A derivative-free approach for a simulation-based optimization problem in healthcare

Hospitals have been challenged in recent years to deliver high quality care with limited resources. Given the pressure to contain costs,developing procedures for optimal resource allocation becomes more and more critical in this context. Indeed, under/overutilization of emergency room and ward resources can either compromise a hospital's ability to provide the best possible care, or result in precious funding going toward underutilized resources. Simulation--based optimization tools then help facilitating the planning and management of hospital services, by maximizing/minimizing some specific indices (e.g. net profit) subject to given clinical and economical constraints. In this work, we develop a simulation--based optimization approach for the resource planning of a specific hospital ward. At each step, we first consider a suitably chosen resource setting and evaluate both efficiency and satisfaction of the restrictions by means of a discrete--event simulation model. Then, taking into account the information obtained by the simulation process, we use a derivative--free optimization algorithm to modify the given setting. We report results for a real--world problem coming from the obstetrics ward of an Italian hospital showing both the effectiveness and the efficiency of the proposed approach

Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has grown: several new applications have arisen where the problem at hand constitutes a subproblem, and several new algorithms have been developed for its efficient solution. This paper therefore serves three purposes. First, it provides an up-to-date extension of the survey of the literature of the field, complementing the survey in Patriksson (2008) with more then 20 books and articles. Second, it contributes improvements of some of these algorithms, in particular with an improvement of the pegging (that is, variable fixing) process in the relaxation algorithm, and an improved means to evaluate subsolutions. Third, it numerically evaluates several relaxation (primal) and breakpoint (dual) algorithms, incorporating a variety of pegging strategies, as well as a quasi-Newton method. Our conclusion is that our modification of the relaxation algorithm performs the best. At least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

Reciprocity-driven Sparse Network Formation

A resource exchange network is considered, where exchanges among nodes are based on reciprocity. Peers receive from the network an amount of resources commensurate with their contribution. We assume the network is fully connected, and impose sparsity constraints on peer interactions. Finding the sparsest exchanges that achieve a desired level of reciprocity is in general NP-hard. To capture near-optimal allocations, we introduce variants of the Eisenberg-Gale convex program with sparsity penalties. We derive decentralized algorithms, whereby peers approximately compute the sparsest allocations, by reweighted l1 minimization. The algorithms implement new proportional-response dynamics, with nonlinear pricing. The trade-off between sparsity and reciprocity and the properties of graphs induced by sparse exchanges are examined.Comment: 19 page