Columbia Business School Research

We consider single-server loss systems with exponential service times and non-stationary Poisson input. We prove that if the arrival rate is given by a periodic function, the proportion of lost customers is convex increasing in the amplitude.

This papers introduces a market-based typology of corporate strategy, which builds on previous typologies (Rumelt 1974, 1982). We argue that, because different markets require different skills for success, firms which concentrate in one market area (consumer or industrial), at given levels of diversification, should achieve superior performance. Empirical tests with a sample of manufacturing firms support this proposed relationship between diversification strategy and financial performance.

Using a birth and death process as an illustrative example, we introduce the notion of alternative representations of stochastic processes and discuss its importance for infinitesimal perturbation analysis derivative estimation. Through a different choice of representation, we are led to an IPA algorithm for a birth and death process better than one discussed by other authors.

This paper considers general (single facility) queueing systems with exponential service times, dealing with a finite number J of distinct customer classes. Performance of the system, as measured by the vector of steady state expected sojourn times of the customer classes (the performance vector) may be controlled by adopting an appropriate preemptive priority discipline.

Often the timing of certain activities has a strong periodic element. Due to circumstances an activity is sometimes made outside the regular cycle, but it does not break the cycle. Thus, the timing of future activities is highly predictable. We provide a stochastic model where the data are not seasonal yet the optimal behaviour has a strong periodic element.

Radial patterns of optical flow produced by observer translation could be used to perceive the direction of self-movement during locomotion, and a number of formal analyses of such patterns have recently appeared. However, there is comparatively little empirical research on the perception of heading from optical flow, and what data there are indicate surprisingly poor performance, with heading errors on the order of 5 degrees–10 degrees.

We consider the polymatroidal flow network model which incorporates two important extensions of the standard maximal flow problem: general concave objective functions of the vector of supplies to a collection of sinks, as well as polymatroidal capacity restrictions on sets of arcs emanating from or pointing to a common node. A number of important applications are reviewed.

We present an exact solution method for a single-server queueing system which alternates between periods in which service can be provided (on-periods) and periods in which the server is out of operation (off-periods). The arrival process is Poisson, on-periods are assumed to have a phase-type distribution, and service times and off-periods are assumed to be arbitrary.

The bid-ask spread can be decomposed into two parts: one part due to asymmetric information and the other part due to other factors such as monopoly power. The part due to asymmetric information attenuates statistical biases in mean return, variance, and serial covariance. Thus, using spread data to adjust for biases in return moments requires knowing not only the spread but the composition of the spread. Furthermore, any spread-estimation procedure using transaction prices must estimate two spread components.

We acknowledge that the behavior of the OSHA and EPA is complex and cannot be explained by simple capture theories, we nonetheless find ample evidence of OSHA and EPA actions that unnecessarily exacerbate or even artificially create indirect effects for political purposes (what we call enforcement asymmetries). Furthermore, despite mounting evidence of the inefficiency of OSHA and EPA, Congress has continued to be uninterested in adequate monitoring of regulatory effect, much less in regulatory reform.

This paper studies the relation between Value Line's successful record in predicting relative stock price movements and the firm size effect. The data suggest little direct relation between the two phenomena. Value Line tends not to rank small firm stocks, and small firm stocks that are ranked are more likely to receive a low rank than large firm stocks. Within each size-sorted quintile of the market, the mean payoffs on costless positions constructed according to Value Line's recommendations are positive.

The authors propose a likelihood-ratio test of the hypothesis that the minimum-variance frontier of a set of K assets coincides with the frontier of this set and another set of N assets. They study the relation between this hypothesis, exact arbitrage pricing, and mutual fund separation. The exact distribution of the test statistic is available. The authors test the hypothesis that the frontier spanned by three size-sorted stock portfolios is the same as the frontier spanned by thirty-three size-sorted stock portfolios.

Heuristic solution methods for combinatorial optimization problems are often based on local neighborhood searches. These tend to get trapped in a local optimum and the final result is often heavily dependent on the starting solution. Simulated annealing methods attempt to avoid these problems by randomizing the procedure so as to allow for occasional changes that worsen the solution. In this paper we provide probabilistic analyses of different designs of these methods.

We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base.

