Mixed-Integer Linear Programming Approach for Life-Cycle Carpet Profit

This paper proposes an mixed-integer linear programming (MILP) model to accurately represent a product life-cycle design considering profit maximization. The model that takes into account the effects on the demand lev-el and a measure of the customer utility considering recycled raw materials and prices of the traditional and modular products. Demand functions for traditional and modular products are considered. Given the presence of bilinear terms in the formulation (for example due to the multiplication of product price for the demand), the multi-parametric disaggregation technique is used to obtain a line-ar model. The developed model is applied to a company that produces tradition-al carpets and it wants to manufacture carpets based on a new modular design where recycled materials must be incorporated. The objective of the company is to maximize the total profit taking into account the design specifications and the selling prices for traditional and modular carpets. In addition, the amount of square meters of traditional carpets must be determined and the take-back rate must be considered. The practical behavior of the formulation is analyzed through computational experiments exploring the analyzed case-study.Sociedad Argentina de Informática e Investigación Operativ

Mixed-Integer Linear Programming Approach for Life-Cycle Carpet Profit

This paper proposes an mixed-integer linear programming (MILP) model to accurately represent a product life-cycle design considering profit maximization. The model that takes into account the effects on the demand lev-el and a measure of the customer utility considering recycled raw materials and prices of the traditional and modular products. Demand functions for traditional and modular products are considered. Given the presence of bilinear terms in the formulation (for example due to the multiplication of product price for the demand), the multi-parametric disaggregation technique is used to obtain a line-ar model. The developed model is applied to a company that produces tradition-al carpets and it wants to manufacture carpets based on a new modular design where recycled materials must be incorporated. The objective of the company is to maximize the total profit taking into account the design specifications and the selling prices for traditional and modular carpets. In addition, the amount of square meters of traditional carpets must be determined and the take-back rate must be considered. The practical behavior of the formulation is analyzed through computational experiments exploring the analyzed case-study.Sociedad Argentina de Informática e Investigación Operativ

Mixed-Integer Linear Programming Approach for Life-Cycle Carpet Profit

This paper proposes an mixed-integer linear programming (MILP) model to accurately represent a product life-cycle design considering profit maximization. The model that takes into account the effects on the demand lev-el and a measure of the customer utility considering recycled raw materials and prices of the traditional and modular products. Demand functions for traditional and modular products are considered. Given the presence of bilinear terms in the formulation (for example due to the multiplication of product price for the demand), the multi-parametric disaggregation technique is used to obtain a line-ar model. The developed model is applied to a company that produces tradition-al carpets and it wants to manufacture carpets based on a new modular design where recycled materials must be incorporated. The objective of the company is to maximize the total profit taking into account the design specifications and the selling prices for traditional and modular carpets. In addition, the amount of square meters of traditional carpets must be determined and the take-back rate must be considered. The practical behavior of the formulation is analyzed through computational experiments exploring the analyzed case-study.Sociedad Argentina de Informática e Investigación Operativ

AzTEC 1.1 mm observations of high-z protocluster environments : SMG overdensities and misalignment between AGN jets and SMG distribution

We present observations at 1.1 mm towards 16 powerful radio galaxies and a radio-quiet quasar at 0.5 > z > 6.3 acquired with the AzTEC camera mounted at the James Clerk Maxwell Telescope and Atacama Submillimeter Telescope Experiment to study the spatial distribution of submillimetre galaxies (SMGs) towards possible protocluster regions. The survey covers a total area of 1.01 sq deg with rms depths of 0.52-1.44 mJy and detects 728 sources above 3σ. We find overdensities of a factor of ~2 in the source counts of three individual fields (4C+23.56, PKS1138-262, and MRC0355-037) over areas of ~200 sq deg. When combining all fields, the source-count analysis finds an overdensity that reaches a factor ≳ 3 at S 1.1mm = 4mJy covering a 1.5-arcmin-radius area centred on the active galactic nucleus. The large size of our maps allows us to establish that beyond a radius of 1.5 arcmin, the radial surface density of SMGs falls to that of a blank field. In addition, we find a trend for SMGs to align closely to a perpendicular direction with respect to the radio jets of the powerful central radio galaxies (73 -14 +13 deg). This misalignment is found over projected comoving scales of 4-20 Mpc, departs from perfect alignment (0 deg) by ~5σ, and apparently has no dependence on SMG luminosity. Under the assumption that the AzTEC sources are at the redshift of the central radio galaxy, the misalignment reported here can be interpreted as SMGs preferentially inhabiting mass-dominant filaments funnelling material towards the protoclusters, which are also the parent structures of the radio galaxies.Peer reviewe

Early Science with the Large Millimeter Telescope: observations of dust continuum and CO emission lines of cluster-lensed submillimetre galaxies at z=2.0-4.7

