A Probabilistic One-Step Approach to the Optimal Product Line Design Problem Using Conjoint and Cost Data

Designing and pricing new products is one of the most critical activities for a firm, and it is well-known that taking into account consumer preferences for design decisions is essential for products later to be successful in a competitive environment (e.g., Urban and Hauser 1993). Consequently, measuring consumer preferences among multiattribute alternatives has been a primary concern in marketing research as well, and among many methodologies developed, conjoint analysis (Green and Rao 1971) has turned out to be one of the most widely used preference-based techniques for identifying and evaluating new product concepts. Moreover, a number of conjoint-based models with special focus on mathematical programming techniques for optimal product (line) design have been proposed (e.g., Zufryden 1977, 1982, Green and Krieger 1985, 1987b, 1992, Kohli and Krishnamurti 1987, Kohli and Sukumar 1990, Dobson and Kalish 1988, 1993, Balakrishnan and Jacob 1996, Chen and Hausman 2000). These models are directed at determining optimal product concepts using consumers' idiosyncratic or segment level part-worth preference functions estimated previously within a conjoint framework. Recently, Balakrishnan and Jacob (1996) have proposed the use of Genetic Algorithms (GA) to solve the problem of identifying a share maximizing single product design using conjoint data. In this paper, we follow Balakrishnan and Jacob's idea and employ and evaluate the GA approach with regard to the problem of optimal product line design. Similar to the approaches of Kohli and Sukumar (1990) and Nair et al. (1995), product lines are constructed directly from part-worths data obtained by conjoint analysis, which can be characterized as a one-step approach to product line design. In contrast, a two-step approach would start by first reducing the total set of feasible product profiles to a smaller set of promising items (reference set of candidate items) from which the products that constitute a product line are selected in a second step. Two-step approaches or partial models for either the first or second stage in this context have been proposed by Green and Krieger (1985, 1987a, 1987b, 1989), McBride and Zufryden (1988), Dobson and Kalish (1988, 1993) and, more recently, by Chen and Hausman (2000). Heretofore, with the only exception of Chen and Hausman's (2000) probabilistic model, all contributors to the literature on conjoint-based product line design have employed a deterministic, first-choice model of idiosyncratic preferences. Accordingly, a consumer is assumed to choose from her/his choice set the product with maximum perceived utility with certainty. However, the first choice rule seems to be an assumption too rigid for many product categories and individual choice situations, as the analyst often won't be in a position to control for all relevant variables influencing consumer behavior (e.g., situational factors). Therefore, in agreement with Chen and Hausman (2000), we incorporate a probabilistic choice rule to provide a more flexible representation of the consumer decision making process and start from segment-specific conjoint models of the conditional multinomial logit type. Favoring the multinomial logit model doesn't imply rejection of the widespread max-utility rule, as the MNL includes the option of mimicking this first choice rule. We further consider profit as a firm's economic criterion to evaluate decisions and introduce fixed and variable costs for each product profile. However, the proposed methodology is flexible enough to accomodate for other goals like market share (as well as for any other probabilistic choice rule). This model flexibility is provided by the implemented Genetic Algorithm as the underlying solver for the resulting nonlinear integer programming problem. Genetic Algorithms merely use objective function information (in the present context on expected profits of feasible product line solutions) and are easily adjustable to different objectives without the need for major algorithmic modifications. To assess the performance of the GA methodology for the product line design problem, we employ sensitivity analysis and Monte Carlo simulation. Sensitivity analysis is carried out to study the performance of the Genetic Algorithm w.r.t. varying GA parameter values (population size, crossover probability, mutation rate) and to finetune these values in order to provide near optimal solutions. Based on more than 1500 sensitivity runs applied to different problem sizes ranging from 12.650 to 10.586.800 feasible product line candidate solutions, we can recommend: (a) as expected, that a larger problem size be accompanied by a larger population size, with a minimum popsize of 130 for small problems and a minimum popsize of 250 for large problems, (b) a crossover probability of at least 0.9 and (c) an unexpectedly high mutation rate of 0.05 for small/medium-sized problems and a mutation rate in the order of 0.01 for large problem sizes. Following the results of the sensitivity analysis, we evaluated the GA performance for a large set of systematically varying market scenarios and associated problem sizes. We generated problems using a 4-factorial experimental design which varied by the number of attributes, number of levels in each attribute, number of items to be introduced by a new seller and number of competing firms except the new seller. The results of the Monte Carlo study with a total of 276 data sets that were analyzed show that the GA works efficiently in both providing near optimal product line solutions and CPU time. Particularly, (a) the worst-case performance ratio of the GA observed in a single run was 96.66%, indicating that the profit of the best product line solution found by the GA was never less than 96.66% of the profit of the optimal product line, (b) the hit ratio of identifying the optimal solution was 84.78% (234 out of 276 cases) and (c) it tooks at most 30 seconds for the GA to converge. Considering the option of Genetic Algorithms for repeated runs with (slightly) changed parameter settings and/or different initial populations (as opposed to many other heuristics) further improves the chances of finding the optimal solution.

