Dual Relaxation Research Articles

Probing aqueous diclofenac potassium: Unveiling molecular interactions through dielectric relaxation spectroscopy and MD simulation

Diclofenac potassium (DK) is a salt and undergoes ionization in an aqueous environment. The detailed information about the molecular structure and interactions of such aqueous ionic solutions holds substantial significance in the field of pharmaceutics. This comprehension facilitates the enhancement of pharmaceutical formulations, leading to improved bioavailability, stability, and therapeutic efficacy. It also contributes to the optimization of drug delivery systems. Molecular interactions in the aqueous solutions of DK were studied using dielectric relaxation spectroscopy (DRS) and molecular dynamic (MD) simulation. In DRS, complex dielectric permittivity, ε∗(f) for aqueous solutions of DK of varying concentrations were measured in the frequency range of 20 Hz to 2 MHz at five different temperatures ranging from 303.15 K to 323.15 K. Complex ac conductivity, σ∗(f) and dc conductivity (σdc) were determined from the complex dielectric permittivity. The effect of concentration and temperature on complex permittivity and allied parameters are discussed. The dielectric spectra of aqueous DK reveal dual relaxation processes i.e., normal (n) relaxation and alpha (α) relaxation. The dielectric strength is predominant for α-process and n-process in the low (0 < X ≤ 0.0299) and high (0.029 < X ≤ 0.0822) concentration range respectively. Moreover, Stoke’s relation between dielectric relaxation time, ion mobility and viscosity of the aqueous solutions is discussed. MD simulation at 303.15 K temperature has also been conducted to get additional information on molecular interactions between DK and/or H2O molecules through hydrogen bonding (HB).

Constructing multi-polarization in metal–organic framework gels for electromagnetic wave absorption via ethanolamine hetero-coordination

Metal–organic framework (MOF) gels offer the potential for tunable electromagnetic wave (EMW) absorption owing to their customizable MOF cross-linked networks and strongly polar liquids. This overcomes the drawbacks of traditional MOF-derived absorbers; however, the corresponding EMW loss mechanism is absent. Here, a zeolite imidazole framework (ZIF) was used as a functional unit in conjunction with ethanolamine (EtA) hetero-coordination and methanol to fabricate ZIF organogels with the desired EMW absorption. The pore size of ZIF maintains the permeability for EtA and the methanol-barrier properties, which results in the formation of free –NH2 and associated –NH2 for EtA. The two corresponding species of dipole polarization losses provide additional EMW attenuation. Furthermore, the intensity inversion of the dual relaxation modes caused by the change in the size of the ZIF colloidal particles was used to improve the EMW absorption for the first time. ZIF organogels exhibited a strong correlation between dielectric properties and metal node species/EtA coordination density/hydrogen bonds, indicating that the absorption properties can be accurately regulated. Me-ZnCo-1 sample demonstrates the optimal effective absorption bandwidth of 6.59 GHz at 2.19 mm. This study not only elucidates the EMW loss mechanism of ZIF organogel networks but also proposes a creative design strategy for EMW-absorbing MOF gels.

Active Distribution Network Expansion Planning Based on Wasserstein Distance and Dual Relaxation

In the future, a high proportion of distributed generations (DG) will be integrated into the distribution network. The existing active distribution network (ADN) planning methods have not fully considered multiple uncertainties, differentiated regulation modes or the cost of multiple types of interconnection switches. Meanwhile, it is difficult to solve large-scale problems at small granularity. Therefore, an expansion planning method of ADN considering the selection of multiple types of interconnection switches is proposed. Firstly, a probability distribution ambiguity set of DG output and electrical-load consumption based on the Wasserstein distance is established for dealing with the issue of source-load uncertainty. Secondly, a distributionally robust optimization model for collaborative planning of distribution network lines and multiple types of switches based on the previously mentioned ambiguity set is established. Then, the original model is transformed into a mixed integer second-order cone programming (SOCP) model by using the convex relaxation method, the Lagrangian duality method and the McCormick relaxation method. Finally, the effectiveness of the proposed method is systematically verified using the example of Portugal 54. The results indicate that the proposed method raises the annual net profit by nearly 5% compared with the traditional planning scheme and improves the reliability and low-carbon nature of the planning scheme.

