Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Health Programming for Clergy: An Overview of Protestant Programs in the United States

The health of clergy is important, and clergy may find health programming tailored to them more effective. Little is known about existing clergy health programs. We contacted Protestant denominational headquarters and searched academic databases and the Internet. We identified 56 clergy health programs and categorized them into prevention and personal enrichment; counseling; marriage and family enrichment; peer support; congregational health; congregational effectiveness; denominational enrichment; insurance/strategic pension plans; and referral-based programs. Only 13 of the programs engaged in outcomes evaluation. Using the Socioecological Framework, we found that many programs support individual-level and institutional-level changes, but few programs support congregational-level changes. Outcome evaluation strategies and a central repository for information on clergy health programs are needed. © 2011 Springer Science+Business Media, LLC.

Information programs for technology adoption: The case of energy-efficiency audits

We analyze technology adoption decisions of manufacturing plants in response to government-sponsored energy audits. Overall, plants adopt about half of the recommended energy-efficiency projects. Using fixed effects logit estimation, we find that adoption rates are higher for projects with shorter paybacks, lower costs, greater annual savings, higher energy prices, and greater energy conservation. Plants are 40% more responsive to initial costs than annual savings, suggesting that subsidies may be more effective at promoting energy-efficient technologies than energy price increases. Adoption decisions imply hurdle rates of 50-100%, which is consistent with the investment criteria small and medium-size firms state they use. © 2003 Elsevier B.V. All rights reserved.