We consider a class of loss systems with exponential service times and a Poisson arrival process with a rate that varies periodically among N levels called seasons. For two special cases, we derive transient and steady-state solutions and provide simple proofs that losses are minimized when the arrival rates for all seasons are equal. In the general case, we describe a straightforward procedure to derive the steady-state probabilities. We also prove that when S=1, the server is generally busier during the high arrival rate seasons.

A model for the systematic evaluation and management of a company's technological resources is proposed as a first step to developing an integrated corporate marketing-technology strategy. The proposed framework raises 4 issues: 1. technology identification, 2. technology additions, 3. technological commercialization, and 4. treatment of individual technologies as interdependent elements making up an integrated, coherent plan. The technological decision nexus involves decisions related to the firm's development and commercialization of its technology.

A new variable rate refining subdivision B4 for the solution of equations with piecewise linear homotopies and restart homotopies is described. The essential virtue of the subdivision B4 is that it offers vast latitude to the user. In particular, the parameters of B4 can be set so one restriction of B4 is that J3 triangulation and another restriction is the octahedral subdivision. More generally, full flexibility is available in the placement of local focal points, and perhaps most importantly, B4 permits the new capability of refining coordinates at variable and independent rates.

It is shown that an incumbent seller who faces a threat of entry into his or her market will sign long-tern contracts that prevent the entry of some lower-cost producers even though they do not preclude entry completely. Moreover, when a seller possesses superior information about the likelihood of entry, it is shown that the length of the contract may act as a signal of the true probability of entry.

Over the past 55 years returns on stock market indexes have on average been higher during the first half-month of calendar quarters 2 through 4 than at other times. Coincidentally, aggregate corporate earnings news arriving at the market during these half-month periods tends to be good, whereas earnings reports arriving later are more likely to convey bad news. In addition firms tend to publish bad-news earnings reports on Mondays, coincident with negative Monday effects in stock returns.

The perturbation generation rule of Suri (Ref. 1) is extended to cases where random variables are not generated by inversion. Conditions are given for the use of other methods. Infinitesimal perturbation analysis is shown to be compatible with common random number techniques in cases where finite-difference approximations are not.

We estimate labor demand equations derived from a (restricted variable) cost function in which "experience" on a technology (proxied by the mean age of the capital stock) enters "non-neutrally." Our specification of the underlying cost function is based on the hypothesis that highly educated workers have a comparative advantage with respect to the adjustment to and implementation of new technologies.

An analysis of the environments of leading manufacturing firms operating in the United States and in Australia produced a series of hypothesized differences in the strategies, organization structures, and market environments of firms in the two countries. Parallel hypotheses about differences between domestic Australian firms and subsidiaries of foreign multinationals operating in Australia were also developed. The hypotheses were by and large supported when tested on data obtained from leading corporations in the two countries.

A nonstationary Markov chain is weakly ergodic if the dependence on the state distribution on the starting state vanishes as time tends to infinity. A chain is strongly ergodic if it is weakly ergodic and converges in distribution. In this paper we show that the two ergodicity concepts are equivalent for finite chains under rather general (and widely verifiable) conditions. We discuss applications to probabalistic analyses of general search methods for combinatorial optimization problems (simulated annealing).

We characterize the sets of mimicking positions with returns that can serve in place of factors in an exact K-factor arbitrage-pricing relation for a set of N assets. All of the sets are K-dimensional nonsingular linear transformations of each other. We interpret three examples of such transformations and discuss empirical considerations. We provide conditions under which the mimicking positions can be expressed as portfolios, and we characterize the relation between mimicking portfolios and the minimum-variance frontier.

Based on observations made during an extensive study of police patrol operations in New York City, we examine the issues of the validity and utility of queueing models of service systems in which adaptive behavior by the (human) customers or servers is likely. We find that in addition to depending on the technical accuracy of its assumptions, the accuracy of such a model will also depend upon the level of managerial control of the system and adequacy of resources.

Evidence of excess volatilities of asset prices compared with those of market fundamentals is often attributed to speculative bubbles. This study demonstrates that bubbles could in theory lead to excess volatility, but it shows that certain variance bounds tests preclude bubbles as an explanation. The evidence ought to be attributed to model misspecification or inappropriate statistical tests. One important misspecification occurs if a researcher incorrectly specifies the time series properties of market fundamentals.