We present Early Science observations with the Large Millimeter Telescope, AzTEC 1.1mm continuum images and wide bandwidth spectra (73-111GHz) acquired with the Redshift Search Receiver, towards four bright lensed submillimetre galaxies identified through the Herschel Lensing Survey-snapshot and the Submillimetre Common-User Bolometer Array-2 Cluster Snapshot Survey. This pilot project studies the star formation history and the physical properties of the molecular gas and dust content of the highest redshift galaxies identified through the benefits of gravitational magnification. We robustly detect dust continuum emission for the full sample and CO emission lines for three of the targets. We find that one source shows spectroscopic multiplicity and is a blend of three galaxies at different redshifts (z=2.040, 3.252, and 4.680), reminiscent of previous high-resolution imaging follow-up of unlensed submillimetre galaxies, but with a completely different search method, that confirm recent theoretical predictions of physically unassociated blended galaxies. Identifying the detected lines as 12CO (Jup=2-5) we derive spectroscopic redshifts, molecular gas masses, and dust masses from the continuum emission. The mean H2 gas mass of the full sample is (2.0±0.2)×1011 M⊙/μ, and the mean dust mass is (2.0±0.2)×109 M⊙/μ, where μ≈2-5 is the expected lens amplification. Using these independent estimations we infer a gas-to-dust ratio of δGDR≈55-75, in agreement with other measurements of submillimetre galaxies. Our magnified high-luminosity galaxies fall on the same locus as other high-redshift submillimetre galaxies, extending the $L^{\prime }_{\rm CO}$-LFIR correlation observed for local luminous and ultraluminous infrared galaxies to higher far-infrared and CO luminositie

AzTEC millimeter survey of the COSMOS field - III. Source catalog over 0.72 sq. deg. and plausible boosting by large-scale structure

We present a 0.72 sq. deg. contiguous 1.1mm survey in the central area of the COSMOS field carried out to a 1sigma ~ 1.26 mJy/beam depth with the AzTEC camera mounted on the 10m Atacama Submillimeter Telescope Experiment (ASTE). We have uncovered 189 candidate sources at a signal-to-noise ratio S/N >= 3.5, out of which 129, with S/N >= 4, can be considered to have little chance of being spurious (< 2 per cent). We present the number counts derived with this survey, which show a significant excess of sources when compared to the number counts derived from the ~0.5 sq. deg. area sampled at similar depths in the Scuba HAlf Degree Extragalactic Survey (SHADES, Austermann et al. 2010). They are, however, consistent with those derived from fields that were considered too small to characterize the overall blank-field population. We identify differences to be more significant in the S > 5 mJy regime, and demonstrate that these excesses in number counts are related to the areas where galaxies at redshifts z < 1.1 are more densely clustered. The positions of optical-IR galaxies in the redshift interval 0.6 < z < 0.75 are the ones that show the strongest correlation with the positions of the 1.1mm bright population (S > 5 mJy), a result which does not depend exclusively on the presence of rich clusters within the survey sampled area. The most likely explanation for the observed excess in number counts at 1.1mm is galaxy-galaxy and galaxy-group lensing at moderate amplification levels, that increases in amplitude as one samples larger and larger flux densities. This effect should also be detectable in other high redshift populations.Comment: 21 pages, 17 figures, accepted for publication in MNRA

Deep 1.1 mm-wavelength imaging of the GOODS-S field by AzTEC/ASTE - I. Source catalogue and number counts

[Abridged] We present the first results from a 1.1 mm confusion-limited map of the GOODS-S field taken with AzTEC on the ASTE telescope. We imaged a 270 sq. arcmin field to a 1\sigma depth of 0.48 - 0.73 mJy/beam, making this one of the deepest blank-field surveys at mm-wavelengths ever achieved. Although our GOODS-S map is extremely confused, we demonstrate that our source identification and number counts analyses are robust, and the techniques discussed in this paper are relevant for other deeply confused surveys. We find a total of 41 dusty starburst galaxies with S/N >= 3.5 within this uniformly covered region, where only two are expected to be false detections. We derive the 1.1mm number counts from this field using both a "P(d)" analysis and a semi-Bayesian technique, and find that both methods give consistent results. Our data are well-fit by a Schechter function model with (S', N(3mJy), \alpha) = (1.30+0.19 mJy, 160+27 (mJy/deg^2)^(-1), -2.0). Given the depth of this survey, we put the first tight constraints on the 1.1 mm number counts at S(1.1mm) = 0.5 mJy, and we find evidence that the faint-end of the number counts at S(850\mu m) < 2.0 mJy from various SCUBA surveys towards lensing clusters are biased high. In contrast to the 870 \mu m survey of this field with the LABOCA camera, we find no apparent under-density of sources compared to previous surveys at 1.1 mm. Additionally, we find a significant number of SMGs not identified in the LABOCA catalogue. We find that in contrast to observations at wavelengths < 500 \mu m, MIPS 24 \mu m sources do not resolve the total energy density in the cosmic infrared background at 1.1 mm, demonstrating that a population of z > 3 dust-obscured galaxies that are unaccounted for at these shorter wavelengths potentially contribute to a large fraction (~2/3) of the infrared background at 1.1 mm.Comment: 21 pages, 9 figures. Accepted to MNRAS