On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Rules of origin : from analysis to reform

General Introduction This thesis can be divided into two main parts :the first one, corresponding to the first three chapters, studies Rules of Origin (RoOs) in Preferential Trade Agreements (PTAs); the second part -the fourth chapter- is concerned with Anti-Dumping (AD) measures. Despite wide-ranging preferential access granted to developing countries by industrial ones under North-South Trade Agreements -whether reciprocal, like the Europe Agreements (EAs) or NAFTA, or not, such as the GSP, AGOA, or EBA-, it has been claimed that the benefits from improved market access keep falling short of the full potential benefits. RoOs are largely regarded as a primary cause of the under-utilization of improved market access of PTAs. RoOs are the rules that determine the eligibility of goods to preferential treatment. Their economic justification is to prevent trade deflection, i.e. to prevent non-preferred exporters from using the tariff preferences. However, they are complex, cost raising and cumbersome, and can be manipulated by organised special interest groups. As a result, RoOs can restrain trade beyond what it is needed to prevent trade deflection and hence restrict market access in a statistically significant and quantitatively large proportion. Part l In order to further our understanding of the effects of RoOs in PTAs, the first chapter, written with Pr. Olivier Cadot, Celine Carrère and Pr. Jaime de Melo, describes and evaluates the RoOs governing EU and US PTAs. It draws on utilization-rate data for Mexican exports to the US in 2001 and on similar data for ACP exports to the EU in 2002. The paper makes two contributions. First, we construct an R-index of restrictiveness of RoOs along the lines first proposed by Estevadeordal (2000) for NAFTA, modifying it and extending it for the EU's single-list (SL). This synthetic R-index is then used to compare Roos under NAFTA and PANEURO. The two main findings of the chapter are as follows. First, it shows, in the case of PANEURO, that the R-index is useful to summarize how countries are differently affected by the same set of RoOs because of their different export baskets to the EU. Second, it is shown that the Rindex is a relatively reliable statistic in the sense that, subject to caveats, after controlling for the extent of tariff preference at the tariff-line level, it accounts for differences in utilization rates at the tariff line level. Finally, together with utilization rates, the index can be used to estimate total compliance costs of RoOs. The second chapter proposes a reform of preferential Roos with the aim of making them more transparent and less discriminatory. Such a reform would make preferential blocs more "cross-compatible" and would therefore facilitate cumulation. It would also contribute to move regionalism toward more openness and hence to make it more compatible with the multilateral trading system. It focuses on NAFTA, one of the most restrictive FTAs (see Estevadeordal and Suominen 2006), and proposes a way forward that is close in spirit to what the EU Commission is considering for the PANEURO system. In a nutshell, the idea is to replace the current array of RoOs by a single instrument- Maximum Foreign Content (MFC). An MFC is a conceptually clear and transparent instrument, like a tariff. Therefore changing all instruments into an MFC would bring improved transparency pretty much like the "tariffication" of NTBs. The methodology for this exercise is as follows: In step 1, I estimate the relationship between utilization rates, tariff preferences and RoOs. In step 2, I retrieve the estimates and invert the relationship to get a simulated MFC that gives, line by line, the same utilization rate as the old array of Roos. In step 3, I calculate the trade-weighted average of the simulated MFC across all lines to get an overall equivalent of the current system and explore the possibility of setting this unique instrument at a uniform rate across lines. This would have two advantages. First, like a uniform tariff, a uniform MFC would make it difficult for lobbies to manipulate the instrument