A Dual Relaxation Method for Neural Network Verification

In the robustness verification of neural networks, formal methods have been used to give deterministic guarantees for neural networks. However, recent studies have found that the verification method of single-neuron relaxation in this field has an inherent convex barrier that affects its verification capability. To address this problem, we propose a new verification method by combining dual-neuron relaxation and linear programming. This method captures the dependencies between different neurons in the same hidden layer by adding a two-neuron joint constraint to the linear programming model, thus overcoming the convex barrier problem caused by relaxation for only a single neuron. Our method avoids the combination of exponential inequality constraints and can be computed in polynomial time. Experimental results show that we can obtain tighter bounds and achieve more accurate verification than single-neuron relaxation methods.

Binary and ternary ferromagnetic alloy/C nanocapsules for improved X-band microwave absorption

The dielectric-magnetic matching effect emerges from the presence of dual dielectric relaxation and multiple magnetic resonances. This phenomenon becomes a strategic approach in the quest to enhance microwave absorption performance by optimizing magnetic components. Herein, binary and ternary ferromagnetic alloy with tunable components embedded in carbon skeleton (core/shell) nanocapsules has been successfully fabricated by one step metal-organic chemical vapor deposition. The core/shell structure design introduces numerous interfaces that amplify dielectric loss stemming from polarization. It is important to emphasize that modifying the composition of magnetic core in these nanocapsules effectively regulates the impedance matching characteristics. As a result, the CoFeNi/C nanocapsules demonstrate an optimal reflection loss (RLmin) of −53.6 dB at a thickness of 2.55 mm, alongside an effective absorption bandwidth of 5.92 GHz at a thickness of 2.05 mm, with a filling ratio as low as 20 wt%. This study has provided valuable insights into a promising avenue for fabricating dielectric-magnetic nanocomposites with outstanding microwave attenuation capabilities through the manipulation of composited elements.

Hepatic steatosis modeling and MRI signal simulations for comparison of single- and dual-R2* models and estimation of fat fraction at 1.5T and 3T

Background and objectiveMagnetic resonance imaging (MRI) has emerged as a noninvasive clinical tool for assessment of hepatic steatosis. Multi-spectral fat-water MRI models, incorporating single or dual transverse relaxation decay rate(s) (R2*) have been proposed for accurate fat fraction (FF) estimation. However, it is still unclear whether single- or dual-R2* model accurately mimics in vivo signal decay for precise FF estimation and the impact of signal-to-noise ratio (SNR) on each model performance. Hence, this study aims to construct virtual steatosis models and synthesize MRI signals with different SNRs to systematically evaluate the accuracy of single- and dual-R2* models for FF and R2* estimations at 1.5T and 3.0T. MethodsRealistic hepatic steatosis models encompassing clinical FF range (0–60 %) were created using morphological features of fat droplets (FDs) extracted from human liver biopsy samples. MRI signals were synthesized using Monte Carlo simulations for noise-free (SNRideal) and varying SNR conditions (5–100). Fat-water phantoms were scanned with different SNRs to validate simulation results. Fat water toolbox was used to calculate R2* and FF for both single- and dual-R2* models. The model accuracies in R2* and FF estimates were analyzed using linear regression, bias plot and heatmap analysis. ResultsThe virtual steatosis model closely mimicked in vivo fat morphology and Monte Carlo simulation produced realistic MRI signals. For SNRideal and moderate-high SNRs, water R2* (R2*W) by dual-R2* and common R2* (R2*com) by single-R2* model showed an excellent agreement with slope close to unity (0.95–1.01) and R2 > 0.98 at both 1.5T and 3.0T. In simulations, the R2*com-FF and R2*W-FF relationships exhibited slopes similar to in vivo calibrations, confirming the accuracy of our virtual models. For SNRideal, fat R2* (R2*F) was similar to R2*W and dual-R2* model showed slightly higher accuracy in FF estimation. However, in the presence of noise, dual-R2* produced higher FF bias with decreasing SNR, while leading to only marginal improvement for high SNRs and in regions dominated by fat and water. In contrast, single-R2* model was robust and produced accurate FF estimations in simulations and phantom scans with clinical SNRs. ConclusionOur study demonstrates the feasibility of creating virtual steatosis models and generating MRI signals that mimic in vivo morphology and signal behavior. The single-R2* model consistently produced lower FF bias for clinical SNRs across entire FF range compared to dual-R2* model, hence signifying that single-R2* model is optimal for assessing hepatic steatosis.

A Biobased Epoxy Vitrimer with Dual Relaxation Mechanism: A Promising Material for Renewable, Reusable, and Recyclable Adhesives and Composites.

