Columbia Business School Research

Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear programming. Also, we apply our bounds to a convex transportation problem.

In continuous review models with a fixed delivery lag T, the state of the system is conveniently described by the net inventory position = (inventory on hand) plus (outstanding orders), in spite of most cost components depending on the actual inventory on hand. To relate these two inventory concepts one observes that the distribution of the inventory on hand at time t + T is determined by the inventory position at time t.

This paper presents methods for solving allocation problems that can be stated as convex knapsack problems with generalized upper bounds. Such bounds may express upper limits on the total amount allocated to each of several subsets of activities. In addition our model arises as a subproblem in more complex mathematical programs. We therefore emphasize efficient procedures to recover optimality when minor changes in the parameters occur from one problem instance to the next. These considerations lead us to propose novel data structures for such problems.

The article focuses on the authors' comments on marketing of consumer information. Authors are somewhat distressed as their original article was severely misinterpreted by researcher Dan Sarel. Two main criticisms of the authors' model and methodology offered by Sarel are that the methodology cannot produce useful guidelines for three reasons: the criteria used in the methodology are inappropriate, the product is of a special nature and other important considerations have been omitted.

Evidence is given in this paper which indicates that corporate insiders time their trades in their firms' stock relative to the date of the disclosure of their forecasts of annual earnings. Further, insiders earn abnormal returns to their joint trading and information dissemination activities, and the paper provides measures of these returns.

Notwithstanding the apparent differences between convex games and minimum cost spanning tree (m.c.s.t.) games, we show that there is a close relationship between these two types of games. This close relationship is realized with the introduction of the group of permutationally convex (p.c.) games. It is shown that a p.c. game has a nonempty core and that both convex games and m.c.s.t, games are permutationally convex.

Suppose n facilities are to be located on a fine segment so as to minimize cost function. One might expect that the facilities' optimal locations have the following interleaving property: if one of the n facilities is removed and if the locations of the others are shifted by reoptimizing, each remaining facility's location shifts toward the location of the one removed, but not farther toward it than the original location of the adjacent facility. This paper presents two models whose solutions have this interleaving property and four examples of such models.

The recent appearance and growth of new delivery systems for dental services is examined from a marketing perspective. Analysis reveals that the growth of low priced, high throughput operations is consistent not only with marketing principles, but with the development of American retail institutions in general. Options for independent dentists in the face of this new competitive environment are discussed.

The article focuses on the author's view on whether consumers can calculate best buys. According to the author, a number of studies have found only a limited incidence of the ability to reason proportionately. Though subjects in these studies were still in their teens, little further development would be probable with their advancement into adulthood. This evidence led to their hypothesis that a significant number of adults would be unable to utilize a proportional reasoning strategy in a simple consumer decision-making context.

Consider a renewal process {X_n, n ≥ 1} for which there is defined an associated sequence of independent and identically distributed random variables {B_n, n ≥ 1} such that B_n is the length of a subinterval of X_n. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process generated by {B_n, n ≥ 1}.

Reprinted in Advances in Financial Economics: Volume I (Theory), Bhattacharya and Constantinides (editors), Roman and Allenhead publishers 1986.

Over the years, there has developed a fairly substantial body of research on the time series of earnings. As a whole, this literature concludes that changes in (annual) accounting earnings are unpredictable, that is, earnings follow a "random walk." Based on this result, some inferences of economic substance (policy) have been claimed. In this paper we reconsider empirical issues which, at least to some extent, have been obscured by this conclusion.

The currently fashionable credit scoring systems are described and subjected to critical analysis. Public policy issues concerning the use of these systems are discussed.

Reviews several books on marketing. "Cases in Public and Nonprofit Marketing," by Christopher H. Lovelock and Charles B. Weinberg; "Marketing for Nonprofit Organization," by Philiph Kotler; "Marketing for Nonprofit Organization," David L. Rados.

This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices.

The cost of external equity capital is higher than the investor-required rate of return because of flotation costs (underwriting expenses and underpricing). Recognizing this, regulatory agencies have generally included an allowance for flotation costs in the authorized cost of capital. The adjustment for flotation costs can have a significant effect on the firm and its consumers.

Focuses on a theory and test of credit rationing. Lending behavior under a fixed interest rate; leverage terms under risk aversion.

This paper considers the solution of Markov decision problems whose parameters can be obtained only via approximating schemes, or where it is computationally preferable to approximate the parameters, rather than employing exact algorithms for their computation. Various models are presented in which this situation occurs. Furthermore, it is shown that a modified value-iteration method may be employed, both for the discounted version and for the undiscounted version of the model, in order to solve the optimality equation and to find optimal policies.

Recent papers have shown that Π^∞_{k = 1} P(k) = lim_m→∞ (P(m) ... P(1)) exists whenever the sequence of stochastic matrices {P(k)}^∞_{k = 1} exhibits convergence to an aperiodic matrix P with a single subchain (closed, irreducible set of states). We show how the limit matrix depends upon P(1).

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation.

The article presents several lender supply and borrower demand conditions for a leverage structure of interest rates. The paper presents a model of the credit transaction between individuals embedded in a competitive credit market. In this model, the individual has to decide on the optimal allocation of his initial investible capital K, among a risk asset with random rate of return R-1 available to all investors, a riskless asset with return s-1 and lending to or borrowing from another individual. Short sales of the risk asset are not permitted.

This paper demonstrates that it will be impossible, by observing an agent's demand behavior, to either refute or confirm the general taste change hypothesis without substantially restricting the class of eligible preferences.

The Arrow-Debreu intertemporal general equilibrium paradigm is typically interpreted as suggesting that contingent claims markets need not reopen as time passes and uncertainty resolves. We show that this property, if satisfied, has strong implications for the structure of agents' preferences and for the updating of probabilistic beliefs.

We examine the relative effects of several service order disciplines on important operating characteristics of queues in which customers request a random number of servers. This class of queues is characterized by customers who cannot begin service until all required servers are available. We show that for many systems in this class, it is possible to define a new service order disciplien which is more efficient than FIFO with respect to one or more measures such as expected waiting time, probability of delay, etc.

Analysis of state and privately owned enterprises in industrialized market economies leads to the identification of differences in objectives and strategy between the two enterprise types. A series of propositions is developed that contrasts the behavior of state and privately owned corporations.

Subjects at four age levels (kindergarten, fourth grade, eighth grade, and college) made preference judgments for a set of consumer products varying on four dimensions. Though product preferences reflected independently assessed dimension ratings, subjects had preferences on more dimensions than they took into account in the product ratings. Not until late adolescence did subjects integrate their preferences on two or more dimensions.

We consider the Policy Iteration Algorithm for undiscounted Markov Renewal Programs. Previous specifications of the policy evaluation part of this algorithm all required the analysis of the chain structure for each policy generated. The purpose of this paper is to provide a unique specification of the value sectors as well as an anticycling rule which avoids parsing the transition probability matrices into their subchains.