at the margin. This argument is standard in the political-economy literature and has been used time and again in support of reductions in the variance of tariffs (together with standard welfare considerations). Second, uniformity across lines is the only way to eliminate the indirect source of discrimination alluded to earlier. Only if two countries face uniform RoOs and tariff preference will they face uniform incentives irrespective of their initial export structure. The result of this exercise is striking: the average simulated MFC is 25% of good value, a very low (i.e. restrictive) level, confirming Estevadeordal and Suominen's critical assessment of NAFTA's RoOs. Adopting a uniform MFC would imply a relaxation from the benchmark level for sectors like chemicals or textiles & apparel, and a stiffening for wood products, papers and base metals. Overall, however, the changes are not drastic, suggesting perhaps only moderate resistance to change from special interests. The third chapter of the thesis considers whether Europe Agreements of the EU, with the current sets of RoOs, could be the potential model for future EU-centered PTAs. First, I have studied and coded at the six-digit level of the Harmonised System (HS) .both the old RoOs -used before 1997- and the "Single list" Roos -used since 1997. Second, using a Constant Elasticity Transformation function where CEEC exporters smoothly mix sales between the EU and the rest of the world by comparing producer prices on each market, I have estimated the trade effects of the EU RoOs. The estimates suggest that much of the market access conferred by the EAs -outside sensitive sectors- was undone by the cost-raising effects of RoOs. The chapter also contains an analysis of the evolution of the CEECs' trade with the EU from post-communism to accession. Part II The last chapter of the thesis is concerned with anti-dumping, another trade-policy instrument having the effect of reducing market access. In 1995, the Uruguay Round introduced in the Anti-Dumping Agreement (ADA) a mandatory "sunset-review" clause (Article 11.3 ADA) under which anti-dumping measures should be reviewed no later than five years from their imposition and terminated unless there was a serious risk of resumption of injurious dumping. The last chapter, written with Pr. Olivier Cadot and Pr. Jaime de Melo, uses a new database on Anti-Dumping (AD) measures worldwide to assess whether the sunset-review agreement had any effect. The question we address is whether the WTO Agreement succeeded in imposing the discipline of a five-year cycle on AD measures and, ultimately, in curbing their length. Two methods are used; count data analysis and survival analysis. First, using Poisson and Negative Binomial regressions, the count of AD measures' revocations is regressed on (inter alia) the count of "initiations" lagged five years. The analysis yields a coefficient on measures' initiations lagged five years that is larger and more precisely estimated after the agreement than before, suggesting some effect. However the coefficient estimate is nowhere near the value that would give a one-for-one relationship between initiations and revocations after five years. We also find that (i) if the agreement affected EU AD practices, the effect went the wrong way, the five-year cycle being quantitatively weaker after the agreement than before; (ii) the agreement had no visible effect on the United States except for aone-time peak in 2000, suggesting a mopping-up of old cases. Second, the survival analysis of AD measures around the world suggests a shortening of their expected lifetime after the agreement, and this shortening effect (a downward shift in the survival function postagreement) was larger and more significant for measures targeted at WTO members than for those targeted at non-members (for which WTO disciplines do not bind), suggesting that compliance was de jure. A difference-in-differences Cox regression confirms this diagnosis: controlling for the countries imposing the measures, for the investigated countries and for the products' sector, we find a larger increase in the hazard rate of AD measures covered by the Agreement than for other measures.

