NOTA 13 OTRAS NOTAS DE INVERSIONES
RESERVA DE DESCALCE SEGUROS CON CUENTA DE INVERSIÓN (CUI)
CRAM is a reverse multi-unit auction developed by Coughlan, Gates, and Myung (Coughlan et al., 2013), where the auction incorporates both monetary and non-monetary incentives (NMIs). These NMIs may include examples such as geographic stability for follow-on orders, career intermission programs, and post-graduate educational opportunities, in addition to whatever other future policy may develop. Utilizing CRAM should meet retention goals just like the simple uniform-price auction, but CRAM also provides the opportunity to reduce costs by retaining aviators who receive utility from the NMIs instead of receiving a simple monetary payment.
Like both the simple uniform-price auction and the QUAD auction, each aviator submits a bid for the cash bonus for additional obligated service; in addition, aviators select which NMIs they want to receive as well. Sealed bids are collected and the seller’s bid is developed from the combination of cash and NMIs. A pre-determined quantity of offers is selected from the lowest bids and the accepted offers receive a bonus equal to the cost of the first excluded bid. The actual bonus composition includes some cash amount from the cut-off bid, plus any NMIs selected, minus the cost of those NMIs. Refer to the model description for the exact computation.
In this type of auction, since NMIs are included, optimal bidding strategies must include the value of the NMI for each individual. The monetary value will equal the reservation price minus the value of the combination of NMIs. Individuals should, therefore, only select NMIs where the value of the NMI exceeds the cost of the NMI. See Myung for additional insight into bidding strategies.
1. Model Description
Aviators (A ) are characterized by their bids (i b ) which includes cash bonus and i some set of NMIs if desired, and reservation prices (r ). The objective of i A is to i maximize payoff (p ), the cash bonus and NMI combination(s), by submitting their bids. i The number of aviators participating in the auction is denoted by N. The Navy’s objective is retaining M of N aviators. For this research’s example, focus was placed on a simplified case of three NMIs, (e, f and g ), but there is flexibility to adjust the number of NMIs to match strategic manpower goals and opportunities. Aviators may select any combination of these NMIs, and each NMI increases the bid by a corresponding amount, E , c F , and c G which are the costs of providing these NMIs. c
Each aviator provides personal valuation for the NMIs offered, E i F and i G . The i
adjusted bids ( ) are calculated in the following manner:
{
}
*
i i c c c
b
=
b
+eE
+
fF
+
gG
The sealed bids are received during the auction period and ranked from lowest to highest
( ){ }
* 1 N i i b= and, without loss of generality, let if . The M lowest bids
are retained; in the case that multiples bids of b are submitted, the tie will be broken M* randomly. The cut-off bid is then set tobM*+1, or the first excluded bid. Aviators for who
*
i
b bM*+1 are selected to receive a bonus, selected for retention, and incur the required service obligation. Bonuses are bestowed in the following manner:
{
*}
1
(
)
(
)
(
)
i M i c i c i C
p
=
b
++e E
−
E
+
f F
−F
+
g G
−G
where e, f, g each = 1if NMI selected; 0 if NMI not selected
All retained aviators will receive, at a minimum, the bonus amount submitted in his or her bid while most will receive a bonus larger than the initial bid ( ). CRAM is developed so that aviators would only select NMIs when the value each aviator derives from receiving it exceeds the cost of selecting it (e.g. ).
Aviators who are not selected receive no bonus but are still eligible to remain in the aviation community. Alternatively, they may laterally transfer to another community, reserve component, or separate from Active Duty at the completion of their MSR.
2. Example Auction
Table 13 provides an example of the CRAM auction. The retention goals match the example found in the simple uniform-price auction example in Table 9. Additionally, overall reservation prices are held the same, indicating no change in the reservation values each aviator places on the obligated service. The three available NMIs are listed as
e, f , andg , each with an associated cost of $10,000. Aviators who select any or all of the NMIs have the associated costs added to their overall CRAM bid. Aviators that did not select any NMIs received no adjustment to their original bids.
After adjusting for the adjustments, the bids are re-ranked and the cutoff established at bM*+1 = $91,000. Retained aviators receive the NMIs requested and $91,000
less the cost of the requested NMIs. In this example, aviators received excess utility from the NMIs while the Navy reduced the total monetary costs by $160,000, for a savings of 16.5% compared to the simple uniform-price auction.
V.
AVIATON RETENTION SURVEY AND METHODOLOGY
Utilizing a comparable study from previous research (Kelso, 2014), a survey of Naval Aviators from Lieutenant Junior Grade (O-2) to Commander (O-5) was developed to compare the current ACCP program against three auction mechanisms: Uniform-Price Auction, QUAD Auction, and CRAM. The survey was designed to collect individual performance history, to include FITREP promotion recommendations and career milestones, as well as reservation prices for agreeing to serve additional years of obligated service. Individual preferences for specific non-monetary incentives (NMIs) were addressed and respective values for each NMI were assigned by each respondent. Qualitative assessments of various aspects of Navy life and their impact on propensity to remain in service were asked to establish possible elements of retention issues. This data was then used to model all three auction mechanisms based on projected retention rates and costs from FY-2013 under the current ACCP system in order to determine market prices and values.