We investigate computational and mechanism design aspects of scarce resource allocation, where the primary rationing mechanism is through waiting times. Specifically we consider allocating medical treatments to a population of patients. Each patient needs exactly one treatment, and can choose from @math hospitals. Hospitals have different costs, which are fully paid by a third party ---the "payer". The payer has a fixed budget @math , and each hospital will have its own waiting time. At equilibrium, each patient will choose his most preferred hospital given his intrinsic preferences and the waiting times. The payer thus computes the waiting times so that at equilibrium the budget constraint is satisfied and the social welfare is maximized. We first show that the optimization problem is NP-hard, yet if the budget can be relaxed to @math for an arbitrarily small @math , then the optimum under budget @math can be approximated efficiently. Next, we study the endogenous emergence of waiting time from the dynamics between hospitals and patients, and show that there is no need for the payer to explicitly enforce the optimal waiting times. Under certain conditions, all he need is to enforce the amount of money he wants to pay to each hospital. The dynamics will always converge to the desired waiting times in finite time. We then go beyond equilibrium solutions and investigate the optimization problem over a much larger class of mechanisms containing the equilibrium ones as special cases. With two hospitals, we show that under a natural assumption on the patients' preference profiles, optimal welfare is in fact attained by the randomized assignment mechanism, which allocates patients to hospitals at random subject to the budget constraint, but avoids waiting times. Finally, we discuss potential policy implications of our results, as well as follow-up directions and open problems.
The role of waiting time can be studied either from the supply side, namely, how waiting times interact with the hospitals' incentives, or from the demand side, namely, how they interact with the patients' incentives. In @cite_1 the authors give a thorough analysis of existing policies on reducing waiting times by affecting the incentives of either side. Our model focuses on the demand side, and below we discuss some other works that also focus on this side.
@cite_1
2004972267 2058115997 1592804782 1976263021
This paper compares policies to tackle excessive waiting times for elective surgery in 12 OECD countries. It is found that waiting times may be reduced by acting on the supply of or on the demand for surgery (or both). On the supply side, evidence suggests that both capacity and financial incentives towards productivity can play an important role. On the demand side, inducing a raising of clinical thresholds may reduce waiting times but may also provoke tension between clinicians and policy makers. Preliminary evidence also suggests that an increase in private health insurance coverage may reduce waiting times. We examine the role of quality and waiting time in health insurance when there is ex post moral hazard. Quality and waiting time provide additional instruments to control demand and potentially can improve the trade-off between optimal risk bearing and optimal consumption of health care. We show that optimal quality is lower than it would be in the absence of ex post moral hazard. But it is never optimal to have a positive waiting time if the marginal cost of waiting is higher for patients with greater benefits from health care. We deal with a cost-allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context of several medical procedures, a certain demand for treatment and a maximum average waiting-time guaranteed by the government. We show that the sharing of an operating-theatre to treat patients of different medical disciplines leads to a cost reduction. We then compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the recovery time, we characterize the conditions under which the co-operation among treatments has a positive impact on the post-operative costs. Finally, a numerical example, constructed on the basis of real data, is provided to highlight the main features of our model. Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process in some cyclic production systems (that is, reduction in switchover times can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some explicit formulas that provide additional insight and characterization of this anomaly. More specifically, we show that, for both of these models, there exist simple formulas that define for each queue a critical value z* of the mean total setup time z per cycle such that, if z < z*, then the expected waiting time at that queue will be minimized if the server is forced to idle for a constant length of time z*- z every cycle; also, for the symmetric polling model, we give a simple explicit formula for the expected waiting time and the critical value z* that minimizes it.