This study presents the synthesis of a novel biobased epoxy monomer derived from vanillin and cystamine, incorporating imine and disulfide exchangeable groups within its structure. A series of epoxy-based vitrimers with two simultaneous exchange relaxation processes have been produced using this monomer. These exchange mechanisms operate without the need for any catalyst. Four different amine curing agents have been employed to achieve vitrimers with glass transition temperatures around 100 °C and excellent thermal stability. Through dynamic-mechanical analyses, thermomechanical properties and vitrimeric characteristics have been investigated, revealing remarkably fast stress relaxation at relatively low temperatures without significant creep below the glass transition temperature. Leveraging the dual exchange mechanism, the chemical degradability of these vitrimers has been explored through two accessible methodologies, and the material's reformation after degradation has been demonstrated in both cases. Furthermore, the material has been mechanically recycled, maintaining almost the same properties. Finally, these materials have been used to fabricate and recycle carbon-fiber-reinforced composite material and reversible adhesives, showcasing their promising potential applications.

Compositional design of C-coated multi-elemental alloy nanoparticles for superior microwave absorption

Exploring improved electromagnetic wave absorption performance in magnetic components involves capitalizing on dual dielectric relaxation and multiple magnetic resonances, ultimately giving rise to a dielectric-magnetic matching effect. Herein, a one-step Metal-organic Chemical Vapor Deposition (MOCVD) method has been utilized to fabricate C-coated ternary and quaternary alloy nanoparticles (FeCoNi, FeCoNiCu, FeCoNiMg, and FeCoNiMn) with tunable magnetization. The results affirm that the capabilities of impedance matching and electromagnetic wave attenuation can be significantly regulated by compositing nanoparticles with different elements. The optimized C-coated FeCoNiMg nanoparticles demonstrate an exceptional capacity for electromagnetic wave attenuation, achieving a reflection loss value of −51.8 dB at a matched thickness of 2.9 mm. Moreover, the absorption bandwidth significantly broadens to 7.60 GHz (10.4 – 18.0 GHz) with a thickness of 2.7 mm. The exceptional performance in electromagnetic attenuation is credited to the dielectric loss and improved impedance matching characteristics induced by the C-coated FeCoNiMg nanoparticles. The findings from this study will be beneficial in the development of lightweight and highly effective electromagnetic wave absorbers using magnetic alloy nanoparticles.

Synthesis and electrorheological behaviour of silica-coated porous metal-organic frameworks

In this paper, Ti-based metal-organic frameworks (MOF-Ti) with internal holes were prepared by a solvothermal method. The Stöber hydrolysis method was used to coat silicon dioxide (SiO2) on the surface of MOF-Ti with ethyl silicate as the silicon source, and the conductivity of the composite particles was controlled by the amount of TEOS added. Furthermore, core-shell MOF-Ti@SiO2 composite nanoparticles were successfully synthesized. Some analyses were performed to determine the morphology, crystal structure, elemental state, and N2 adsorption/desorption properties of MOF-Ti@SiO2 composite particles, and the results show that the synthesis of core/shell structure composite particles was successful. The electrorheological fluid (ERF) with a concentration of 10 wt% made from composite particles demonstrated good electrorheological (ER) performance and anti-settlement capacity. It has been found that the amount of TEOS has a significant impact on the ER performance of ERFs. Furthermore, it is also found in dielectric performance analysis that MOF-Ti with internal holes exhibited a distinctive dual relaxation peak in the ERFs and showed stronger interfacial polarization after SiO2 coating, which is useful for enhanced ER behaviour.

How the spin state tunes the slow magnetic relaxation field dependence in spin crossover cobalt(II) complexes.