The Nicastrin ectodomain adopts a highly thermostable structure

Nicastrin is a type I transmembrane glycoprotein, which is part of the high molecular weight gamma-secretase complex. gamma-Secretase is one of the key players associated with the generation of Alzheimer's disease pathology, since it liberates the neurotoxic amyloid beta-peptide. Four proteins Nicastrin, anterior pharynx-defective-1 (Aph-1), presenilin enhancer-2 (Pen-2) and Presenilin are essential to form the active gamma-secretase complex. Recently it has been shown, that Nicastrin has a key function in stabilizing the mature gamma-secretase complex and may also be involved in substrate recognition. So far no structural data for the Nicastrin ectodomain or any other gamma-secretase component are available. We therefore used Circular Dichroism (CD) spectroscopy to demonstrate that Nicastrin, similar to its homologues, the Streptomyces griseus aminopeptidase (SGAP) and the transferrin receptor (TfR), adopts a thermostable secondary structure. Furthermore, the Nicastrin ectodomain has an exceptionally high propensity to refold after thermal denaturation. These findings provide evidence to further support the hypothesis that Nicastrin may share evolutionary conserved properties with the aminopeptidase and the transferrin receptor family

Assembly, trafficking and function of gamma-secretase

gamma-Secretase catalyzes the final cleavage of the beta-amyloid precursor protein to generate amyloid-beta peptide, the principal component of amyloid plaques in the brains of patients suffering from Alzheimer's disease. Here, we review the identification of gamma-secretase as a protease complex and its assembly and trafficking to its site(s) of cellular function. In reconstitution experiments, gamma-secretase was found to be composed of four integral membrane proteins, presenilin (PS), nicastrin (NCT), PEN-2 and APH-1 that are essential and sufficient for gamma-secretase activity. PS, which serves as a catalytic subunit of gamma-secretase, was identified as a prototypic member of novel aspartyl proteases of the GxGD type. In human cells, gamma-secretase could be further defined as a heterogeneous activity consisting of distinct complexes that are composed of PS1 or PS2 and APH-1a or APH-1b homologues together with NCT and PEN-2. Using green fluorescent protein as a reporter we localized PS and gamma-secretase activity at the plasma membrane and endosomes. Investigation of gamma-secretase complex assembly in knockdown and knockout cells of the individual subunits allowed us to develop a model of complex assembly in which NCT and APH-1 first stabilize PS before PEN-2 assembles as the last component. Furthermore, we could map domains in PS and PEN-2 that govern assembly and trafficking of the complex. Finally, Rer1 was identified as a PEN-2-binding protein that serves a role as an auxiliary factor for gamma-secretase complex assembly. Copyright (c) 2006 S. Karger AG, Basel

Quantum Yu-Shiba-Rusinov dimers

Magnetic adatoms on a superconducting substrate undergo a quantum phase transition as their exchange coupling to the conduction electrons increases. For quantum spins, this transition is accompanied by screening of the adatom spin. Here, we explore the consequences of this screening for the phase diagrams and subgap excitation spectra of dimers of magnetic adatoms coupled by hybridization of their Yu-Shiba-Rusinov states and spin-spin interactions. We specifically account for higher spins, single-ion anisotropy, Ruderman-Kittel-Kasuya-Yosida coupling, and Dzyaloshinsky-Moriya interactions relevant in transition-metal and rare-earth systems. Our flexible approach based on a zero-bandwidth approximation provides detailed physical insight and is in excellent qualitative agreement with available numerical-renormalization group calculations on monomers and dimers. Remarkably, we find that even in the limit of large impurity spins or strong single-ion anisotropy, the phase diagrams for dimers of quantum spins remain qualitatively distinct from phase diagrams based on classical spins, highlighting the need for a theory of quantum Yu-Shiba-Rusinov dimers.Comment: 17 pages, 12 figure

Modulation of receptor cycling by neuron-enriched endosomal protein of 21 kD

Although correct cycling of neuronal membrane proteins is essential for neurite outgrowth and synaptic plasticity, neuron-specific proteins of the implicated endosomes have not been characterized. Here we show that a previously cloned, developmentally regulated, neuronal protein of unknown function binds to syntaxin 13. We propose to name this protein neuron-enriched endosomal protein of 21 kD (NEEP21), because it is colocalized with transferrin receptors, internalized transferrin (Tf), and Rab4. In PC12 cells, NEEP21 overexpression accelerates Tf internalization and recycling, whereas its down-regulation strongly delays Tf recycling. In primary neurons, NEEP21 is localized to the somatodendritic compartment, and, upon N-methyl-d-aspartate (NMDA) stimulation, the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor subunit GluR2 is internalized into NEEP21-positive endosomes. NEEP21 down-regulation retards recycling of GluR1 to the cell surface after NMDA stimulation of hippocampal neurons. In summary, NEEP21 is a neuronal protein that is localized to the early endosomal pathway and is necessary for correct receptor recycling in neurons

