Optimal Talent Management of the Acquisition Workforce in Response to COVID-19: Dynamic Programming Approach

As the economic impact of the COVID-19 pandemic lingers, with the speed of recovery still uncertain, the state of the civilian labor market will impact the public sector. Specifically, the relatively stable and insulated jobs in the Department of Defense (DoD) are expected to be perceived as more attractive for the near future. This implies changes in DoD worker quit behavior that present both a challenge and an opportunity for the DoD leadership in retaining high-quality, experienced talent. The authors use a unique panel dataset of DoD civilian acquisition workers and a dynamic programming approach to simulate the impact of the pandemic on employee retention rates under a variety of recovery scenarios. Their findings posit that workers will choose not to leave the DoD while the civilian sector suffers from the impact of the pandemic. This allows leadership to more easily retain experienced workers. However, once the civilian sector has recovered enough, these same workers quit at an accelerated rate, making gains in talent only temporary. These results imply that while the DoD can take short-run advantage of negative shocks to the civilian sector to retain and attract high-quality employees, long-run retention will be achieved through more fundamental reforms to personnel policy that make DoD jobs more attractive, no matter the state of the civilian labor market.

Optimal portfolios for the DC pension fund with mispricing under the HARA utility framework

<p style='text-indent:20px;'>This paper studies the optimal portfolio selection for defined contribution (DC) pension fund with mispricing. We adopt the general hyperbolic absolute risk averse (HARA) utility to describe the risk performance of the pension fund managers. The financial market comprises a risk-free asset, a pair of mispriced stocks, and the market index. Using the dynamic programming approach, we construct the Hamilton-Jacobi-Bellman (HJB) equation and obtain the explicit expressions for optimal portfolio choices with two methods. Finally, numerical analysis is presented to illustrate the sensitivity of the optimal portfolios to parameters of the financial market and contribution process. <b>200</b> words.</p>

Controlling forever love

A stable and rewarding love relationship is considered a key ingredient for happiness in Western culture. Building a successful long-term relationship can be viewed as a control engineering problem, where the control variable is the effort to be made to keep the relationship alive and well. We introduce a new mathematical model for the effort control problem of a couple in love who wants to stay together forever. The problem can be naturally formulated as a dynamic game in continuous time with nonlinearities. Adopting a dynamic programming approach, a tractable computational formulation of the problem is proposed together with an accompanying algorithm to find numerical solutions of the couple’s effort problem. The computational analysis of the model is used to explore feeling trajectories, effort control paths, happiness, and stabilization mechanisms for different types of successful couples. In particular, the simulation analysis provides insight into the pattern of change of both marital quality and effort making in intact marriages and how they are affected by certain level of heterogamy in the couple.

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

This paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

On some estimation problems for nonlinear dynamic systems

Two problems of nonlinear guaranteed estimation for states of dynamical systems are considered. It is supposed that unknown measurable in $t$ disturbances are linearly included in the equation of motion and are additive in the measurement equations. These disturbances are constrained by nonlinear integral functionals, one of which is analog of functional of the generalized work. The studied problem consists in creation of the information sets according to measurement data containing the true position of the trajectory. The dynamic programming approach is used. If the first functional requires solving a nonlinear equation in partial derivatives of the first order which is not always possible, then for functional of the generalized work it is enough to find a solution of the linear Lyapunov equation of the first order that significantly simplifies the problem. Nevertheless, even in this case it is necessary to impose additional conditions on the system parameters in order for the system trajectory of the observed signal to exist. If the motion equation is linear in state variable, then many assumptions are carried out automatically. For this case the issue of mutual approximation of information sets via inclusion for different functionals is discussed. In conclusion, the most transparent linear quadratic case is considered. The statement is illustrated by examples.

Dynamic Programming Algorithms for Computing Optimal Knockout Tournaments

We study competitions structured as hierarchically shaped single-elimination tournaments. We define optimal tournaments by maximizing attractiveness such that the topmost players will have the chance to meet in higher stages of the tournament. We propose a dynamic programming algorithm for computing optimal tournaments and we provide its sound complexity analysis. Based on the idea of the dynamic programming approach, we also develop more efficient deterministic and stochastic sub-optimal algorithms. We present experimental results obtained with the Python implementation of all the proposed algorithms regarding the optimality of solutions and the efficiency of the running time.