A multi-period and multi-product optimizer for cooperative supply chains

Members in a traditional supply chain compete to reduce their individual costs. But total cost is minimized in a cooperative, or a corporate managed, supply chain. A lower average cost and a lower cost variation are achieved by cooperative individual members in the long-run. The problem is formulated and solved as an integrated flow network. Previous research is expanded to include multi-period and multi-product cooperative supply chain with possibility of holding inventory in a multi-stage, multi-member setup. A Cooperative Supply Optimizer System (CSOS), a software-based coordination mechanism, is developed for large chains. It gathers operational information from members of the supply chain, and then guides them on ordering decisions for a minimum cost of the entire supply chain. Simulation results indicate an approximately 26% reduction in total supply chain costs, utilizing this formulation over a competitive setup. As the holding costs increase, the problem decomposes into single period (Just-in-time) again. The disturbing bullwhip effect disappears in cooperative supply chains

Chiral perturbation theory in a magnetic background - finite-temperature effects

We consider chiral perturbation theory for SU(2) at finite temperature $T$ in a constant magnetic background $B$. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as between $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field. The increase of $T_c$ as a function of $B$ is in agreement with most model calculations but in disagreement with recent lattice calculations.Comment: 24 pages and 9 fig

Inverse magnetic catalysis in field theory and gauge-gravity duality

We investigate the surface of the chiral phase transition in the three-dimensional parameter space of temperature, baryon chemical potential and magnetic field in two different approaches, the field-theoretical Nambu-Jona-Lasinio (NJL) model and the holographic Sakai-Sugimoto model. The latter is a top-down approach to a gravity dual of QCD with an asymptotically large number of colors and becomes, in a certain limit, dual to an NJL-like model. Our main observation is that, at nonzero chemical potential, a magnetic field can restore chiral symmetry, in apparent contrast to the phenomenon of magnetic catalysis. This "inverse magnetic catalysis" occurs in the Sakai-Sugimoto model and, for sufficiently large coupling, in the NJL model and is related to the physics of the lowest Landau level. While in most parts our discussion is a pedagogical review of previously published results, we include new analytical results for the NJL approach and a thorough comparison of inverse magnetic catalysis in the two approaches.Comment: 37 pages, 11 figures, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Magnetic Catalysis: A Review

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.Comment: 37 pages, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee. Version 2: references adde

Lattice QCD Simulations in External Background Fields

We discuss recent results and future prospects regarding the investigation, by lattice simulations, of the non-perturbative properties of QCD and of its phase diagram in presence of magnetic or chromomagnetic background fields. After a brief introduction to the formulation of lattice QCD in presence of external fields, we focus on studies regarding the effects of external fields on chiral symmetry breaking, on its restoration at finite temperature and on deconfinement. We conclude with a few comments regarding the effects of electromagnetic background fields on gluodynamics.Comment: 31 pages, 10 figures, minor changes and references added. To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

A quantitative examination of competition, coopetition and cooperation in supply chains

Traditionally, the members of a supply chain compete to reduce their individual costs. However, as collaborative supply chain approach is urged within industries to reduce the overall costs, either full cooperation or partial coopetition is considered by the members. In cooperative approach, members benefit from lower overall costs and lower cost variations. But individually, some seem better off in a competitive approach in a single period considering their local costs. Coopetition, or partial cooperation, may be suggested as a compromise to lower overall supply chain costs, while members choose alliances towards lower average costs and cost variations.A multi-stage, multi-member, multi-product and single period supply chain model is considered with deterministic demand, capacity and cost. Product prices are assumed to be constant. The objective is to minimize total production and distribution costs of the overall chain. Four distinct cases are considered, modeled, simulated and compared. These cases are complete competition, integrated cooperation, two-stage supply chain partition, and partial coopetition. Quantitative conclusions from the cost performance ratios are drawn using the simulation results