Aβ43‐producing PS1 FAD mutants cause altered substrate interactions and respond to γ‐secretase modulation

Abnormal generation of neurotoxic amyloid‐β peptide (Aβ) 42/43 species due to mutations in the catalytic presenilin 1 (PS1) subunit of γ‐secretase is the major cause of familial Alzheimer's disease (FAD). Deeper mechanistic insight on the generation of Aβ43 is still lacking, and it is unclear whether γ‐secretase modulators (GSMs) can reduce the levels of this Aβ species. By comparing several types of Aβ43‐generating FAD mutants, we observe that very high levels of Aβ43 are often produced when presenilin function is severely impaired. Altered interactions of C99, the precursor of Aβ, are found for all mutants and are independent of their particular effect on Aβ production. Furthermore, unlike previously described GSMs, the novel compound RO7019009 can effectively lower Aβ43 production of all mutants. Finally, substrate‐binding competition experiments suggest that RO7019009 acts mechanistically after initial C99 binding. We conclude that altered C99 interactions are a common feature of diverse types of PS1 FAD mutants and that also patients with Aβ43‐generating FAD mutations could in principle be treated by GSMs

The high-affinity binding site for tricyclic antidepressants resides in the outer vestibule of the serotonin transporter

The structure of the bacterial leucine transporter from Aquifex aeolicus (LeuT(Aa)) has been used as a model for mammalian Na+/Cl--dependent transporters, in particular the serotonin transporter (SERT). The crystal structure of LeuT(Aa) liganded to tricyclic antidepressants predicts simultaneous binding of inhibitor and substrate. This is incompatible with the mutually competitive inhibition of substrates and inhibitors of SERT. We explored the binding modes of tricyclic antidepressants by homology modeling and docking studies. Two approaches were used subsequently to differentiate between three clusters of potential docking poses: 1) a diagnostic SERTY95F mutation, which greatly reduced the affinity for [H-3] imipramine but did not affect substrate binding; 2) competition binding experiments in the presence and absence of carbamazepine (i.e., a tricyclic imipramine analog with a short side chain that competes with [3H] imipramine binding to SERT). Binding of releasers (para-chloroamphetamine, methylene-dioxy-methamphetamine/ecstasy) and of carbamazepine were mutually exclusive, but Dixon plots generated in the presence of carbamazepine yielded intersecting lines for serotonin, MPP+, paroxetine, and ibogaine. These observations are consistent with a model, in which 1) the tricyclic ring is docked into the outer vestibule and the dimethyl-aminopropyl side chain points to the substrate binding site; 2) binding of amphetamines creates a structural change in the inner and outer vestibule that precludes docking of the tricyclic ring; 3) simultaneous binding of ibogaine (which binds to the inward-facing conformation) and of carbamazepine is indicative of a second binding site in the inner vestibule, consistent with the pseudosymmetric fold of monoamine transporters. This may be the second low-affinity binding site for antidepressants

Presenilin-1 affects trafficking and processing of βAPP and is targeted in a complex with nicastrin to the plasma membrane

Amyloid β-peptide (Aβ) is generated by the consecutive cleavages of β- and γ-secretase. The intramembraneous γ-secretase cleavage critically depends on the activity of presenilins (PS1 and PS2). Although there is evidence that PSs are aspartyl proteases with γ-secretase activity, it remains controversial whether their subcellular localization overlaps with the cellular sites of Aβ production. We now demonstrate that biologically active GFP-tagged PS1 as well as endogenous PS1 are targeted to the plasma membrane (PM) of living cells. On the way to the PM, PS1 binds to nicastrin (Nct), an essential component of the γ-secretase complex. This complex is targeted through the secretory pathway where PS1-bound Nct becomes endoglycosidase H resistant. Moreover, surface-biotinylated Nct can be coimmunoprecipitated with PS1 antibodies, demonstrating that this complex is located to cellular sites with γ-secretase activity. Inactivating PS1 or PS2 function by mutagenesis of one of the critical aspartate residues or by γ-secretase inhibitors results in delayed reinternalization of the β-amyloid precursor protein and its accumulation at the cell surface. Our data suggest that PS is targeted as a biologically active complex with Nct through the secretory pathway to the cell surface and suggest a dual function of PS in γ-secretase processing and in trafficking