Optimal search for a moving target with the option to wait

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

The growth in military expenditure in Germany 1951–2011: did parties matter?

We examine whether government ideology was correlated with the growth in military expenditure in Germany over the period 1951–2011. Using various measures of government ideology, the results do not show any effect. The exception is an ideology measure based on the Comparative Manifesto Project (left-right scale): using this measure, the results show that the growth in military expenditure increased by about 2.4 percentage points, when the ideology variable (right-wing) increased by one standard deviation. This effect, however, is based on observations until the early 1960s and cannot be generalized. The major political parties agreed on how to evaluate international risks and threats. Government ideology retired to the background. We conjecture that the consensus among the major parties will persist – even if military spending needs to be increased in response to new international risks and threats.     

Decomposing inventory routing problems with approximate value functions

We present a time decomposition for inventory routing problems. The methodology is based on valuing inventory with a concave piecewise linear function and then combining solutions to single‐period subproblems using dynamic programming techniques. Computational experiments show that the resulting value function accurately captures the inventory's value, and solving the multiperiod problem as a sequence of single‐period subproblems drastically decreases computational time without sacrificing solution quality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010