Breaking the Cycle: How the News and Markets Created a Negative Feedback Loop in COVID-19
New research from CBS Professor Harry Mamaysky reveals how negativity in the news and markets can escalate a financial crisis.
New research from CBS Professor Harry Mamaysky reveals how negativity in the news and markets can escalate a financial crisis.
Adapted from “Global Value Chains in Developing Countries: A Relational Perspective from Coffee and Garments,” by Laura Boudreau of Columbia Business School, Julia Cajal Grossi of the Geneva Graduate Institute, and Rocco Macchiavello of the London School of Economics.
Adapted from “Online Advertising as Passive Search,” by Raluca M. Ursu of New York University Stern School of Business, Andrey Simonov of Columbia Business School, and Eunkyung An of New York University Stern School of Business.
This paper from Columbia Business School, “Meaning of Manual Labor Impedes Consumer Adoption of Autonomous Products,” explores marketing solutions to some consumers’ resistance towards autonomous products. The study was co-authored by Emanuel de Bellis of the University of St. Gallen, Gita Johar of Columbia Business School, and Nicola Poletti of Cada.
Co-authored by John B. Donaldson of Columbia Business School, “The Macroeconomics of Stakeholder Equilibria,” proposes a model for a purely private, mutually beneficial financial agreement between worker and firm that keeps decision-making in the hands of stockholders while improving the employment contract for employees.
At Columbia Business School, our faculty members are at the forefront of research in their respective fields, offering innovative ideas that directly impact the practice of business today. A quick glance at our publication on faculty research, CBS Insights, will give you a sense of the breadth and immediacy of the insight our professors provide.
As a student at the School, this will greatly enrich your education. In Columbia classrooms, you are at the cutting-edge of industry, studying the practices that others will later adopt and teach. As any business leader will tell you, in a competitive environment, being first puts you at a distinct advantage over your peers. Learn economic development from Ray Fisman, the Lambert Family Professor of Social Enterprise and a rising star in the field, or real estate from Chris Mayer, the Paul Milstein Professor of Real Estate, a renowned expert and frequent commentator on complex housing issues. This way, when you complete your degree, you'll be set up to succeed.
Columbia Business School in conjunction with the Office of the Dean provides its faculty, PhD students, and other research staff with resources and cutting edge tools and technology to help push the boundaries of business research.
Specifically, our goal is to seamlessly help faculty set up and execute their research programs. This includes, but is not limited to:
All these activities help to facilitate and streamline faculty research, and that of the doctoral students working with them.
We analyze a class of stochastic and dynamic vehicle routing problems in which demands arrive randomly over time and the objective is minimizing waiting time. In our previous analysis ([5] and [6]) on this problem, we needed to assume uniformly distributed demand locations and Poisson arrivals. In this paper, using quite different techniques, we are able to extend our results to the more realistic case where demand locations have an arbitrary distribution and arrivals follow a general renewal process.
We develop a simple O(n log n) solution method for the standard lot-sizing model with backlogging and a study horizon of n periods. Production costs are fixed plus linear and holding and backlogging costs are linear with general time-dependent parameters. The algorithm has linear [O(n)] time complexity for several important subclasses of the general model. We show how a slight adaptation of the algorithm can be used for the detection of a minimal forecast horizon and associated planning horizon.
We consider distribution systems with a single depot and many retailers each of which faces external demands for a single item that occurs at a specific deterministic demand rate. All stock enters the systems through the depot where it can be stored and then picked up and distributed to the retailers by a fleet of vehicles, combining deliveries into efficient routes. We extend earlier methods for obtaining low complexity lower bounds and heuristics for systems without central stock.
We investigate the stability of waiting-time derivatives when inputs to a queueing system-service times and interarrival times-depend on a parameter. We give conditions under which the sequence of waiting-time derivatives admits a stationary distribution, and under which the derivatives converge to the stationary regime from all initial conditions. Further hypotheses ensure that the expectation of a stationary waiting-time derivative is, in fact, the derivative of the expected stationary waiting time.
We consider a production/distribution network represented by a general directed acyclic network. Each node is associated with a specific "product" or item at a given location and/or production stage. An arc (i, j) indicates that item i is used to "produce" item j. External demands may occur at any of the network's nodes. These demands occur continuously at item specific constant rates. Components may be assembled in any given proportions.
