Branch-cut-and-price for the vehicle routing problem with simultaneous pickup and delivery

This work proposes a Branch-cut-and-price (BCP) approach for the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We also deal with a particular case of the VRPSPD, known as the Vehicle Routing Problem with Mixed Pickup and Delivery. The BCP algorithm was tested in well-known benchmark instances involving up to 200 customers. Four instances were solved for the first time and some LBs were improved.     

Extraction by reversed micelles of the intrecellular enzyme xylose reductase

Applied Biochemistry and Biotechnology - Xylose reductase enzyme (EC 1.1.1.21) produced by Candidaguilliermondii in sugarcane bagasse was extracted by reversed micelles of N-benzyl-N-dodecyl-N-bis...     

Formulations for a problem of petroleum transportation

Oil tankers play a fundamental role in every offshore petroleum supply chain and due to its high price, it is essential to optimize its use. Since this optimization requires handling detailed operational aspects, complete optimization models are typically intractable. Thus, a usual approach is to solve a tactical level model prior to optimize the operational details. In this case, it is desirable that tactical models are as precise as possible to avoid too severe adjustments in the next optimization level. In this paper, we study tactical models for a crude oil transportation problem by tankers. We did our work on the top of a previous paper found in the literature. The previous model considers inventory capacities and discrete lot sizes to be transported, aiming to meet given demands over a finite time horizon. We compare several formulations for this model using 50 instances from the literature and proposing 25 new harder ones. A column generation-based heuristic is also proposed to find good feasible solutions with less computational burden than the heuristics of the commercial solver used.     

The time dependent traveling salesman problem: polyhedra and algorithm

The time dependent traveling salesman problem (TDTSP) is a generalization of the classical traveling salesman problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet-defining cuts. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving almost all instances from the TSPLIB with up to 107 vertices.     

<em>In Vitro </em>and <em>in </em><em>Vivo</em> Antitumor Effect of Trachylobane-360, a Diterpene from<em> Xylopia langsdorffiana</em>

Trachylobane-360 (ent-7α-acetoxytrachyloban-18-oic acid) was isolated from Xylopia langsdorffiana. Studies have shown that it has weak cytotoxic activity against tumor and non-tumor cells. This study investigated the in vitro and in vivo antitumor effects of trachylobane-360, as well as its cytotoxicity in mouse erythrocytes. In order to evaluate the in vivo toxicological aspects related to trachylobane-360 administration, hematological, biochemical and histopathological analyses of the treated animals were performed. The compound exhibited a concentration-dependent effect in inducing hemolysis with HC₅₀ of 273.6 μM, and a moderate in vitro concentration-dependent inhibitory effect on the proliferation of sarcoma 180 cells with IC₅₀ values of 150.8 μM and 150.4 μM, evaluated by the trypan blue exclusion test and MTT reduction assay, respectively. The in vivo inhibition rates of sarcoma 180 tumor development were 45.60, 71.99 and 80.06% at doses of 12.5 and 25 mg/kg of trachylobane-360 and 25 mg/kg of 5-FU, respectively. Biochemical parameters were not altered. Leukopenia was observed after 5-FU treatment, but this effect was not seen with trachylobane-360 treatment. The histopathological analysis of liver and kidney showed that both organs were mildly affected by trachylobane-360 treatment. Trachylobane-360 showed no immunosuppressive effect. In conclusion, these data reinforce the anticancer potential of this natural diterpene.     

Invariant circles for homogeneous polynomial vector fields on the 2-dimensional sphere

LexX be a homogeneous polynomial vector field of degreen≥3 on S² having finitely many invariant circles. Then, for such a vector fieldX we find upper bounds for the number of invariant circles, invariant great circles, invariant circles intersecting at a same point and parallel circles with the same director vector. We give examples of homogeneous polynomial vector fields of degree 3 on S² having finitely many invariant circles which are not great circles, which are limit cycles, but are not great circles and invariant great circles that are limit cycles. Moreover, for the casen=3 we determine the maximum number of parallel invariant circles with the same director vector. The authors are partially supported by a MCYT grant BFM2002-04236-C02-02 and by a CIRIT grant number 2001SGR 00173.     

Planar Beurling Transform and Bergman Type Spaces

In this paper we describe the actions of the operator $S_\mathbb{D }$ or its adjoint $S_\mathbb{D }^*$ on the poly-Bergman spaces of the unit disk $\mathbb{D }.$ Let $k$ and $j$ be positive integers. We prove that $(S_\mathbb{D })^{j}$ is an isometric isomorphism between the true poly-Bergman subspace $\mathcal{A }_{(k)}^2(\mathbb{D })\ominus N_{(k),j}$ onto the true poly-Bergman space $\mathcal{A }_{(j+k)}^2(\mathbb{D }),$ where the linear space $N_{(k),j}$ have finite dimension $j.$ The action of $(S_\mathbb{D })^{j-1}$ on the canonical Hilbert base for the Bergman subspace $\mathcal{A }^2(\mathbb{D })\ominus \mathcal{P }_{j-1},$ gives a Hilbert base $\{ \phi _{ j , k } \}_{ k }$ for $\mathcal{A }_{(j)}^2(\mathbb{D }).$ It is shown that $\{ \phi _{ j , k } \}_{ j, k }$ is a Hilbert base for $L^2(\mathbb{D },d A)$ such that whenever $j$ and $k$ remain constant we obtain a Hilbert base for the true poly-Bergman space $\mathcal{A }_{(j)}^2(\mathbb{D })$ and $\mathcal{A }_{(-k)}^2(\mathbb{D }),$ respectively. The functions $\phi _{ j , k }$ are polynomials in $z$ and $\overline{z}$ and are explicitly given in terms of the $(2,1)$ -hypergeometric polynomials. We prove explicit representations for the true poly-Bergman kernels and the Koshelev representation for the poly-Bergman kernels of $\mathbb{D }.$ The action of $S_\Pi $ on the true poly-Bergman spaces of the upper half-plane $\Pi $ allows one to introduce Hilbert bases for the true poly-Bergman spaces, and to give explicit representations of the true poly-Bergman and poly-Bergman kernels.