Restoration of connexin 40 (cx40) in Renin-producing cells reduces the hypertension of cx40 null mice.

Connexin 40 (Cx40) is expressed by the renin-producing cells (RSCs) of the kidneys and the endothelial cells of blood vessels. Cx40 null mice (Cx40(-/-)) feature a much increased renin synthesis and secretion, which results in chronic hypertension, and also display an altered endothelium-dependent relaxation of the aorta because of reduced eNOS levels and nitric oxide production. To discriminate the effect of Cx40 in renin secretion and vascular signaling, we targeted Cx40 to either the RSCs or the endothelial cells of Cx40 null mice. When compared with Cx40(-/-) controls, the animals expressing Cx40 in RSCs were less hypertensive and featured reduced renin levels, still numerous RSCs outside the wall of the afferent arterioles. In contrast, mice expressing Cx40 in the endothelial cells were as hypertensive as Cx40(-/-) mice, in spite of control levels of Cx37 and eNOS. Our data show that blood pressure is improved by restoration of Cx40 expression in RSCs but not in endothelial cells, stressing the prominent role of renin in the mouse hypertension linked to loss of Cx40.

Oxidative-nitrosative stress and systemic vascular function in highlanders with and without exaggerated hypoxemia.

BACKGROUND: Acute exposure to high altitude stimulates free radical formation in lowlanders, yet whether this persists during chronic exposure in healthy, well-adapted and maladapted highlanders suffering from chronic mountain sickness (CMS) remains to be established. METHODS: Oxidative-nitrosative stress (as determined by the presence of the biomarkers ascorbate radical [A •- ], via electron paramagnetic resonance spectroscopy, and nitrite [NO 2 2 ], via ozone-based chemiluminescence) was assessed in venous blood of 25 male highlanders in Bolivia living at 3,600 m with CMS (n 5 13, CMS 1 ) and without CMS (n 5 12, CMS 2 ). Twelve age- and activity-matched, healthy, male lowlanders were examined at sea level and during acute hypoxia. We also measured fl ow-mediated dilatation (FMD), arterial stiffness defined by augmentation index normalized for a heart rate of 75 beats/min (AIx-75), and carotid intima-media thickness (IMT). RESULTS: Compared with normoxic lowlanders, oxidative-nitrosative stress was moderately increased in the CMS 2 group ( P , .05), as indicated by elevated A •- (3,191 457 arbitrary units [AU] vs 2,640 445 AU) and lower NO 2 2 (206 55 nM vs 420 128 nM), whereas vascular function remained preserved. This was comparable to that observed during acute hypoxia in lowlanders in whom vascular dysfunction is typically observed. In contrast, this response was markedly exaggerated in CMS 1 group (A •- , 3,765 429 AU; NO 2 2 , 148 50 nM) compared with both the CMS 2 group and lowlanders ( P , .05). This was associated with systemic vascular dysfunction as indicated by lower ( P , .05 vs CMS 2 ) FMD (4.2% 0.7% vs 7.6% 1.7%) and increased AIx-75 (23% 8% vs 12% 7%) and carotid IMT (714 127 m M vs 588 94 m M). CONCLUSIONS: Healthy highlanders display a moderate, sustained elevation in oxidative-nitrosative stress that, unlike the equivalent increase evoked by acute hypoxia in healthy lowlanders, failed to affect vascular function. Its more marked elevation in patients with CMS may contribute to systemic vascular dysfunction.

Analysis of susceptibility to human immunodeficiency virus 1 (HIV-1) by comparative genetics