We derive conditions under which the increments of a vector process are associated—i.e., under which all pairs of increasing functions of the increments are positively correlated. The process itself is associated if it is generated by a family of associated and monotone kernels. We show that the increments are associated if the kernels are associated and, in a suitable sense, convex. In the Markov case, we note a connection between associated increments and temporal stochastic convexity.
Common random numbers (CRN) is a widely-used technique for reducing variance in comparing stochastic systems through simulation. Its popularity derives from its intuitive appeal and ease of implementation. However, though CRN has been observed to work well with a broad range of models, the class of systems for which it is provably advantageous has remained rather limited.
A generalized semi-Markov scheme models the structure of a discrete event system, such as a network of queues. By studying combinatorial and geometric representations of schemes we find conditions for second-order properties—convexity/concavity, sub/supermodularity—of their event epochs and event counting processes. A scheme generates a language of easible strings of events. We show that monotonicity of the event epochs is equivalent to this language forming an antimatroid with repetition.
We establish stochastic monotonicity of the event epoch sequences of generalized semi-Markov processes through the structure of the generalized semi-Markov schemes on which they are based. Our main condition states, roughly, that the occurrence of more events in the short run never leads to the activation of less events in the long run.
The reorder point/reorder quantity policies, also referred to as (r, Q) policies, are widely used in industry and extensively studied in the literature. However, for a period of almost 30 years there has been no efficient algorithm for computing optimal control parameteres for such policies. In this paper, we present a surprisingly simple and efficient algorithm for the determination of an optimal (r*, Q*) policy. The computational complexity of the algorithm is linear in Q*.
Countable-state, continuous-time Markov chains are often analyzed through simulation when simple analytical expressions are unavailable. Simulation is typically used to estimate costs or performance measures associated with the chain and also characteristics like state probabilities and mean passage times. Here we consider the problem of estimating derivatives of these types of quantities with respect to a parameter of the process. In particular, we consider the case where some or all transition rates depend on a parameter.
This paper concerns dynamic part dispatch decisions in electronic test systems with random yield. A discrete time, multiproduct, miltistage production system is used as a model for the test system with the objective to minimize the sum of inventory holding, backlogging, and overtime costs over a finite horizon. Exact results for such systems have been limited to either single-stage, multiple time period, or multistage, single time period problems with a single product. Here we develop two approximate policies: the linear decision rule, and the myopic resource allocation.
This paper establishes connections between two derivative estimation techniques: infinitesimal perturbation analysis (IPA) and the likelihood ratio or score function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based on multiplicative smoothing.
We consider inventory systems with several distinct items. Demands occur at constant, item specific rates. The items are interdependent because of jointly incurred fixed procurement costs: The joint cost structure reflects general economies of scale, merely assuming a monotonicity and concavity (submodularity) property. Under a power-of-two policy each item is replenished with constant reorder intervals which are power-of-two multiples of some fixed or variable base planning period.
A computer-based system for diagnosing bladder cancer is described. Typically, an object falls into one of two classes: Well or Not-well. The Well class contains the cells that will actually be useful for diagnosing bladder cancer; the Not-well class includes everything else. Several descriptive features are extracted from each object in the image and then fed to a multilayer perceptron, which classifies them as Well or Not-well. The perceptron's superior classification abilities reduces the number of computer misclassification errors to a level tolerable for clinical use.
Infinitesimal perturbation analysis is a technique for estimating derivatives of performance indices from simulation or observation of discrete event systems. Such derivative estimates are useful in performing optimization and sensitivity analysis through simulation. A general formulation of finite-horizon perturbation analysis derivative estimates is given, and then sufficient conditions for their use is presented with a variety of queuing systems.
For 0<K'<K≤∞, we obtain a K'-capacity queue from a K-capacity queue through a random time change and a truncation, provided arrivals are Poisson or service is exponential. In the case of an M/G/1/K queue, the time change erases service intervals that begin with more than K' customers in the systems. This constructions yields a straightforward sample path proof of Keilson's result on the proportionality of the ergodic queue length probabilities in M/G/1/K queues.
