Motivated by the Bike Angels Program in New York's Citi Bike and Boston's Blue Bikes, we study the use of (registered) volunteers to re-position empty bikes for riders in a bike sharing system. We propose a method that can be used to deploy the volunteers in the system, based on the real time distribution of the bikes in different stations. To account for (random) route demand in the network, we solve a related transshipment network design model and construct a sparse structure to restrict the re-balancing activities of the volunteers (concentrating re-balancing activities on essential routes). We also develop a comprehensive simulation model using a threshold-based policy to deploy the volunteers in real time, to test the effect of choice restriction on volunteers (suitably deployed) to re-position bikes. We use the Hubway system in Boston (with 60 stations) to demonstrate that using a sparse structure to concentrate the re-balancing activities of the volunteers, instead of allowing all admissible flows in the system (as in current practice), can reduce the number of re-balancing moves by a huge amount, losing only a small proportion of demand satisfied.

We study the bundle size pricing (BSP) problem where a monopolist sells bundles of products to customers, and the price of each bundle depends only on the size (number of items) of the bundle. Although this pricing mechanism is attractive in practice, finding optimal bundle prices is difficult since it involves characterizing distributions of the maximum partial sums of order statistics. In this paper, we propose to solve the BSP problem under a class of choice model using only the first and second moments of customer valuations. We show that the BSP problem under this model is convex and can be efficiently solved using off-the-shelf solvers. Our approach is flexible in optimizing any given bundle sizes, and numerical results show that it performs very well compared with state-of-the-art heuristics.

We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithm balances a global criterion (routing time) with a local criterion (maximum queue size) and shows how to get simultaneous good bounds for both. For this particular problem, approximating the routing time well, even without considering the queue sizes, was open. We then consider a class of such local vs. global problems in the context of covering integer programs and show how to improve the local criterion by a logarithmic factor by losing a constant factor in the global criterion.

We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several well-known and new formulations for the problem. We further establish a connection between the multiway cut and the maximum-weighted independent set problem. This leads to the study of several instances of the multiway cut problem through the theory of perfect graphs. We also introduce a new randomized rounding argument to study the sharpness of these formulations. © 1999 John Wiley & Sons, Inc. Networks 34: 102–114, 1999

Abstract. We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithmbalances a global criterion (routing time) with a local criterion (maximum queue size) and shows how to get simultaneous good bounds for both. For this particular problem, approximating the routing time well, even without considering the queue sizes, was open. We then consider a class of such local vs. global problems in the context of covering integer programs and show how to improve the local criterion by a logarithmic factor by losing a constant factor in the global criterion.