Diehr G, Tamura H
Department of Management Science, Graduate School of Business Administration, University of Washington, Seattle 98195.
Health Serv Res. 1989 Aug;24(3):329-47.
Tamura, Lauer, and Sanborn (1985) reported a multiple regression approach to the problem of determining a cost reimbursement (rate-setting) formula for facilities providing long-term care (nursing homes). In this article we propose an alternative approach to this problem, using an absolute-error criterion instead of the least-squares criterion used in regression, with a variety of side constraints incorporated in the derivation of the formula. The mathematical tool for implementation of this approach is linear programming (LP). The article begins with a discussion of the desirable characteristics of a rate-setting formula. The development of a formula with these properties can be easily achieved, in terms of modeling as well as computation, using LP. Specifically, LP provides an efficient computational algorithm to minimize absolute error deviation, thus protecting rates from the effects of unusual observations in the data base. LP also offers modeling flexibility to impose a variety of policy controls. These features are not readily available if a least-squares criterion is used. Examples based on actual data are used to illustrate alternative LP models for rate setting.
田村、劳尔和桑伯恩（1985年）报告了一种多元回归方法，用于确定为提供长期护理服务的机构（疗养院）制定成本报销（费率设定）公式的问题。在本文中，我们针对这个问题提出了一种替代方法，使用绝对误差准则而非回归中使用的最小二乘准则，并在公式推导中纳入了各种附带约束条件。实施此方法的数学工具是线性规划（LP）。本文首先讨论了费率设定公式应具备的理想特征。利用线性规划，从建模和计算的角度都可以轻松实现具有这些特性的公式的开发。具体而言，线性规划提供了一种有效的计算算法，以最小化绝对误差偏差，从而使费率免受数据库中异常观测值的影响。线性规划还提供了建模灵活性，可施加各种政策控制。如果使用最小二乘准则，则这些功能并不容易实现。基于实际数据的示例用于说明费率设定的替代线性规划模型。