This paper is concerned with the general dynamic lot size model, or (generalized) Wagner-Whitin model. Let n denote the number of periods into which the planning horizon is divided. We describe a simple forward algorithm which solves the general model in 0(n log n) time and 0(n) space, as opposed to the well-known shortest path algorithm advocated over the last 30 years with 0(n2) time.
In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation.
Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models (as opposed to logical models) of discrete event systems. Here we take the view that GSMPs and SPNS are essentially automata (generators) driven by input sequences that determine the timing of events. This view combines the deterministic, logical aspects and the stochastic, timed aspects of the two models.
We analyze a continuous-time, two-stage production/inventory system. In the first stage, a common intermediate product is produced in batches, and possibly stored. In the second phase, the intermediate product is fabricated into n distinct finished products. Several finished products may be included in a single production batch of limited capacity to exploit economies of scale. We propose a planning methodology to address the combined problem of joint setup costs and capacity limits (per setup).
Let x(j) be the expected reward accumulated up to hitting an absorbing set in a Markov chain, starting from state j. Suppose the transition probabilities and the one-step reward function depend on a parameter, and denote by y(j) the derivative of x(j) with respect to that parameter. We estimate y(0) starting from the respective Poisson equations that x = [x(0),x(l), . . . ] and y = [y(0),y(l), . . . ] satisfy.
In this paper, a new algorithm for computing optimal (s, S) policies is derived based upon a number of new properties of the infinite horizon cost function c(s, S) as well as a new upper bound for optimal order-up-to levels S* and a new lower bound for optimal reorder levels s*. The algorithm is simple and easy to understand. Its computational complexity is only 2.4 times that required to evaluate a (specific) single (s, S) policy. The algorithm applies to both periodic review and continuous review inventory systems.
We examine the effects of nonstationarity on the performance of multiserver queueing systems withe exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular quesion: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary.
We examine the effects of nonstationarity on the performance of multiserver queueing systems withe exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular quesion: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary.
We establish strong consistency (i.e., almost sure convergence) of infinitesimal perturbation analysis (IPA) estimators of derivatives of steady-state means for a broad class of systems. Our results substantially extend previously available results on steady-state derivative estimation via IPA.
In recent years, there has been a surge of research into methods for estimating derivatives of performance measures from sample paths of stochastic systems. In the case of queueing systems, typical performance measures are mean queue lengths, throughputs, etc., and the derivatives estimated are with respect to system parameters, such as parameters of service and interarrival time distributions. Derivative estimates potentially offer a general means of optimizing performance, and are useful in sensitivity analysis.
In many important combinatorial optimization problems, such as bin packing, allocating customer classes to queueing facilities, vehicle routing, multi-item inventory replenishment and combined routing/inventory control, an optimal partition into groups needs to be determined for a finite collection of objects; each is characterized by a single attribute. The cost is often separable in the groups and the group cost often depends on the cardinality and some aggregate measure of the attributes, such as the sum or the maximum element.
We empirically explore the accuracy of an easily computed approximation for long run, average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. The pointwise stationary approximation is computed by integrating over time (that is taking the expectation of) the formula for the stationary performance measure with the arrival rate that applies at each point in time.
We empirically explore the accuracy of an easily computed approximation for long run, average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. The pointwise stationary approximation is computed by integrating over time (that is taking the expectation of) the formula for the stationary performance measure with the arrival rate that applies at each point in time.
This paper concerns production allocation in multicell manufacturing systems. The production objective is to track a nonstationary demand as closely as possible when the demand is near or exceeds the capacity of the system. The contribution of this paper is threefold. First, a series of approximations are proposed to obtain a model that is realistic while admitting a tractable solution. Second, we derive a general result on the second-order finite-time (transient) statistics of a continuous-time Markov chain.
In estimating functions of continuous-time Markov chains via simulation, one may reduce variance and computation by simulating only the embedded discrete-time chain. To estimate derivatives (with respect to transition probabilities) of functions of discrete-time Markov chains, we propose embedding them in continuous-time processes. To eliminate the additional variance and computation thereby introduced, we convert back to discrete time. For a restricted class of chains, we may embed in a continuous-time Markov chain and apply perturbation analysis estimation.
A new high-performance algorithmic switched-current memory cell with greatly improved charge injection per- formance is described. The new cell uses algorithmic means to achieve an improvement in charge injection of two orders of magnitude and does not rely on matching.
