One size does not fit all: personalized incentives in military compensation

A critical element in implementing a compensation scheme including nonmonetary incentives (NMIs) is recognizing that preferences vary widely across Service members. There are at least three sources of variability: across different population classes, across individuals within a population class, and across NMI packages for a particular individual. Surveys across different military communities, ranks, and years of Service show the difficulty of identifying any NMI that has significant value for even 50% of the active duty force. At the same time, approximately 80% of the surveyed Service members expressed a significant positive value for at least one NMI. Therefore, one-size-fits-all incentive packages will not be nearly as effective as more personalized incentive packages. The authors discuss variability in Service member NMI preferences and outline an approach to implementing personalized NMI packages in military compensation through a sealed-bid reverse auction, where Service members select individual NMIs from a “cafeteria-style” menu of options.     

The asymptotic joint distribution of the state occupancy times in an alternating renewal process

An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function F_i, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let U_i(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (U_i(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.     

Extrapolation of the mean lifetime of a large population from its preliminary survival history

A large population of independent identical units having finite mean lifetime T is observed. From the history A(y) of cumulative arrivals and the history B(y) of cumulative removals in the interval 0 ≦ y ≦ τ one must predict at time τ the desired T . Two lifetime predictors X(τ) and Y(τ) and related simple predictors obtained from A(y) and B(y) are shown to converge to T with a rate of convergence dependent on the structure of the failure rate function of the units. This dependence is studied theoretically and numerically.     

A method for reducing coefficients in integer linear inequalities

Approaches are considered for the reduction of coefficients in linear integer inequalities. It is shown that coefficients may be reduced easily in many practical examples. The (0-1) problem is also reconsidered and certain areas of exploration developed.