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D escending mechanisms for procurement (or, ascending mechanisms for selling) have been well-recognized for their simplicity from the viewpoint of bidders-they require less bidder sophistication as compared to sealed-bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms.

A mechanism for self propulsion of deformable vesicle has been proposed, vesicle moves by sensing the self-generated chemical gradient. Like many molecular motors they suffer strong perturbations from the environment in which they move as a result of thermal fluctuations and do not rely on inertia for their propulsion. Motion of the vesicle is driven by an asymmetric distribution of reaction products. The propulsive velocity of the device is calculated as well as the scale of the velocity fluctuations. We present the simulation results on velocity of vesicle, reorientation of vesicle, and shape transformation of vesicles.