A Neural-Tabu Search Heuristic for the Real Time Vehicle Routing Problem

The Real Time Vehicle Routing Problem RTVRP is a dynamic routing problem where requests are generated dynamically during the operation horizon without any previous knowledge. Received requests need to be answered as fast as possible and then assigned to a vehicle to be served. Due to timing constraints of the RTVRP, a solving approach should give the best compromise between the cost of the provided solution and the computation time needed to find it. In this paper, we present a neural-tabu search solving scheme for the RTVRP. The developed approach is composed by two phases; The first part consists of learning and reproducing previous routing decisions using a feed forward neural network with a particular structure. The second phase is based on a tabu search heuristic that takes its initial solution from the assignment provided by the neural module. If the reaction time is still available, the tabu search module will continue ameliorating the final solution. To evaluate the proposed approach a set of problems are simulated and solved. The obtained results are compared to those given by the First Come First Served FCFS and Nearest Neighbor NN policies and also to the optimal solutions provided by the GNU Linear Programming Kit GLPK.      

Central simple superalgebras with anti-automorphisms of order two of the first kind

By a theorem of Albert's, a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the Brauer group. Our main purpose is to develop the theory of existence of anti-automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over K, where K is a field of arbitrary characteristic. First we need to generalize the Skolem–Noether Theorem to the superalgebra case. Then we show which kind of finite dimensional central simple superalgebras have an anti-automorphism of order 2 of the first kind.     

The economic order quantity repair and waste disposal model with entropy cost

As markets have become more and more competitive, disorder has become a prevailing characteristic of modern production systems that are operating in complex, dynamic and uncertain environments. Minimizing disorder in these production systems requires stringent control measures by management, with costs that are usually hidden or difficult to estimate. Not accounting for these costs leads to less efficient production systems. This paper postulates that the behaviour of production systems very much resembles that of physical systems. Such a parallel suggests that improvements to production systems may be achievable by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). The applicability of these laws is demonstrated in a simple reverse supply chain context, where products are collected and later repaired at some rate while other products might be disposed outside according to some waste disposal rate. Numerical examples are provided.     

Asymptotics of solutions of nonautonomous second-order ordinary differential equations close to linear equations

We find asymptotic representations for certain classes of solutions of nonautonomous second-order differential equations that are close, in a certain sense, to linear equations. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 230–241, April–June, 2008.     

Competitive [2,3]- and [1,2]-oxonium ylide rearrangements. Concerted or stepwise?

The axial-equatorial conformational isomer distribution of the reactant diazoacetoacetate or its metal carbene intermediate is reflected in Rh(II) catalyzed oxonium ylide forming reactions of 3-(trans-2-arylvinyl)tetrahydropyranone-5-diazoacetoacetates that afford diastereoisomeric products for both the symmetry-allowed [2,3]- and the formally symmetry-forbidden [1,2]-oxonium ylide rearrangements.     

Simultaneous liquid-liquid extraction of dibenzyl disulfide, 2,6-di-tert-butyl-p-cresol, and 1,2,3-benzotriazole from power transformer oil prior to GC and HPLC determination

2,6-Di-tert-butyl-p-cresol (DBPC), dibenzyl disulfide (DBDS), and 1,2,3-benzotriazole (BTA) are additives that may be found concomitantly in the oil matrix of power transformer. DBPC and DBDS act as antioxidants while, BTA is a corrosion inhibitor that protects copper conductors inside the transformer unit from corrosion. A powerful analytical method is, therefore, required to determine these additives at trace levels in the transformer oil. This work describes a unique single liquid-liquid extraction pretreatment step prior to the determination of the components by gas chromatography (GC) and high-performance liquid chromatography (HPLC) techniques. The optimum volume ratio used in the pretreatment step was determined as 5:2:5 for mineral oil/n-hexane/acetonitrile, respectively. Relatively, the method is simple and quick with a minimal use of solvents. Analytical results indicate that the method is relatively sensitive, accurate, and precise for each of the three components in fresh and used mineral oil. The calibration curves for the three components demonstrate a significant increase in sensitivities. Detection limits found were, 100 mg L(-1) (0.01% w/v), 0.80 mg L(-1) , and 2.04 mg L(-1) for DBPC, DBDS, and BTA, respectively. The Student's t values determined at 95% confidence level indicate that there is no significant difference between the experimental means obtained by this method and the standard method for each component.     

Two-product inventory management with fixed costs and supply uncertainty

This paper determines the optimal ordering policy for a two-product, periodic-review inventory problem in which the probability of supply availability is unknown. Moreover, there are two different fixed costs assigned to each product. Demand rates are random variables with known probability density functions, and the supply availability for each product is updated at the beginning of each time period. We prove the optimality of (s,S) policy with a monotone switching curve that indicates the priority of production, where the order-up-to levels and the reorder points are functions of supply availability information. A simple computation is proposed to calculate the two threshold levels. Bayesian updating helps to manage the optimal ordering policy by updating supply disruption information. Numerical results show that improving the accuracy of the forecast leads to making a better ordering decision and eliminating the negative effect of supply disruption on the total cost.     

Largeur et nilpotence

The notion of a large set in an arbitrary group is introduced in analogy to the generic sets in an algebraic or stable group. The question is studied which properties “satisfied largely” by a group hold on the entire group.

ZUSAMMENFASSUNG. Wir definieren den Begriff einer groβen Teilmenge einer be-liebigen Gruppe in Analogie zu den generischen Mengen einer algebraischen oder stabilen Gruppe und untersuchen, welche “grofiteils erfullten” Gruppeneigenschaften fur die ganze Gruppe gelten müssen.     

Crystal structure of a silver(I) complex with the 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid)

The reaction between freshly precipitated silver oxide Ag₂O and an aqueous solution of tetrabenzenecarboxylic acid H₄L leads to the anhydrous Ag₂H₂L complex. It crystallizes in the space groupP2₁/c, witha=6.457(1),b=8.180(1),c=9.982(1) Å, β=97.83(1)°,V=522.3(1) ?³,Z=2,d=2.976 g cm⁻³. This structure is a three dimensional polymeric network polymer without any silver...silver interaction. The silver environment is a bipyramid trigonal polyhedron with three short bond distances in the equatorial plane (Ag−O=2.255(2), 2.295(2), and 2.499(2) Å) and two longer bond distances in axial positions (Ag−O=2.558(2) and 2.617(2) Å). Thus, the silver polyhedron involves five different ligands. It is noteworthy that the (H₂L₂)²⁻ ligand is located around an inversion centre.