Application of Robust Optimization to the Sawmill Planning Problem

Optimization models have been used to support decision making in the forest industry for a long time. However, several of those models are deterministic and do not address the variability that is present in some of the data. Robust Optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible scenarios of the data within a given uncertainty set. This paper presents the application of the Robust Optimization Methodology to a Sawmill Planning Problem. In the particular case of this problem, variability is assumed in the yield coefficients associated to the cutting patterns used. The main results show that the loss in the function objective value (the “Price of Robustness”), due to computing robust solutions, is not excessive. Moreover, the computed solutions remain feasible for a large proportion of randomly generated scenarios, and tend to preserve the structure of the nominal solution. We believe that these results provide an application area for Robust Optimization in which several source of uncertainty are present.     

Wisp-like structures in vertical gas–liquid pipe flow revealed by wire mesh sensor studies

A conductance wire mesh sensor system has been employed on a vertical 67 mm diameter pipe with the up flow of air and water mixtures. The measuring system provides time and cross-sectionally resolved information about the spatial distribution of the phases. Statistical information can be extracted and used to identify flow patterns. The fully resolved data has revealed a hitherto unreported structure has been seen in churn flow which could be linked to the wisps in wispy-annular flow.     

Synthesis of 5,10-dideazaminopterin

The synthesis of 5,10-dideazaaminopterin by two independent routes is described. Condensation of the piperidine enamine of 4-p-carbomethoxyphenylbutyraldehyde ( 4 ) with ethoxymethylenemalononitrile followed by treatment of the resultant arylethylenaminomalononitrile ( 5 ) with methanolic ammonia produced 2-amino-3-cyano-5-p-carbomethoxyphenethylpyridine ( 6 ). Cyclization of the aminocyanopyridine with guanidine afforded 4-amino-4-deoxy-5,10-dideazapteroic acid ( 8 ). Coupling of the pteroate intermediate with glutamate yielded the target 5,10-dideazaaminopterin ( 10 ). Alternatively, reduction of 2,4-diamino-6-formyl-5-deazapteridine ( 11 ) with sodium borohydride gave the 6-hydroxymethyl compound 12 . Conversion to the bromide was followed by alkylation of dimethyl homoterephthalate to afford methyl 4-amino-4-deoxy-10-carbomethoxy-5,10-dideazapteroate ( 14 ). Decarboxylation with ester cleavage (sodium cyanide in dimethyl sulfoxide at 180°) also gave the diaminopteroic acid ( 8 ). 5,10-dideazaaminopterin ( 10 ) was an effective growth inhibitorof folate dependent bacteria, S. faecium and L. casei.