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The recent COVID-19 outbreak and severe natural disasters make the design of the humanitarian supply chain network (HSCN) a crucial strategic issue in a pre-disaster scenario. The HSCN design problem deals with the location/allocation of emergency response facilities (ERFs). This paper aims to propose and demonstrate how to design an efficient HSCN configuration under the risk of ERF disruptions.

This paper considers four performance measures simultaneously for the HSCN design by formulating a weighted goal programming (WGP) model. Solving the WGP model with different weight values assigned to each performance measure generates various HSCN configurations. This paper transforms a single-stage network into a general two-stage network, treating each HSCN configuration as a decision-making unit with two inputs and two outputs. Then a two-stage network data envelopment analysis (DEA) approach is applied to evaluate the HSCN schemes for consistently identifying the most efficient network configurations.

Among various network configurations generated by the WGP, the single-stage DEA model does not consistently identify the top-ranked HSCN schemes. In contrast, the proposed transformation approach identifies efficient HSCN configurations more consistently than the single-stage DEA model. A case study demonstrates that the proposed transformation method could provide a more robust and consistent evaluation for designing efficient HSCN systems. The proposed approach can be an essential tool for federal and local disaster response officials to plan a strategic design of HSCN.

This study presents how to transform a single-stage process into a two-stage network process to apply the general two-stage network DEA model for evaluating various HSCN configurations. The proposed transformation procedure could be extended for designing some supply chain systems with conflicting performance metrics more effectively and efficiently.

The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.

The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.

The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.

In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

We consider the kernel-based classifier proposed by Younso (2017). This nonparametric classifier allows for the classification of missing spatially dependent data. The weak consistency of the classifier has been studied by Younso (2017). The purpose of this paper is to establish strong consistency of this classifier under mild conditions. The classifier is discussed in a multi-class case. The results are illustrated with simulation studies and real applications.

In this paper, the main focus is on supply and demand auction systems with resource pooling in modern supply chain from a theoretical modeling perspective. The supply and demand auction systems in modern supply chains among manufacturers and suppliers serve as information sharing mechanisms. The purpose of this paper is to match the supply and demand such that a modern supply chain can achieve incentive compatibility and economic efficiency. The authors design such a supply and demand auction system that can integrate resources to efficiently match the supply and demand.

The authors propose three theoretic models of modern supply chain auctions with resource pooling according to the Vickrey auction principle. They are supply auction model with demand resource pooling, demand auction model with supply resource pooling, and double auction model with demand and supply resource pooling. For the proposed auction models, the authors present three corresponding algorithms to allocate resources in the auction process by linear programming, and study the incentive compatibility and define the Walrasian equilibriums for the proposed auction models. The authors show that the solutions of the proposed algorithms are Walrasian equilibriums.

By introducing the auction mechanism, the authors aim to realize the following three functions. First is price mining: auction is an open mechanism with multiple participants. Everyone has his own utility and purchasing ability. So, the final price reflects the market value of the auction. Second is dynamic modern supply chain construction: through auction, firm can find appropriate partner efficiently. Third is resources integration: in business practices, especially in modern supply chain auctions, auctioneers can integrate resources and ally buyers or sellers to gain more efficiency in auctions.

In the paper, the authors propose three theoretic models and corresponding algorithms of modern supply chain auctions with resource pooling according using the Vickrey auction principle, which achieves three functions: price mining, dynamic modern supply chain construction and resources integrating. Besides, these proposed models are much closer to practical settings and may have potential applications in modern supply chain management.

In this work, the authors are interested in the notion of vector valued and set valued Pettis integrable pramarts. The notion of pramart is more general than that of martingale. Every martingale is a pramart, but the converse is not generally true.

In this work, the authors present several properties and convergence theorems for Pettis integrable pramarts with convex weakly compact values in a separable Banach space.

The existence of the conditional expectation of Pettis integrable mutifunctions indexed by bounded stopping times is provided. The authors prove the almost sure convergence in Mosco and linear topologies of Pettis integrable pramarts with values in (cwk(E)) the family of convex weakly compact subsets of a separable Banach space.

The purpose of the present paper is to present new properties and various new convergence results for convex weakly compact valued Pettis integrable pramarts in Banach space.

In the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is described by an N-uplet of N-functions satisfying the Δ₂-condition, within the fulfilling of anisotropic Sobolev-Orlicz space. In addition, the resulting analysis requires the development of some new aspects of the theory in this field. The source term is merely integrable.

An approximation procedure and some priori estimates are used to solve the problem.

The authors prove the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. The resulting analysis requires the development of some new aspects of the theory in this field.

To the best of the authors’ knowledge, this is the first paper that investigates the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain.

The purpose of this article is to determine necessary and sufficient conditions in order that (D, K) to be an S-accr pair, where D is an integral domain and K is a field which contains D as a subring and S is a multiplicatively closed subset of D.

The methods used are from the topic multiplicative ideal theory from commutative ring theory.

Let S be a strongly multiplicatively closed subset of an integral domain D such that the ring of fractions of D with respect to S is not a field. Then it is shown that (D, K) is an S-accr pair if and only if K is algebraic over D and the integral closure of the ring of fractions of D with respect to S in K is a one-dimensional Prüfer domain. Let D, S, K be as above. If each intermediate domain between D and K satisfies S-strong accr*, then it is shown that K is algebraic over D and the integral closure of the ring of fractions of D with respect to S is a Dedekind domain; the separable degree of K over F is finite and K has finite exponent over F, where F is the quotient field of D.

Motivated by the work of some researchers on S-accr, the concept of S-strong accr* is introduced and we determine some necessary conditions in order that (D, K) to be an S-strong accr* pair. This study helps us to understand the behaviour of the rings between D and K.