A novel family of cobalt(II) compounds with tridentate pyridine-2,6-diiminephenyl type ligands featuring electron-withdrawing substituents of general formula [Co(n-XPhPDI)2](ClO4)2·S [n-XPhPDI = 2,6-bis(N-n-halophenylformimidoyl)pyridine with n = 4 (1-3) and 3 (4); X = I (1), Br (2 and 4) and Cl (3); S = MeCN (1 and 2) and EtOAc (3)] has been synthesised and characterised by single-crystal X-ray diffraction, electron paramagnetic resonance, and static (dc) and dynamic (ac) magnetic measurements combined with theoretical calculations. The structures of 1-4 consist of mononuclear bis(chelating) cobalt(II) complex cations, [CoII(n-XPhPDI)2]2+, perchlorate anions, and acetonitrile (1 and 2) or ethyl acetate (3) molecules of crystallisation. This unique series of mononuclear six-coordinate octahedral cobalt(II) complexes displays both thermally-induced low-spin (LS)/high-spin (HS) transition and field-induced slow magnetic relaxation in both LS and HS states. A complete LS ↔ HS transition occurs for 1 and 2, while it is incomplete for 4, one-third of the complexes being HS at low temperatures. In contrast, 3 remains HS in all the temperature range. 1 and 2 show dual spin relaxation dynamics under the presence of an applied dc magnetic field (Hdc), with the occurrence of faster- (FR) and slower-relaxing (SR) processes at lower (Hdc = 1.0 kOe) and higher fields (Hdc = 2.5 kOe), respectively. On the contrary, 3 and 4 exhibit only SR and FR relaxations, regardless of Hdc. Overall, the distinct field-dependence of the single-molecule magnet (SMM) behaviour along with this family of spin-crossover (SCO) cobalt(II)-n-XPhPDI complexes is dominated by Raman mechanisms and, occasionally, with additional temperature-independent Intra-Kramer [LS or HS (D > 0)] or Quantum Tunneling of Magnetisation mechanisms [HS (D < 0)] also contributing.

Single-molecule magnet behavior in heterometallic decanuclear [Ln2Fe8] (Ln = Y, Dy, Ho, Tb, Gd) coordination clusters.

Five decanuclear lanthanide-iron clusters, formulated as [Ln2Fe8(hmp)10(μ2-OH)4(μ3-OH)2(μ4-O)4(H2O)6]·6ClO4·xH2O (x ≈ 8, Ln = Y for 1; x ≈ 6, Ln = Dy for 2; x ≈ 6, Ln = Ho for 3; x ≈ 7, Ln = Tb for 4; x ≈ 7, Ln = Gd for 5, Hhmp = 2-(hydroxymethyl)pyridine), have been synthesized and structurally characterized. Single-crystal structural analysis reveals that the cluster consists of six face-sharing defective cubane units. Dynamic magnetic investigations indicated that cluster 2 exhibits single-molecule magnet behavior under a zero dc field eliciting an effective energy barrier of Ueff = 17.76 K and a pre-exponential factor of τ0 = 7.93 × 10-8 s. Investigation of the performance of a series of FeIII-DyIII SMMs indicates that the relatively low energy barrier in 2 is associated with the weak ferromagnetic coupling between FeIII and DyIII ions, while the strength of ferromagnetic interaction in these clusters is mainly related to the bond distances between DyIII and O atoms coordinated to FeIII ions. Clusters 3 and 4 exhibit similar dual relaxation pathways under their respective optimal external applied dc field, where the direct relaxation process occurs in the low-frequency area, which impedes the extraction of the Ueff, while the secondary relaxation process appears at a higher frequency, which is probably a connection with intermolecularly driven relaxation. Our findings offer a magneto-structural correlation model for further investigating the single-molecule magnet behavior in lanthanide-iron systems.

Optical Pump-Terahertz Probe Diagnostics of the Carrier Dynamics in Diamonds.

Diamond is a promising material for terahertz applications. In this work, we use a non-invasive optical pump-terahertz probe method to experimentally study the photoinduced carrier dynamics in doped diamond monocrystals and a new diamond-silicon composite. The chemical vapor deposited diamond substrate with embedded silicon microparticles showed two photoinduced carrier lifetimes (short lifetime on the order of 4 ps and long lifetime on the order of 200 ps). The short lifetime is several times less than in boron-doped diamonds and nitrogen-doped diamonds which were grown using a high temperature-high pressure technique. The observed phenomenon is explained by the transport of photoexcited carriers across the silicon-diamond interface, resulting in dual relaxation dynamics. The observed phenomenon could be used for ultrafast flexible terahertz modulation.

Two Pairs of Homochiral Parallelogram-like Dy4 Cluster Complexes with Strong Magneto-Optical Properties.

