Market split and basis reduction: towards a solution of the Cornuejols-Dawande instances

Previously, G. Cornuejols and M. Dawande (1998) proposed a set of 0-1 linear programming instances that proved to be very hard to solve by traditional methods, and in particular by linear programming based branch-and-bound. They offered these market split instances as a challenge to the integer programming community. The market split problem can be formulated as a system of linear diophantine equations in 0-1 variables. We use the algorithm of K. Aardal et al. (1998) based on lattice basis reduction. This algorithm is not restricted to deal with market split instances only but is a general method for solving systems of linear diophantine equations with bounds on the variables. We show computational results from solving both feasibility and optimization versions of the market split instances with up to 7 equations and 60 variables and discuss various branching strategies and their effect on the number of enumerated nodes. To our knowledge, the largest feasibility and optimization instances solved before had 6 equations and 50 variables, and 4 equations and 30 variables, respectively. We also present a probabilistic analysis describing how to compute the probability of generating infeasible market split instances. By generating instances in the way prescribed by Cornuejols and Dawande, one obtains relatively many feasible instances for sizes larger than 5 equations and 40 variable

Hydrogel coated monoliths for enzymatic hydrolysis of penicillin G

The objective of this work was to develop a hydrogel-coated monolith for the entrapment of penicillin G acylase (E. coli, PGA). After screening of different hydrogels, chitosan was chosen as the carrier material for the preparation of monolithic biocatalysts. This protocol leads to active immobilized biocatalysts for the enzymatic hydrolysis of penicillin G (PenG). The monolithic biocatalyst was tested in a monolith loop reactor (MLR) and compared with conventional reactor systems using free PGA, and a commercially available immobilized PGA. The optimal immobilization protocol was found to be 5 g l−1 PGA, 1% chitosan, 1.1% glutaraldehyde and pH 7. Final PGA loading on glass plates was 29 mg ml−1 gel. For 400 cpsi monoliths, the final PGA loading on functionalized monoliths was 36 mg ml−1 gel. The observed volumetric reaction rate in the MLR was 0.79 mol s−1 m−3monolith. Apart from an initial drop in activity due to wash out of PGA at higher ionic strength, no decrease in activity was observed after five subsequent activity test runs. The storage stability of the biocatalysts is at least a month without loss of activity. Although the monolithic biocatalyst as used in the MLR is still outperformed by the current industrial catalyst (immobilized preparation of PGA, 4.5 mol s−1 m−3catalyst), the rate per gel volume is slightly higher for monolithic catalysts. Good activity and improved mechanical strength make the monolithic bioreactor an interesting alternative that deserves further investigation for this application. Although moderate internal diffusion limitations have been observed inside the gel beads and in the gel layer on the monolith channel, this is not the main reason for the large differences in reactor performance that were observed. The pH drop over the reactor as a result of the chosen method for pH control results in a decreased performance of both the MLR and the packed bed reactor compared to the batch system. A different reactor configuration including an optimal pH profile is required to increase the reactor performance. The monolithic stirrer reactor would be an interesting alternative to improve the performance of the monolith-PGA combination

Using column generation for gate planning at Amsterdam Airport Schiphol

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