Parameter optimization in differential geometry based solvation models

Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and nonpolar interactions in a self-consistent framework. Our earlier study indicates that DG based nonpolar solvation model outperforms other methods in nonpolar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and nonploar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.Comment: 19 pages, 12 figures, convex optimizatio

Managing demand uncertainty: probabilistic selling versus inventory substitution

Demand variability is prevailing in the current rapidly changing business environment, which makes it difficult for a retailer that sells multiple substitutable products to determine the optimal inventory. To combat demand uncertainty, both strategies of inventory substitution and probabilistic selling can be used. Although the two strategies differ in operation, we believe that they share a common feature in combating demand uncertainty by encouraging some customers to give up some specific demand for the product to enable demand substitution. It is interesting to explore which strategy is more advantageous to the retailer. We endogenize the inventory decision and demonstrate the efficiency of probabilistic selling through demand substitution. Then we analyze some special cases without cannibalization, and computationally evaluate the profitability and inventory decisions of the two strategies in a more general case to generate managerial insights. The results show that the retailer should adjust inventory decisions depending on products' substitution possibility. The interesting computational result is that probabilistic selling is more profitable with relatively lower product similarity and higher price-sensitive customers, while inventory substitution outperforms probabilistic selling with higher product similarity. Higher demand uncertainty will increase the profitability advantage of probabilistic selling over inventory substitution.Peer ReviewedPostprint (author's final draft