Two pairs of homochiral Dy(III) tetranuclear cluster complexes derived from (+)/(-)-3-trifluoroacetyl camphor (D-Htfc/L-Htfc), [Dy4(OH)2(L1)4(D-tfc)2(DMF)2]·4DMF (D-1) [H2L1 = (E)-2-(2-hydroxy-3-methoxybenzylideneamino)phenol)]/[Dy4(OH)2(L1)4(L-tfc)2(DMF)2]·4DMF (L-1) and [Dy4(OH)2(L2)4(D-tfc)2(DMF)2]·2H2O·3MeCN (D-2) [H2L2 = (E)-3-(2-hydroxy-3-methoxybenzylideneamino)naphthalen-2-ol]/[Dy4(OH)2(L2)4(L-tfc)2(DMF)2]·2H2O·3MeCN (L-2), were synthesized at room temperature, which have a Dy4 parallelogram-like core. The magnetic studies revealed that D-1 exhibits single-molecule magnet (SMM) behavior under zero dc magnetic field, and its magnetic relaxation has a distinct Raman process in addition to the Orbach process, with the Ueff/k value of 57.5 K and the C value of 28.27 s-1K-2.14; while D-2 displays dual magnetic relaxation behavior at 0 Oe field, with the Ueff/k value 114.8 K for the slow relaxation process (SR) and the C value of 10.656 s-1K-5.80 for the fast relaxation process (FR), respectively. Theoretical calculations indicated that the conjugated groups (phenyl vs naphthyl) of the Schiff base bridging ligands (H2L1 and H2L2) significantly affect the intramolecular magnetic interactions between the Dy3+ ions and ultimately lead to different relaxations. Furthermore, magnetic circular dichroism (MCD) measurements showed that these two pairs of Dy4 enantiomers exhibit strong room temperature magneto-optical Faraday effects; notably, increasing the conjugated group on the Schiff base bridging ligand is beneficial to enhancing the magneto-optical Faraday effects.

Photoresponsive Magnetic Relaxation Behavior of a Highly Stable π···π Interaction-Stacked Framework Based on a DyIII Single-Ion Magnet

Endowing lanthanide single-ion magnets (Ln-SIMs) with high stability and stimulus responsiveness is of significance for the practical applications of these novel magnetic materials, but still of challenge at present. Herein, we report on a highly stable and photoresponsive Ln-SIM system achieved by designing and synthesizing a π···π interaction-stacked framework based on DyIII-SIM (πOF-1). Its molecular formula is [Dy(thqa)] (H3thqa = tris[(8-hydroxyquinoline-2-yl)methylene]amino). Each of its C3-symmetric molecules consists of a thqa3– ligand and a DyIII ion, and it is linked to three neighbors by intermolecular π···π interactions, forming a supermolecular two-dimensional (2D) honeycombed topology. Such unique structure endows πOF-1 with not only air and thermal stability but also excellent chemical stability in different solvents, even in alkali solutions, including a 20 M NaOH aqueous solution. Dual magnetic relaxation behavior was observed in πOF-1. Magnetic dilution revealed that it is related to π···π-mediated intermolecular magnetic interactions. More significantly, both the static magnetic susceptibility and the dual-relaxation behavior of πOF-1 show response to photoirradiation, which could be ascribed to the photo-triggered intermolecular π → π* charge transfer (CT). So far as we know, πOF-1 could be the first Ln-SIM system possessing both a high stability and photoresponsiveness, and also the first photoresponsive Ln-SIM supermolecular system that does not rely on the single-crystal to single-crystal (SCSC) structural transformation. Its successful design and synthesis suggests that the introduction of π···π interactions can be a new strategy to fabricate stable and/or photoresponsive Ln-SIMs.

Preparation of Co@C composite with ultra-wide microwave absorption bandwidth

Co@C composite with an ultra-wide microwave absorption bandwidth was prepared using Co-organic framework@phenolic resin (Co-MOF@PR) as a precursor. In comparison with other composites, the prepared Co@C composite exhibited a wider effective absorption bandwidth (Table 1). At 2.8 mm matching thickness, the obtained minimum reflection loss (RL) was −48.02 dB and the effective absorption bandwidth (RL < -10 dB) was up to 8.20 GHz (9.65–17.85 GHz). The excellent properties can be attributed to the good co-frequency synergy between dual polarization relaxation and dual exchange resonance which greatly improves the impedance matching and dielectric properties of the composite. These results suggested that the prepared Co@C composite can be used for high-frequency (10–18 GHz) microwave absorption.

Multiobjective Optimization for Adaptive Offloading in Distributed Multiuser MIMO Cell-Free 6G Networks

By offloading some computational tasks to the edge server, edge computing can help relieve the increasing computation burden of mobile users and improve the quality of experience of users. In this paper, we investigate the computation offloading in edge computing-enabled multiuser cell-free (CF) multi-input multi-output (MIMO) networks with multiple building baseband units (BBUs). The user association, transmit covariances, CPU-cycle frequencies, and allocated bandwidths are jointly optimized to minimize two objectives: the energy consumption of mobile devices (MDs) and execution delay of tasks. We formulate it as a vector optimization problem and adopt the scalarization technique to transform it into a scalar mixed integer nonlinear programming (MINLP). Then, to solve the MINLP, we introduce user sorting into the framework of branch and bound and propose a sorted MD association (MDA) method. Two key issues are tackled in the proposed MDA, i.e., the lower bound of the MINLP and the updation of incumbent solution. For the first issue, we present a Lagrangian dual relaxation algorithm based on subgradient projection, while the second one involving another nonconvex minimization problem, we propose a successive convex approximation (SCA) based algorithm to solve it. Finally, extensive simulations demonstrate that the proposed method is able to reduce the system cost significantly and achieve better system performance by comparing with the benchmark schemes.