Summary [résumé français voir ci-dessous] From the beginning of the 20th century the world population has been confronted with the human immune deficiency virus 1 (HIV-1). This virus has the particularity to mutate fast, and could thus evade and adapt to the human host. Our closest evolutionary related organisms, the non-human primates, are less susceptible to HIV-1. In a broader sense, primates are differentially susceptible to various retrovirus. Species specificity may be due to genetic differences among primates. In the present study we applied evolutionary and comparative genetic techniques to characterize the evolutionary pattern of host cellular determinants of HIV-1 pathogenesis. The study of the evolution of genes coding for proteins participating to the restriction or pathogenesis of HIV-1 may help understanding the genetic basis of modern human susceptibility to infection. To perform comparative genetics analysis, we constituted a collection of primate DNA and RNA to allow generation of de novo sequence of gene orthologs. More recently, release to the public domain of two new primate complete genomes (bornean orang-utan and common marmoset) in addition of the three previously available genomes (human, chimpanzee and Rhesus monkey) help scaling up the evolutionary and comparative genome analysis. Sequence analysis used phylogenetic and statistical methods for detecting molecular adaptation. We identified different selective pressures acting on host proteins involved in HIV-1 pathogenesis. Proteins with HIV-1 restriction properties in non-human primates were under strong positive selection, in particular in regions of interaction with viral proteins. These regions carried key residues for the antiviral activity. Proteins of the innate immunity presented an evolutionary pattern of conservation (purifying selection) but with signals of relaxed constrain if we compared them to the average profile of purifying selection of the primate genomes. Large scale analysis resulted in patterns of evolutionary pressures according to molecular function, biological process and cellular distribution. The data generated by various analyses served to guide the ancestral reconstruction of TRIM5a a potent antiviral host factor. The resurrected TRIM5a from the common ancestor of Old world monkeys was effective against HIV-1 and the recent resurrected hominoid variants were more effective against other retrovirus. Thus, as the result of trade-offs in the ability to restrict different retrovirus, human might have been exposed to HIV-1 at a time when TRIM5a lacked the appropriate specific restriction activity. The application of evolutionary and comparative genetic tools should be considered for the systematical assessment of host proteins relevant in viral pathogenesis, and to guide biological and functional studies. Résumé La population mondiale est confrontée depuis le début du vingtième siècle au virus de l'immunodéficience humaine 1 (VIH-1). Ce virus a un taux de mutation particulièrement élevé, il peut donc s'évader et s'adapter très efficacement à son hôte. Les organismes évolutivement le plus proches de l'homme les primates nonhumains sont moins susceptibles au VIH-1. De façon générale, les primates répondent différemment aux rétrovirus. Cette spécificité entre espèces doit résider dans les différences génétiques entre primates. Dans cette étude nous avons appliqué des techniques d'évolution et de génétique comparative pour caractériser le modèle évolutif des déterminants cellulaires impliqués dans la pathogenèse du VIH- 1. L'étude de l'évolution des gènes, codant pour des protéines impliquées dans la restriction ou la pathogenèse du VIH-1, aidera à la compréhension des bases génétiques ayant récemment rendu l'homme susceptible. Pour les analyses de génétique comparative, nous avons constitué une collection d'ADN et d'ARN de primates dans le but d'obtenir des nouvelles séquences de gènes orthologues. Récemment deux nouveaux génomes complets ont été publiés (l'orang-outan du Bornéo et Marmoset commun) en plus des trois génomes déjà disponibles (humain, chimpanzé, macaque rhésus). Ceci a permis d'améliorer considérablement l'étendue de l'analyse. Pour détecter l'adaptation moléculaire nous avons analysé les séquences à l'aide de méthodes phylogénétiques et statistiques. Nous avons identifié différentes pressions de sélection agissant sur les protéines impliquées dans la pathogenèse du VIH-1. Des protéines avec des propriétés de restriction du VIH-1 dans les primates non-humains présentent un taux particulièrement haut de remplacement d'acides aminés (sélection positive). En particulier dans les régions d'interaction avec les protéines virales. Ces régions incluent des acides aminés clé pour l'activité de restriction. Les protéines appartenant à l'immunité inné présentent un modèle d'évolution de conservation (sélection purifiante) mais avec des traces de "relaxation" comparé au profil général de sélection purifiante du génome des primates. Une analyse à grande échelle a permis de classifier les modèles de pression évolutive selon leur fonction moléculaire, processus biologique et distribution cellulaire. Les données générées par les différentes analyses ont permis la reconstruction ancestrale de TRIM5a, un puissant facteur antiretroviral. Le TRIM5a ressuscité, correspondant à l'ancêtre commun entre les grands singes et les groupe des catarrhiniens, est efficace contre le VIH-1 moderne. Les TRIM5a ressuscités plus récents, correspondant aux ancêtres des grands singes, sont plus efficaces contre d'autres rétrovirus. Ainsi, trouver un compromis dans la capacité de restreindre différents rétrovirus, l'homme aurait été exposé au VIH-1 à une période où TRIM5a manquait d'activité de restriction spécifique contre celui-ci. L'application de techniques d'évolution et de génétique comparative devraient être considérées pour l'évaluation systématique de protéines impliquées dans la pathogenèse virale, ainsi que pour guider des études biologiques et fonctionnelles

