A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

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.

The impact of investment in education on economic development: Spain in comparative perspective (1860-2000)

Throughout the 19th century and until the mid-20th century, in terms of long-terminvestment in human capital and, above all, in education, Spain lagged far behind theinternational standards and, more specifically, the levels attained by its neighbours inEurope. In 1900, only 55% of the population could read; in 1950, the figure was 93%.This no doubt contributed to a pattern of slower economic growth in which thephysical strength required for agricultural work, measured here through height, had alarger impact than education on economic growth. It was not until the 1970s, with thearrival of democracy, that the Spanish education system was modernized and theinfluence of education on economic growth increased.

Insider Trading and Real Investment

In this paper I analyze the effects of insider trading on real investmentand the insurance role of financial markets. There is a single entrepreneurwho, at a first stage, chooses the level of investment in a risky business.At the second stage, an asset with random payoff is issued and then the entrepreneurreceives some privileged information on the likely realization of productionreturn. At the third stage, trading occurs on the asset market, where theentrepreneur faces the aggregate demand coming from a continuum of rationaluniformed traders and some noise traders. I compare the equilibrium withinsider trading (when the entrepreneur trades on her inside information in theasset market) with the equilibrium in the same market without insider trading. Ifind that permitting insider trading tends to decrease the level of realinvestment. Moreover, the asset market is thinner and the entrepreneur's netsupply of the asset and the hedge ratio are lower, although the asset priceis more informative and volatile.

Economic growth and investment in the Arab world

This paper analyses the economic growth performance in the Arab world overthe last forty years. The Arab world has managed to reduce povertyperformance despite its relatively disappointing growth performance. Werelate this poor performance of both oil and non-oil producers toinvestment. Contrary to widespread belief, we do not find evidence that lowquantity of investment is the main of low growth. The decline in theinvestment rate followed rather than preceded the reduction in the aggregategrowth rate. We conclude that the low quality of investment projects is thekey determinant of growth. The excessive reliance on public investment, thelow quality of financial institutions, the bad business environment (due topolitical and social instability and to excessive public intervention andoverregulation) and the low quality of human capital are importantdeterminants of systematically unproductive investment decisions and, thus,low economic growth.

Financial intermediation and equity investment with costly monitoring

This paper studies the efficiency of equilibria in a productive OLG economy where the process of financial intermediation is characterized by costly state verification. Both competitive equilibria and Constrained Pareto Optimal allocations are characterized. It is shown that market outcomes can be socially inefficient, even when a weaker notion than Pareto optimality is considered.

Is lumpy investment really irrelevant for the business cycle?

New-Keynesian (NK) models can only account for the dynamic effects of monetary policy shocks if it is assumed that aggregate capital accumulation is much smoother than it would be the case under frictionless firm-level investment, as discussed in Woodford (2003, Ch. 5). We find that lumpy investment, when combined with price stickiness and market power of firms,can rationalize this assumption. Our main result is in stark contrast with the conclusions obtained by Thomas (2002) in the context of a real business cycle (RBC) model. We use our model to explain the economic mechanism behind this difference in the predictions of RBC and NK theory.

Short-term investment and equilibrium multiplicity

I study the effects of the heterogeneity of traders'horizon in the context of a 2-period NREE model whereall traders are risk averse. Owing to inventory effects,myopic trading behavior generates multiplicity ofequilibria. In particular, two distinct patterns arise.Along the first equilibrium, short term tradersanticipate higher second period price reaction toinformation arrival and, owing to risk aversion,scale back their trading intensity. This, in turn,reduces both risk sharing and information impoundinginto prices enforcing a high returns' volatility-lowprice informativeness equilibrium. In the second one,the opposite happens and a low volatility-high priceinformativeness equilibrium arises.

Does foreign direct investment crowd out domestic entrepreneurship?