A thermoviscoelastic finite deformation constitutive model based on dual relaxation mechanisms for amorphous shape memory polymers

ABSTRACT This paper proposes a new thermoviscoelastic finite deformation model incorporating dual relaxation mechanisms to predict the complete thermo-mechanical response of amorphous shape memory polymers. The model is underpinned by the detailed microscopic molecular mechanism and effectively reflects the current understanding of the glass transition phenomenon. Novel evolution rules are obtained from the model to characterize the viscous flow, and a new theory named an internal stress model is introduced and combined with the dual relaxation mechanisms to capture the stress recovery. The rationality of the constitutive model is verified as the theoretical results agree well with the experimental data. Moreover, the constitutive model is further simplified to facilitate engineering applications, and it can roughly capture the characteristics of shape memory polymers.

Win-Win Cooperation: Magnetic relaxation switching biosensor for chloramphenicol detection based on the pipet platform and antigen-driven enzyme-free dual signal amplification strategy

Herein, we developed an enzyme-free dual signal amplification magnetic relaxation switching biosensor to detect the high hazard chloramphenicol based on the significant advantages of the pipet platform (low cost and easy operation). The competitive immunoassay was carried out by coating the polydopamine-modified pipets with the antibody, causing a content change of trigger DNA-chloramphenicol-antigen conjugate (the first signal amplification) in the supernatant. This triggered the aggregation of magnetic nanoparticles with three-dimensional DNA network structures (the second signal amplification) for chloramphenicol quantitative analysis by changes in transverse relaxation time (T2). The pipet platform can simplify the sample pretreatment process to eliminate the potential interference with magnetic probes. Its low-cost combined with the enzyme-free strategy greatly reduces the overall detection expenses. The antigen-driven dual signal amplification strategy not only has high sensitivity (1.37 pg/mL), but also provides an alternative path for the efficient combination of immunoassay and DNA signal amplification.

Distributionally robust transactive control for active distribution systems with SOP-connected multi-microgrids

The increasing demand for distributed energy and active load increases the risk of voltage violations in active distribution systems. This paper proposes a distributionally robust transactive control method for local energy trading and network operation management of active distribution systems with interconnected microgrids. In particular, the emerging SOP technology is used for the flexible connection of the multi-microgrids (MMGs). First, the local energy interactive market between distribution network operator (DNO) and regional microgrids is constructed to simultaneously solve the economic and security problems of distribution networks considering the energy trading scenarios and various operational constraints. Then, the dual relaxation technique is used to transform the two-layer structure model into a single-layer model. Furthermore, the single-layer game model is further transformed into a two-stage distributed robust problem considering the uncertainties of load demand and renewable power outputs, and the second stage of the problem is decomposed into multiple parallel subproblems without dual information. Finally, numerical simulations on IEEE-33 test system verify the advantages and effectiveness of the proposed method.

Two-stage stochastic nonlinear winner determination for logistics service procurement auctions under quantity discounts

Quantity discount is a frequently adopted scheme that has not been explicitly investigated in logistics service procurement auctions. This paper focuses on a revised winner determination problem under quantity discounts and demand uncertainty for a fourth-party logistics (4PL) provider in a combinatorial reverse auction. To characterize our research problem, a two-stage stochastic nonlinear programming model is constructed. Inspired by the idea of sample average approximation (SAA), the nonlinear model is reformulated as a deterministic mixed integer linear programming model by using a linearization technique with superior expressions. Since the reformulation has a large number of decision variables and constraints, we integrate SAA with a dual decomposition Lagrangian relaxation technique (DDLR) to develop a solution method called SAA-DDLR. Numerical experiments are conducted to illustrate the effectiveness and applicability of our model and method. Sensitivity analysis reveals that both the 4PL and 3PLs can benefit from the quantity discount scheme. Managerial insights are drawn for the 4PL to run a cost-effective logistics system in the presence of quantity discounts.