No abstract

In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

In the last few years, several articles have proposed decision trees (DTs) as an alternative to computerized adapted tests (CATs). These works have focused on showing the differences between the two methods with the aim of identifying the advantages of each of them and thus determining when it is preferable to use one method or another. In this article, Tree-CAT, a new technique for building CATs is presented. Unlike the existing work, Tree-CAT exploits the similarities between CATs and DTs. This technique allows the creation of CATs that minimise the mean square error in the estimation of the examinee's ability level, and controls the item's exposure rate. The decision tree is sequentially built by means of an innovative algorithmic procedure that selects the items associated with each of the tree branches by solving a linear program. In addition, our work presents further advantages over alternative item selection techniques with exposure control, such as instant item selection or simultaneous administration of the test to an unlimited number of participants. These advantages allow accurate on-line CATs to be implemented even when the item selection method is computationally costly.

This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.

In this article we propose the use of an information-content based measure as a proxy for supply chain complexity. The focus of our research is the problem of structural complexity in the supply chain, i.e. the complexity emanating from the proliferation of products, channels and markets. Notwithstanding it is widely agreed among practitioners that this proliferation damages supply chains, rendering them less efficient, there is still need for a mechanism for measuring structural complexity and evaluating its impact on the firm's performance. In an attempt to filling this void, we propose a definition that originates from the firm's business strategy and, based on it, suggest the direct use of entropy as a more austere measure for structural complexity than other available alternatives, which rely heavily in the use of typically hard to acquire data. We show that the suggested measure has some interesting mathematical properties (to which we refer to as internal consistency) together with the capability of reproducing certain empirical regularities observed in supply chain management (external consistency). Moreover, the proposed measure has attributes that are not present in other measures: it requires a limited and easily accessible amount of data, it allows direct comparison between firms or business units, and it is a useful tool for assessing the impact on structural complexity of alternative managerial decisions (the look-ahead property). Numerical examples are provided.