A randomized concave programming method for choice network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing froman offer set, have recently become popular in assortment optimization and revenue management.The dynamic program for these models is intractable and approximated by a deterministiclinear program called the CDLP which has an exponential number of columns. However, whenthe segment consideration sets overlap, the CDLP is difficult to solve. Column generationhas been proposed but finding an entering column has been shown to be NP-hard. In thispaper we propose a new approach called SDCP to solving CDLP based on segments and theirconsideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound onthe dynamic program but coincides with CDLP for the case of non-overlapping segments. Ifthe number of elements in a consideration set for a segment is not very large (SDCP) can beapplied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by(i) simulations, called the randomized concave programming (RCP) method, and (ii) by addingcuts to a recent compact formulation of the problem for a latent multinomial-choice model ofdemand (SBLP+). This latter approach turns out to be very effective, essentially obtainingCDLP value, and excellent revenue performance in simulations, even for overlapping segments.By formulating the problem as a separation problem, we give insight into why CDLP is easyfor the MNL with non-overlapping considerations sets and why generalizations of MNL posedifficulties. We perform numerical simulations to determine the revenue performance of all themethods on reference data sets in the literature.

A tractable consideration set structure for network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offerset, have recently become popular in assortment optimization and revenue management. The dynamicprogram for these models is intractable and approximated by a deterministic linear program called theCDLP which has an exponential number of columns. When there are products that are being consideredfor purchase by more than one customer segment, CDLP is difficult to solve since column generationis known to be NP-hard. However, recent research indicates that a formulation based on segments withcuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In thispaper we investigate the structure of the consideration sets that make the two formulations exactly equal.We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give acounterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation.We derive two classes of valid inequalities called flow and synchronization inequalities to further improve(SDCP+), based on cycles in the consideration set structure. We give a numeric study showing theperformance of these cycle-based cuts.

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.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Actions of β2-adrenoceptor agonist drug on human soleus muscle contraction.

PURPOSE: The effects of β(2)-agonists on human skeletal muscle contractile properties, particularly on slow fibers, are unclear. Moreover, it remains to be ascertained whether central motor drive (CMD) during voluntary contractions could counter for eventual contractile alterations induced by β(2)-agonists. This study investigated central and peripheral neuromuscular adjustments induced by β(2)-agonist terbutaline on a predominantly slow human muscle, the soleus. METHODS: Ten recreationally active men ingested either a single dose of 8 mg of terbutaline or placebo in a randomized double-blind order (two experimental sessions). Isometric plantarflexion torque was measured during single and tetanic (10 and 100 Hz) stimulations as well as during submaximal and maximal voluntary contractions (MVC). Twitch peak torque and half-relaxation time were calculated. CMD was estimated via soleus electromyographic recordings obtained during voluntary contractions performed at approximately 50% MVC. RESULTS: MVC and twitch peak torque were not modified by terbutaline. Twitch half-relaxation time was 28% shorter after terbutaline administration compared with placebo (P < 0.001). Tetanic torques at 10 and 100 Hz were significantly lower after terbutaline intake compared with placebo (-40% and -24% respectively, P < 0.001). Despite comparable torque of submaximal voluntary contractions in the two conditions, CMD was 7% higher after terbutaline ingestion compared with placebo (P < 0.01). CONCLUSION: These results provide evidence that terbutaline modulates the contractility of the slow soleus muscle and suggest that the increased CMD during submaximal contractions may be viewed as a compensatory adjustment of the central nervous system to counter the weakening action induced by terbutaline on the contractile function of slow muscle fibers.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Job creation under liquidity constraints: The Spanish case

This paper shows that liquidity constraints restrict jobcreation even when labor markets are flexible. In a dynamicmodel of labor demand, I show that in an environment of imperfect capital and imperfect labor markets, firms usetemporary contracts to relax financial constraints. Evidence for the predictions of the model is presented using Spanish data from the CBBE (Central de Balances del Banco de España - Balance Sheet data from the Bank of Spain). It is shown that firms substitute temporary laborfor permanent one and use less debt as their financial position improves. In particular, it is rejected that Spanish firms operate in an environment of free capital markets and of no labor adjustment costs. The labor reform of 1984, which created temporary contracts, implied to some extent a relaxation of liquidity constraints.Accordingly, firms used these contracts more extensivelyand used less debt; however, as capital markets continueto be imperfect, permanent job creation continues to beslow. Consequently, relaxation of liquidity constraints should also be part of a job creation strategy.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.