Analysis of an Alternative Military Healthcare Benefit Design

Abstract

The Military Compensation and Retirement Modernization Commission was established by the Congress in 2013 to perform a systematic review of military compensation to address rising costs and other trends. Their recommendation for reforming the TRICARE health care program was sweeping, and differed greatly from earlier proposals that focused on increasing beneficiary cost shares. Specifically, the commission proposed overhauling the current benefit delivery model and replacing it with a premium-based insurance model offering a menu of DoD-sponsored private health plans. The analysis presented here is based on work that supported the commission by estimating the budgetary impact of its proposed reforms. Results indicate that movement towards the premium-based model would produce an annual budgetary cost savings in the $2 billion to $4 billion range, with a best savings estimate of $3.2 billion.     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Limiting survival functions of self‐similar structures

We show the existence of a unique analytic single parameter limiting survival function arising from the repeated composition of a coherent structure as the number of components tends to infinity. Examples include the repeated composition process of the bridge structure. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Some approximations in multi-item,multi-echelon inventory systems for recoverable items

The optimization problem as formulated in the METRIC model takes the form of minimizing the expected number of total system backorders in a two-echelon inventory system subject to a budget constraint. The system contains recoverable items – items subject to repair when they fail. To solve this problem, one needs to find the optimal Lagrangian multiplier associated with the given budget constraint. For any large-scale inventory system, this task is computationally not trivial. Fox and Landi proposed one method that was a significant improvement over the original METRIC algorithm. In this report we first develop a method for estimating the value of the optimal Lagrangian multiplier used in the Fox-Landi algorithm, present alternative ways for determining stock levels, and compare these proposed approaches with the Fox-Landi algorithm, using two hypothetical inventory systems – one having 3 bases and 75 items, the other 5 bases and 125 items. The comparison shows that the computational time can be reduced by nearly 50 percent. Another factor that contributes to the higher requirement for computational time in obtaining the solution to two-echelon inventory systems is that it has to allocate stock optimally to the depot as well as to bases for a given total-system stock level. This essentially requires the evaluation of every possible combination of depot and base stock levels – a time-consuming process for many practical inventory problems with a sizable system stock level. This report also suggests a simple approximation method for estimating the optimal depot stock level. When this method was applied to the same two hypotetical inventory systems indicated above, it was found that the estimate of optimal depot stock is quite close to the optimal value in all cases. Furthermore, the increase in expected system backorders using the estimated depot stock levels rather than the optimal levels is generally small.     

Allocation of resources to randomly occurring opportunities

An allocation problem is considered in lvhich different kinds of resources must be allocated to various activities, within a given time period. The opportunities for allo'cation appear randomly during this period. Certain assumptions about the values of possible allocations and the distribution of occurrences of opportunities lead to a dynamic programming formulation of the problem. This leads to a system of ordinary differential equations which are (in theory) solvable recursively, and can be solved numerically to any desired degree of precision. An example is given for the allocation of aircraft-carried weapons to targets of opportunity.     

Geometric programming with multiplicative slack variables

A posynomial geometric programming problem formulated so that the number of objective function terms is equal to the number of primal variables will have a zero degree of difficulty when augmented by multiplying each constraint term by a slack variable and including a surrogate constraint composed of the product of the slack variables, each raised to an undetermined negative exponent or surrogate multiplier. It is assumed that the original problem is canonical. The exponents in the constraint on the product of the slack variables must be estimated so that the associated solution to the augmented problem, obtained immediately, also solves the original problem. An iterative search procedure for finding the required exponents, thus solving the original problem, is described. The search procedure has proven quite efficient, often requiring only two or three iterations per degree of difficulty of the original problem. At each iteration the well-known procedure for solving a geometric programming problem with a zero degree of difficulty is used and so computations are simple. The solution generated at each iteration is optimal for a problem which differs from the original problem only in the values of some of the constraint coefficients, so intermediate solutions provide useful information.