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All European countries are building structures to support collection and recovery of electric and electronic waste (WEEE). In this work, the study of a Portuguese recovery network is presented. A MILP model is developed in order to determine the best WEEE network structure as well as the associated optimal plan. Several different analyses are performed.

This paper explores the designing principles to create resilient Supply Chains ({SC)} with the ability to return, rapidly, to the initial stage or to an improved one after a disturbance occurrence. Supply chain disturbances and failure modes are identified and discussed. The concept of resilience applied to {SCs} is defined and explored; a conceptual {SC} Resilience Index and a {SC} Resilience Indicator are proposed. A framework for the design of resilient supply chains is introduced, identifying main {SC} characteristic that can be modified to increase {SC} resilience and to mitigate its inherent vulnerability. An exploratory simulation study is presented to test the design of alternative {SC} scenarios.

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We give a survey on generalized Krein algebras \(K_{p,q}^{\alpha,\beta}\) and their applications to Toeplitz determinants. Our methods originated in a paper by Mark Krein of 1966, where he showed that \(K_{2,2}^{1/2,1/2}\) is a Banach algebra. Subsequently, Widom proved the strong Szeg\H{o} limit theorem for block Toeplitz determinants with symbols in \((K_{2,2}^{1/2,1/2})_{N\times N}\) and later two of the authors studied symbols in the generalized Krein algebras \((K_{p,q}^{\alpha,\beta})_{N\times N}\), where \(\lambda:=1/p+1/q=\alpha+\beta\) and \(\lambda=1\). We here extend these results to \(0<\lambda<1\). The entire paper is based on fundamental work by Mark Krein, ranging from operator ideals through Toeplitz operators up to Wiener-Hopf factorization.

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Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let φH(n) be the smallest number φ such that every graph G of order n admits an H-decomposition with at most φ parts. In the paper it is proved that φH(n)=tr−1(n)+o(n2) for every graph H of chromatic number r≥3, where tr(n) is the maximum size of an r-partite graph of order n. Moreover, when H is bipartite, the authors determine φH(n) with a constant additive error.