Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

Zur Chemie der Meldrumsäure

The enolic form of cyclic compounds like 4-hydroxycoumarin,-2-pyronones,-2-pyridones and cyclohexane-1,3-diones yields malonyl heterocycles by heating withMeldrum acid.Enolisierbare Ringverbindungen vom Typ des 4-Hydroxycumarins,-2-pyronons und-2-pyridons sowie des 1,3-Cyclohexandions schließen beim Erhitzen mitMeldrumsäure Ringe zu Malonyl-heterocyclen.

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Herrn Prof. Dr.H. Nowotny gewidment.     

Removability of polar sets for harmonic functions

A classical result of G. Bouligand states that bounded harmonic functions can be extended across closed polar sets. F.-Y. Maeda replaced the boundedness assumption by the condition of energy finiteness for harmonic spaces with Green function.This paper proves this result for generalP-harmonic spaces and shows that the extension property for a harmonic functionu and the condition of energy finiteness are equivalent to a majorization property foru ² .     

The conserved protein kinase-A target motif in synapsin of Drosophila is effectively modified by pre-mRNA editing

Background  

Synapsins are abundant synaptic vesicle associated phosphoproteins that are involved in the fine regulation of neurotransmitter release. The Drosophila member of this protein family contains three conserved domains (A, C, and E) and is expressed in most or all synaptic terminals. Similar to mouse mutants, synapsin knock-out flies show no obvious structural defects but are disturbed in complex behaviour, notably learning and memory.