Budget-feasible Maximum Nash Social Welfare is Almost Envy-free

The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016 and TEAC 2019) that an allocation maximizing the NSW is envy-free up to one good (EF1). In this paper, we are interested in the fairness of the NSW in a budget-feasible allocation problem, in which each item has a cost that will be incurred to the agent it is allocated to, and each agent has a budget constraint on the total cost of items she receives. We show that a budget-feasible allocation that maximizes the NSW achieves a 1/4-approximation of EF1 and the approximation ratio is tight. The approximation ratio improves gracefully when the items have small costs compared with the agents' budgets; it converges to 1/2 when the budget-cost ratio approaches infinity.

The Social Costs of Side Trading

We study resource allocation under private information when the planner cannot prevent bilateral side trading between consumers and firms. Adverse selection and side trading severely restrict feasible trades: each marginal quantity must be fairly priced given the consumer types who purchase it. The resulting social costs are twofold. First, second-best efficiency and robustness to side trading are in general irreconcilable requirements. Second, there actually exists only one budget-feasible allocation robust to side trading, which deprives the planner from any capacity to redistribute resources between different types of consumers. We discuss the relevance of our results for insurance and financial markets.

Adjusting Daily Inpatient Bed Allocation to Smooth Emergency Department Occupancy Variation

Study Objective: Overcrowding in emergency departments (ED) is an increasingly common problem in Taiwanese hospitals, and strategies to improve efficiency are in demand. We propose a bed resource allocation strategy to overcome the overcrowding problem. Method: We investigated ED occupancy using discrete-event simulation and evaluated the effects of suppressing day-to-day variations in ED occupancy by adjusting the number of empty beds per day. Administrative data recorded at the ED of Taichung Veterans General Hospital (TCVGH) in Taiwan with 1500 beds and an annual ED volume of 66,000 visits were analyzed. Key indices of ED quality in the analysis were the length of stay and the time in waiting for outward transfers to in-patient beds. The model is able to analyze and compare several scenarios for finding a feasible allocation strategy. Results: We compared several scenarios, and the results showed that by reducing the allocated beds for the ED by 20% on weekdays, the variance of daily ED occupancy was reduced by 36.25% (i.e., the percentage of reduction in standard deviation). Conclusions: This new allocation strategy was able to both reduce the average ED occupancy and maintain the ED quality indices.

Vote budgets and Dodgson’s method of marks

We examine voting rules that are inspired by Dodgson’s method of marks (to be distinguished from the procedure that is commonly referred to as Dodgson’s rule) by means of two criteria. Each voter decides how to allocate a vote budget (which is common to all voters, and need not be exhausted) to the candidates. Our first criterion is a richness condition: we demand that, for any possible preference ordering a voter may have, there is a feasible allocation of votes that reflects these preferences. A (tight) lower bound on the vote budget is established. Adding a strategy-proofness condition as a second criterion, we recommend that the vote budget be given by the lower bound determined in our first result.

The asymptotic maximal procedure for subject randomization in clinical trials

The maximal procedure is a restricted randomization method that maximizes the number of feasible allocation sequences under the constraints of the maximum tolerated imbalance and the allocation sequence length. It assigns an equal probability to all feasible sequences. However, its implementation is not easy due to the lack of the Markovian property of the conditional allocation probabilities. In this paper, we propose the asymptotic maximal procedure, which replaces the sequence-length-dependent conditional allocation probabilities with their asymptotic values. The new randomization procedure is compared with the original maximal procedure and few other randomization procedures with the maximum tolerated imbalance via simulations and is found to be a practical choice for future clinical trials.

ADAPTIVE RESOURCE ALLOCATION TO MAXIMIZE RUN-OUT TIMES

We introduce a method for maximizing the run-out time for a system where the number of components available to make repairs is finite, and some of the components may be substituted for one another. The objective is to maximize the time at which the earliest run-out of any component occurs. The approach proposed here is to find the minimum time horizon such that no feasible allocation exists for a related linear programming problem. An adaptive version of this algorithm is proposed as a heuristic for the stochastic problem.