The focus of this “OR framing paper” is to introduce the operations research (OR) community to the need for new mathematical modeling of an influenza pandemic and its control. By reviewing relevant history and literature, one key concern that emerges relates to how a population’s heterogeneity may affect disease progression. Another is to explore within a modeling framework “social distancing” as a disease progression control method, where social distancing refers to steps aimed at reducing the frequency and intensity of daily human-to-human contacts. To depict social contact behavior of a heterogeneous population susceptible to infection, a nonhomogeneous probabilistic mixing model is developed. Partitioning the population of susceptibles into subgroups, based on frequency of daily human contacts and infection propensities, a stylistic difference equation model is then developed depicting the day-to-day evolution of the disease. This simple model is then used to develop a preliminary set of results. Two key findings are (1) early exponential growth of the disease may be dominated by susceptibles with high human contact frequencies and may not be indicative of the general population’s susceptibility to the disease, and (2) social distancing may be an effective nonmedical way to limit and perhaps even eradicate the disease. Much more decision-focused research needs to be done before any of these preliminary findings may be used in practice.

Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.

We consider the problem of finding maximum capacity routes between all pairs of nodes in a network.

In a queuing process, let 1/λ be the mean time between the arrivals of two consecutive units, L be the mean number of units in the system, and W be the mean time spent by a unit in the system. It is shown that, if the three means are finite and the corresponding stochastic processes strictly stationary, and, if the arrival process is metrically transitive with nonzero mean, then L = λW.

Modern electronic markets have been characterized by a relentless drive toward faster decision making. Significant technological investments have led to dramatic improvements in latency, the delay between a trading decision and the resulting trade execution. We describe a theoretical model for the quantitative valuation of latency. Our model measures the trading frictions created by the presence of latency, by considering the optimal execution problem of a representative investor. Via a dynamic programming analysis, our model provides a closed-form expression for the cost of latency in terms of well-known parameters of the underlying asset. We implement our model by estimating the latency cost incurred by trading on a human time scale. Examining NYSE common stocks from 1995 to 2005 shows that median latency cost across our sample roughly tripled during this time period. Furthermore, using the same data set, we compute a measure of implied latency and conclude that the median implied latency decreased by approximately two orders of magnitude. Empirically calibrated, our model suggests that the reduction in cost achieved by going from trading on a human time scale to a low latency time scale is comparable with other execution costs faced by the most cost efficient institutional investors, and it is consistent with the rents that are extracted by ultra-low latency agents, such as providers of automated execution services or high frequency traders.

In the newsvendor problem, a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period. This simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory, which comprises a vast literature focusing on operational efficiency. Typically in this literature, market parameters such as demand and selling price are exogenous. However, incorporating these factors into the model can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level. In this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously. We provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base. We also review and develop insight into a dynamic inventory extension of this problem, and motivate the applicability of such models.

This paper considers the optimal location of p facilities in the plane, under the assumption that all travel occurs according to the Manhattan (or rectilinear or I1) metric in the presence of impenetrable barriers to travel. Facility users are distributed over a finite set of demand points, with the weight of each point proportional to its demand intensity. Each demand point is assigned to the closest facility. The objective is to locate facilities so as to minimize average Manhattan travel distance to a random demand. We show that an optimal set of facility locations can be drawn from a finite set of candidate points, all of which are easy to determine.

We evaluate, by means of mathematical programming formulations, the relative technical and scale efficiencies of decision making units (DMUs) when some of the inputs or outputs are exogenously fixed and beyond the discretionary control of DMU managers. This approach further develops the work on efficiency evaluation and on estimation of efficient production frontiers known as data envelopment analysis (DEA). We also employ the model to provide efficient input and output targets for DMU managers in a way that specifically accounts for the fixed nature of some of the inputs or outputs. We illustrate the approach, using real data, for a network of fast food restaurants.

A linear control algorithm is proposed for the computer operation of a signalized traffic intersection. A theoretical analysis of the algorithm under the assumption of constant vehicular arrival and departure rates shows that the control is stable under unsaturated conditions, and with proper choice of control constants usually gives a rapid convergence to a limit cycle that minimizes the average delay.

We consider a machine with a single real variable x that describes its state. Jobs J1, …, JN are to be sequenced on the machine. Each job requires a starting state A, and leaves a final state Bi. This means that Ji can be started only when x = Ai and, at the completion of the job, x = Bi. There is a cost, which may represent time or money, etc., for changing the machine state x so that the next job may start. The problem is to find the minimal cost sequence for the N jobs. This problem is a special case of the traveling salesman problem. We give a solution requiring only 0(N2) simple steps. A solution is also provided for the bottleneck form of this traveling salesman problem under special cost assumptions. This solution permits a characterization of those directed graphs of a special class which possess Hamiltonian circuits.