In analyzing firm entry and exit across Belgian manufacturing industries,this paper presents evidence that import competition and foreign directinvestment discourage entry and stimulate exit of domestic entrepreneurs.These results are in line with theoretical occupational choice modelsthat predict foreign direct investment would crowd out domesticentrepreneurs through their selections in product and labor markets.However, the empirical results also suggest that this crowding out effectmay be moderated or even reversed in the long-run due to the long termpositive effects of FDI on domestic entrpreneurship as a result oflearning, demonstration, networking and linkage effects between foreignand domestic firms.

Financing constraints, irreversibility and investment dynamics

We develop a model of an industry with many heterogeneous firms that face both financingconstraints and irreversibility constraints. The financing constraint implies that firmscannot borrow unless the debt is secured by collateral; the irreversibility constraint thatthey can only sell their fixed capital by selling their business. We use this model to examinethe cyclical behavior of aggregate fixed investment, variable capital investment, and outputin the presence of persistent idiosyncratic and aggregate shocks. Our model yields threemain results. First, the effect of the irreversibility constraint on fixed capital investmentis reinforced by the financing constraint. Second, the effect of the financing constraint onvariable capital investment is reinforced by the irreversibility constraint. Finally, the interactionbetween the two constraints is key for explaining why input inventories and materialdeliveries of US manufacturing firms are so volatile and procyclical, and also why they arehighly asymmetrical over the business cycle.

Testing financing constraints on firm investment using variable capital

We consider a dynamic multifactor model of investment with financing imperfections,adjustment costs and fixed and variable capital. We use the model to derive a test offinancing constraints based on a reduced form variable capital equation. Simulation resultsshow that this test correctly identifies financially constrained firms even when the estimationof firms investment opportunities is very noisy. In addition, the test is well specified inthe presence of both concave and convex adjustment costs of fixed capital. We confirmempirically the validity of this test on a sample of small Italian manufacturing companies.

Firm-specific investment, sticky prices and the Taylor principle

According to the Taylor principle a central bank should adjust the nominal interest rate by more than one-for-one in response to changes in current inflation. Most of the existing literature supports the view that by following this simple recommendation a central bank can avoid being a source of unnecessary fluctuations in economic activity. The present paper shows that this conclusion is not robust with respect to the modelling of capital accumulation. We use our insights to discuss the desirability of alternative interest raterules. Our results suggest a reinterpretation of monetary policy under Volcker and Greenspan: The empirically plausible characterization of monetary policy can explain the stabilization of macroeconomic outcomes observed in the early eighties for the US economy. The Taylor principle in itself cannot.

Health investment complementarities under competing risks

Applying the competing--risks model to multi--cause mortality,this paper provides a theoretical and empirical investigation of the positive complementarities that occur between disease--specific policy interventions. We argue that since an individual cannot die twice, competing risks imply that individuals will not waste resources on causes that are not the most immediate, but will make health investments so as to equalize cause--specific mortality. However, equal mortality risk from a variety of diseases does not imply that disease--specific public health interventions are a waste. Rather, a cause--specific intervention produces spillovers to other disease risks, so that the overall reduction in mortality will generally be larger than the direct effect measured on the targeted disease. The assumption that mortality from non--targeted diseases remains the same after a cause--specific intervention under--estimates the true effect of such programs, since the background mortality is also altered as a result of intervention. Analyzing data from one of the most important public health programs ever introduced, the Expanded Program on Immunization (EPI) of the United Nations, we find evidence for the existence of such complementarities, involving causes that are not biomedically, but behaviorally, linked.

Pitfalls in the modeling of forward-looking price setting and investment decisions

The present paper makes progress in explaining the role of capital for inflation and output dynamics. We followWoodford (2003, Ch. 5) in assuming Calvo pricing combined with a convex capital adjustment cost at the firm level. Our main result is that capital accumulation affects inflation dynamics primarily through its impact on the marginal cost. This mechanism is much simpler than the one implied by the analysis in Woodford's text. The reason is that his analysis suffers from a conceptual mistake, as we show. The latter obscures the economic mechanism through which capital affects inflation and output dynamics in the Calvo model, as discussed in Woodford (2004).