An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns

We consider the stochastic linear knapsack problem in which costs are known with certainty but returns are independent, normally distributed random variables. The objective is to maximize the probability that the overall return equals or exceeds a specified target value. A previously proposed preference order dynamic programming-based algorithm has been shown to be potentially suboptimal. We offer an alternative hybrid DP/branch-and-bound algorithm that both guarantees optimality and significantly outperforms generating the set of Pareto optimal returns.© 1993 John Wiley & Sons, Inc.     

Control-variate selection criteria

For multiresponse simulations requiring point and confidence-region estimators of the mean response, we propose control-variate selection criteria that minimize mean-square confidence-region volume in two situations: (a) Only the mean control vector is known, and standard linear control-variate estimation procedures are used. (b) Covariances among controls are also known and are incorporated into new linear control-variate estimation procedures. An example illustrates the performance of these selection criteria.     

Techniques for establishing ergodic and recurrence properties of continuous-valued markov chains

We present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a “mean drift” criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity. The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting-time-dependent service times, dams with general and random-release rules, the s-S inventory model, and feedback models.     

Multiple-attribute decision making with partial information: The comparative hypervolume criterion

A new approach is presented for analyzing multiple-attribute decision problems in which the set of actions is finite and the utility function is additive. The problem can be resolved if the decision makers (or group of decision makers) specifies a set of nonnegative weights for the various attributes or criteria, but we here assume that the decision maker(s) cannot provide a numerical value for each such weight. Ordinal information about these weights is therefore obtained from the decision maker(s), and this information is translated into a set of linear constraints which restrict the values of the weights. These constraints are then used to construct a polytope W of feasible weight vectors, and the subsets H_i (polytopes) of W over which each action a_i has the greatest utility are determined. With the Comparative Hypervolume Criterion we calculate for each action the ratio of the hypervolume of H_i to the hypervolume of W and suggest the choice of an action with the largest such ratio. Justification of this choice criterion is given, and a computational method for accurately approximating the hypervolume ratios is described. A simple example is provided to evaluate the efficiency of a computer code developed to implement the method.     

Between Man and Nature: The Enduring Wisdom of Sir Halford J. Mackinder

This article argues for the continued relevance of the work and theories of the British Geostrategist Sir Halford J. Mackinder (1861-1947). It asserts that commentators and scholars who seek to marginalise Mackinder have too often dismissed his theories without setting them in the context of their continued endorsement in crucial areas of the globe. After 1945, despite his theories being tainted by association with Nazi Germany and Imperial Japan, both Moscow and Washington recognised the utility of Mackinder’s work and tailored policy accordingly. The end of Cold War saw Mackinder fall out of favour as his model was deemed unsuitable for policy analysis by a number of influential thinkers. It is argued here that, in recent years, the arena of international politics has seen a rehabilitation of Mackinder, accompanied by a resurgence of interest in Geopolitics. Finally, the piece examines those areas of the contemporary globe where Mackinder’s influence is greatest.