Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

Simple models for multi-attribute choice with many alternatives: When it does and does not pay to face tradeoffs with binary attributes

Working Paper no longer available. Please contact the author.

Consumer Advisory Bulletin, Hang up on long distance slamming!, January 2008

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A simple adaptive procedure leading to correlated equilibrium

We propose a simple adaptive procedure for playing a game. In thisprocedure, players depart from their current play with probabilities thatare proportional to measures of regret for not having used other strategies(these measures are updated every period). It is shown that our adaptiveprocedure guaranties that with probability one, the sample distributionsof play converge to the set of correlated equilibria of the game. Tocompute these regret measures, a player needs to know his payoff functionand the history of play. We also offer a variation where every playerknows only his own realized payoff history (but not his payoff function).

Take-the-best and other simple strategies: Why and when they work 'well' in binary choice

The effectiveness of decision rules depends on characteristics of bothrules and environments. A theoretical analysis of environments specifiesthe relative predictive accuracies of the lexicographic rule 'take-the-best'(TTB) and other simple strategies for binary choice. We identify threefactors: how the environment weights variables; characteristics of choicesets; and error. For cases involving from three to five binary cues, TTBis effective across many environments. However, hybrids of equal weights(EW) and TTB models are more effective as environments become morecompensatory. In the presence of error, TTB and similar models do not predictmuch better than a naïve model that exploits dominance. We emphasizepsychological implications and the need for more complete theories of theenvironment that include the role of error.

Simple method for detection of MYH11 DNA rearrangements in patients with inv(16)(p13q22) and acute myeloid leukemia.

The pericentric inversion on chromosome 16 [inv(16)(p13q22)] and related t(16;16)(p13;q22) are recurrent aberrations associated with acute myeloid leukemia (AML) M4 Eo. Both abberations result in a fusion of the core binding factor beta (CBFB) and smooth muscle myosin heavy chain gene (MYH11). A selected genomic 6.9-kb BamHl probe detects MYH11 DNA rearrangements in 18 of 19 inv(16)/t(16;16) patients tested using HindIII digested DNA. The rearranged fragments were not detectable after remission in two cases tested, while they were present after relapse in one of these two cases tested.

World population growth and fertility patterns, 1960-2000. A simple model explaining the evolution of world's fertility during the second half of the 20th Century

In this paper we attempt to describe the general reasons behind the world populationexplosion in the 20th century. The size of the population at the end of the century inquestion, deemed excessive by some, was a consequence of a dramatic improvementin life expectancies, attributable, in turn, to scientific innovation, the circulation ofinformation and economic growth. Nevertheless, fertility is a variable that plays acrucial role in differences in demographic growth. We identify infant mortality, femaleeducation levels and racial identity as important exogenous variables affecting fertility.It is estimated that in poor countries one additional year of primary schooling forwomen leads to 0.614 child less per couple on average (worldwide). While it may bepossible to identify a global tendency towards convergence in demographic trends,particular attention should be paid to the case of Africa, not only due to its differentdemographic patterns, but also because much of the continent's population has yet toexperience improvement in quality of life generally enjoyed across the rest of theplanet.