Optimal consignment stocking policies for a supply chain under different system constraints

The research aims are to enable the decision maker of an integrated vendor-buyer system under Consignment Stock (CS) policy to make the optimal/sub-optimal production/replenishment decisions when some general and realistic critical factors are considered. In the system, the vendor produces one product at a finite rate and ships the outputs by a number of equal-sized lots within a production cycle. Under a long-term CS agreement, the vendor maintains a certain inventory level at the buyer’s warehouse, and the buyer compensates the vendor only for the consumed products. The holding cost consists of a storage component and a financial component. Moreover, both of the cases that the unit holding costs may be higher at the buyer or at the vendor are considered. Based upon such a system, four sets of inventory models are developed each of which considers one more factor than the former. The first set of models allows a controllable lead-time with an additional investment and jointly determines the shipping size, the number of shipments, and the lead time, that minimize the yearly joint total expected cost (JTEC) of the system. The second set of models considers a buyer’s capacity limitation which causes some shipments to be delayed so that the arrival of these shipments does not cause the buyer’s inventory to go beyond its limitation. As a result, the number of delayed shipments is added as the fourth decision variable. A variable demand rate is allowed in the third set of models. Uncertainty caused by the varying demand are controlled by a safety factor, which becomes the fifth decision variable. Finally, the risk of obsolescence of the product is considered in the fourth model. The first model is solved analytically, whereas the rest are not, mainly because of the complexity of the problem and the number of variables being considered. Three doubly-hybrid meta-heuristic algorithms that combine two different hybrid meta-heuristic algorithms are developed to provide a solution procedure for the rest of models. Numerical experiments illustrate the solution procedures and reveal the effects of the buyer’s capacity limitation, the effects of the variable demand rate, and the effects of the risk of obsolescence, on the system. Furthermore, sensitivity analysis shows that some of the system parameters (such as the backorder penalty, the extra space penalty, the ratio of the unit holding cost of the vendor over that of the buyer) are very influential to the joint system total cost and the optimal solutions of the decision variables

Zc(3900)Z_c(3900) as a DDˉ∗D\bar{D}^* molecule from the pole counting rule

A comprehensive study on the nature of the $Z_c(3900)$ resonant structure is carried out in this work. By constructing the pertinent effective Lagrangians and considering the important final-state-interaction effects, we first give a unified description to all the relevant experimental data available, including the $J/\psi\pi$ and $\pi\pi$ invariant mass distributions from the $e^+e^-\to J/\psi\pi\pi$ process, the $h_c\pi$ distribution from $e^+e^-\to h_c\pi\pi$ and also the $D\bar D^{*}$ spectrum in the $e^+e^-\to D\bar D^{*}\pi$ process. After fitting the unknown parameters to the previous data, we search the pole in the complex energy plane and find only one pole in the nearby energy region in different Riemann sheets. Therefore we conclude that $Z_c(3900)$ is of $D\bar D^*$ molecular nature, according to the pole counting rule method~[Nucl.~Phys.~A543, 632 (1992); Phys.~Rev.~D 35,~1633 (1987)]. We emphasize that the conclusion based upon the pole counting method is not trivial, since both the $D\bar D^{*}$ contact interactions and the explicit $Z_c$ exchanges are introduced in our analyses and they lead to the same conclusion.Comment: 21 pages, 9 figures. To match the published version in PRD. Additional discussion on the spectral density function is include

A kilonova associated with GRB 070809

For on-axis typical short gamma-ray bursts (sGRBs), the forward shock emission is usually so bright that renders the identification of kilonovae (also known as macronovae) in the early afterglow ($t<0.5$ d) phase rather challenging. This is why previously no thermal-like kilonova component has been identified at such early time except in the off-axis dim GRB 170817A associated with GW170817. Here we report the identification of an unusual optical radiation component in GRB 070809 at $t\sim 0.47$ d, thanks plausibly to the very-weak/subdominant forward shock emission. The optical emission with a very red spectrum is well in excess of the extrapolation of the X-ray emission that is distinguished by an unusually hard spectrum, which is at odds with the forward shock afterglow prediction but can be naturally interpreted as a kilonova. Our finding supports the speculation that kilonovae are ubiquitous , and demonstrates the possibility of revealing the neutron star merger origin with the early afterglow data of some typical sGRBs that take place well beyond the sensitive radius of the advanced gravitational wave detectors and hence the opportunity of organizing dedicated follow-up observations for events of interest.Comment: 20 pages, 5 figures, published in Nature Astronom

Dibromidobis(1,10-phenanthroline-κ2 N,N′)cadmium(II)

The title compound, [CdBr2(C12H8N2)2], synthesized by the hydro­thermal reaction of Cd(CH3COO)2·2H2O with NaBr and 1,10-phenanthroline, has the CdII cation coordinated by two Br− anions and four N atoms from two 1,10-phenanthroline ligands in a distorted octa­hedral geometry. The crystal packing is stabilized by inter­molecular π–π inter­actions with centroid–centroid distances 3.572 (1) and 3.671 (1) Å together with C—H⋯Br hydrogen bonds

3,3′-(2-Oxocyclo­pentane-1,3-di­yl)dipropane­nitrile

The complete mol­ecule of the title compound, C11H14N2O, is generated by crystallographic twofold symmetry, with the C=O group lying on the rotation axis. In the crystal structure, weak C—H⋯N inter­actions form zigzag chains of mol­ecules