problem (HNDP). The object of the HNDP is to identify the least cost, two-level hierarchical network. The network must include a primary path from a predetermined starting node to a predetermined terminus node. In addition, each node not on the primary path must be connected to some node on that path by means of a secondary path. The problem is initially formulated as an integer linear program. An heuristic is then presented which employs a K shortest path algorithm, and a minimum spanning tree algorithm. Heuristic results of two sample problems are presented and compared to the results obtained by solving the integer LP formulation. Potential applications of the formulation are also discussed.     

Equilibrium network design of shared-vehicle systems

An equilibrium network design model is formulated to determine the optimal configuration of a vehicle sharing program (VSP). A VSP involves a fleet of vehicles (bicycles, cars, or electric vehicles) positioned strategically across a network. In a flexible VSP, users are permitted to check out vehicles to perform trips and return the vehicles to stations close to their destinations. VSP operators need to determine an optimal configuration in terms of station locations, vehicle inventories, and station capacities, that maximizes revenue. Since users are likely to use the VSP resources only if their travel utilities improve, a generalized equilibrium based approach is adopted to design the system. The model takes the form of a bi-level, mixed-integer program. Model properties of uniqueness, inefficiency of equilibrium, and transformations that lead to an exact solution approach are presented. Computational tests on several synthetic instances demonstrate the nature of the equilibrium configuration, the trade-offs between operator and user objectives, and insights for deploying such systems.     

Optimizing fracture design based on a novel RBF neural network

The factors affecting performance of fractured wells are analyzed in this work. The static and dynamic geologic data of fractured well and fracturing treatment parameters obtained from 51 fractured wells in sand reservoirs of Zhongyuan oilfield are analyzed by applying the grey correlation method. Ten parameters are screened, including penetrability, porosity, net thickness, oil saturation, water cut, average daily production, and injection rate, amount cementing front spacer, amount sand-carrying agent and amount sand. With the novel Radial Basis Function neural network model based on immune principles, 13 parameters of 42 wells out of 51 are used as the input samples and the stimulation ratios as the output samples. The nonlinear interrelationship between the input samples and output samples are investigated, and a productivity prediction model of optimizing fracture design is established. The data of the rest 7 wells are used to test the model. The results show that the relative errors are all less than 7%, which proves that the novel Radial Basis Function neural network model based on immune principles has less calculation, high precision and good generalization ability.     

Equilibrium charges of multi-period allocation mechanisms for network services

Several new network services require a periodical resource allocation. For this purpose several auction-based multi-period allocation mechanisms have been proposed. This article derives explicitly resulting equilibrium charges in a simple mathematical model, i.e., constant session holding times, identical bandwidth request and independently identically uniformly distributed bids for the multi-period VCG and the PRENORM mechanism. In the same manner the expected revenue of the network provider can be calculated. Moreover, the analysis leads to an important condition for the protection parameter α of the PRENORM mechanism, such that the charging system does not break down. This research was partly financed by the Austrian Science Fund under contract number P18161-N13 (“Control of heterogenous systems”).     

Models for a Steiner multi-ring network design problem with revenues

The Steiner multi-ring network design problem with revenues consists of designing node-disjoint multiple rings connected by a specific node (hub) and passing through all the nodes with high priority of service and some of the nodes with low priority of service. The number of nodes in each ring has an upper bound to assure a certain level of service. Besides the usual arc link costs, we also consider revenues between each pair of nodes in the same ring, even when they are not connected by a direct link. The objective is to minimize the difference between the total connection cost and total revenue. The problem is a generalization of the problem studied in Gouveia and Pires (Eur J Oper Res 133:21–31, 2001a) and it can also be seen as a combination of variants of two NP-Hard problems, the vehicle routing problem and the maximum edge-weighted clique problem. We introduce and discuss two types of integer linear programming formulations and propose some valid inequalities to strengthen the linear programming relaxation. Computational results are presented to evaluate the quality of the linear programming relaxation bounds associated with these formulations as well as efficiency of the models to obtain the optimal integer solutions.     

Tree network design avoiding congestion

We introduce in this paper an optimal method for tree network design avoiding congestion. We see this problem arising in telecommunication and transportation networks as a flow extension of the Steiner problem in directed graphs, thus including as a particular case any alternative approach based on the minimum spanning tree problem. Our multi-commodity formulation is able to cope with the design of centralized computer networks, modern multi-cast multi-party or hub-based transportation trees. The objective in such cases is the minimization of the sum of the fixed (structural) and variable (operational) costs of all the arcs composing an arborescence that links the origin node (switching center, server, station) to every demand node (multi-cast participants, users in general). The non-linear multi-commodity flow model is solved by a generalized Benders decomposition approach.