In most vehicle routing problems, a given set of customers is to be partitioned into a collection of regions each of which is assigned to a single vehicle starting at a depot and returning there after visiting all of the region's customers exactly once in a route. In this paper we consider problem settings where the cost of a route may depend on its length ϑ as well as m, the number of points on the route, according to some general function f(ϑ,m), assumed to be nondecreasing and concave in ϑ.
PASTA (Poisson Arrivals See Time Averages) is a term coined by R. Wolff in his well known 1982 paper. In keeping with Wolff's terminology, we use the term anti-PASTA to refer to the following converse of PASTA. Given that arrivals do indeed see time averages, when must the arrival process necessarily be Poisson? We show that anti-PASTA is satisfied in a pure-jump Markov process, provided that the arrival process corresponds to a subset of the Markov process jumps.
We consider distribution systems with a depot and many geographically dispersed retailers each of which faces external demands occurring at constant, deterministic but retailer specific rates. All stock enters the system through the depot from where it is distributed to the retailers by a fleet of capacitated vehicles combining deliveries into efficient routes. Inventories are kept at the retailers but not at the depot.
We consider a single-server queueing system with Poisson arrivals and general service times. While the server is up, it is subject to breakdowns according to a Poisson process. When the server breaks down, we need to repair the server immediately by initiating one of two available repair operations. The operating costs of the system include customer holding costs, repair costs and running costs. The objective is to find a corrective maintenance policy that minimizes the long-run average operating costs of the system. The problem is formulated as a semi-Markov decision process.
This article treats the dynamic lot size model with quantity discount in purchase price. We study the problem with two different cost structures: the all-units-discount cost structure and the incremental-discount cost structure. We solve the problem under both discount cost structures by dynamic programming algorithms of complexity O(T3) and O(T2), respectively, with T the number of periods in the planning horizon.
Infinitesimal perturbation analysis is a method of obtaining estimates of performance sensitivity through simulation of a stochastic system. Expressions are derived for the limiting value of a broad class of such estimators associated with queueing networks, in terms of the unique solution to a set of linear equations. The approach used is to augment the underlying queueing process with information about which servers have been "perturbed" and by how much.
Two methods are presented for estimating performance derivatives from simulation of multi-class queueing networks for sensitivity analysis. The methods use approximate subnetwork aggregation to reduce the problem to a single-class derivative estimation problem with which a modified infinitesimal perturbation analysis algorithm is used. The modified algorithm treats a subnetwork as though it had been aggregated, but is actually applied to the original (non-aggregated) network.
We consider a single-server queueing system with Poisson arrivals and general service times. While the server is up, it is subject to breakdowns according to a Poisson process. When the server breaks down, we may either repair the server immediately or postpone the repair until some future point in time. The operating costs to the system include customer holding costs, repair costs and running costs. The objective is to find a corrective maintenance policy which minimizes the long-run average operating costs of the system. The problem is formulated as a semi-Markov decision process.
This paper describes efforts to validate a multiple car dispatch queueing (MCD) model of police patrol operations using New York City data. The MCD model was designed for use in a computer system that has been disseminated to many police departments in the U.S. to help planners allocate patrol cars among precincts. It has also been used to evalute specific changes in patrol policy in New York. We define validation as a series of hierarchical procedures ranging from tests of mathematical correctness to evaluations of model robustness.
This paper describes efforts to validate a multiple car dispatch queueing (MCD) model of police patrol operations using New York City data. The MCD model was designed for use in a computer system that has been disseminated to many police departments in the U.S. to help planners allocate patrol cars among precincts. It has also been used to evalute specific changes in patrol policy in New York. We define validation as a series of hierarchical procedures ranging from tests of mathematical correctness to evaluations of model robustness.
In this paper, we develop the control rules for job shop scheduling based on the Flow Rate Control model. We derive optimal control results for job shops with work station in series (transfer line). We use these results to derive rules which are suboptimal, robust against random events, and easy to implement and expand.
The PDF above is a preprint version of the article. The final version may be found at The Annals of Operations Research.
This paper considers an M/G/c queueing system serving a finite number (J) of distinct customer classes. Performance of the system, as measured by the vector of steady-state expected waiting times of the customer classes (the performance vector), may be controlled by adopting an appropriate priority discipline.
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.
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.