Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming

The purpose of this paper is to investigate the problem of constructing an appointment template for scheduling patients at a specific type of multidisciplinary outpatient clinic called an integrated practice unit (IPU). The focus is on developing and solving a stochastic optimization model for a back pain IPU in the face of random arrivals, an uncertain patient mix, and variable service times. The deterministic version of the problem is modeled as a mixed integer program with the objective of minimizing a weighted combination of clinic closing time (duration) and total patient waiting time (length of stay). A two‐stage stochastic program is then derived to account for the randomness and the sequential nature of the decisions. Although it was not possible to solve the two‐stage problem for even a limited number of scenarios, the wait‐and‐see (WS) problem was sufficiently tractable to provide a lower bound on the stochastic solution. The introduction of valid inequalities, limiting indices, and the use of special ordered sets helped to speed up the computations. A greedy heuristic was also developed to obtain solutions much more quickly. Out of practical considerations, it was necessary to develop appointment templates with time slots at fixed intervals, which are not available from the WS solution. The first to be derived was the expected value (EV) template that is used to find the expected value of the EV solution (EEV). This solution provides an upper bound on the objective function value of the two‐stage stochastic program. The average gap between the EEV and WS solutions was 18%. Results from extensive computational testing are presented for the EV template and for our adaptation of three other templates found in the literature. Depending on the relative importance of the two objective function metrics, the results demonstrate the trade‐off that exists between them. For the templates investigated, the “closing time” ranged from an average of 235 to 275 minutes for a 300‐minute session, while the corresponding “total patient time in clinic” ranged from 80 to 71 minutes.     

Discrete stochastic optimization using variants of the stochastic ruler method

We present two random search methods for solving discrete stochastic optimization problems. Both of these methods are variants of the stochastic ruler algorithm. They differ from our earlier modification of the stochastic ruler algorithm in that they use different approaches for estimating the optimal solution. Our new methods are guaranteed to converge almost surely to the set of global optimal solutions under mild conditions. We discuss under what conditions these new methods are expected to converge faster than the modified stochastic ruler algorithm. We also discuss how these methods can be used for solving discrete optimization problems when the values of the objective function are estimated using either transient or steady‐state simulation. Finally, we present numerical results that compare the performance of our new methods with that of the modified stochastic ruler algorithm when applied to solve buffer allocation problems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Unpacking the various meanings of redundancy: from refining the concept to military planning

The authors engage in the debate over waste in military force structure planning by rigorously deconstructing the concept of “redundancy.” First, a typology of redundancy is constructed that provides a common framework for identifying variety among redundant structures. These are labeled “true redundancy,” “expanded capacity,” “portfolio diversification,” and “mission overlap.” Further, a number of mechanisms are identified that produce these types of structures, and show the conditions under which planners may utilize redundant structure in the search for optimization. In sum, the article provides refined concepts for analysts and planners to identify when redundancy is deleterious or beneficial.     

Small world,big guns: globalization,interstate security networks and conventional weapons imports

With the burgeoning influence of emerging markets in Asia, a tectonic shift is taking place in the global security landscape. Asian states are concomitantly arming as their economic clout grows. In light of these developments, security analysts would benefit from a formal means of placing these arms acquisitions in a structural context. Are arms acquisitions on par with the expectations of Asian states, given their structural dispositions, or are recent acquisitions beyond anticipated levels? By using a dynamic panel regression of 187 states from 1950 to 2011, this research predicts arms import volume using the degree of interstate arms linkages, the size of a state's military, and its level of economic development. The technique offers analysts a formal means of distinguishing orthodox behavior in importing conventional weapons from extraneous security motivations. The article concludes by generating near-term forecasts of Asian arms imports and discussing the implications of the technique.     

Newsvendor problems with sequentially revealed demand information

This article analyzes a capacity/inventory planning problem with a one‐time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012     

Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints

This paper addresses a two‐machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non‐availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial‐time approximation schemes, one of which handles the problem with one non‐availability interval on each machine and the other for the problem with several non‐availability intervals on one of the machines. Problems with a more general structure of the non‐availability intervals are not approximable in polynomial time within a constant factor, unless . © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Skewness correction X̄ and R charts for skewed distributions

This paper proposes a skewness correction (SC) method for constructing the and R control charts for skewed process distributions. Their asymmetric control limits (about the central line) are based on the degree of skewness estimated from the subgroups, and no parameter assumptions are made on the form of process distribution. These charts are simply adjustments of the conventional Shewhart control charts. Moreover, the chart is almost the same as the Shewhart chart if the process distribution is known to be symmetrical. The new charts are compared with the Shewhart charts and weighted variance (WV) control charts. When the process distribution is in some neighborhood of Weibull, lognormal, Burr or binomial family, simulation shows that the SC control charts have Type I risk (i.e., probability of a false alarm) closer to 0.27% of the normal case. Even in the case where the process distribution is exponential with known mean, not only the control limits and Type I risk, but also the Type II risk of the SC charts are closer to those of the exact and R charts than those of the WV and Shewhart charts. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 555–573, 2003     

A Criterion for Settling Inconsistencies in Clausewitz’s On War

On War’s unfinished state has been a source of difficulties for interpretation for 180 years. By establishing a hierarchy of revision among the parts, we propose a criterion that can bring any part of On War in line with the most advanced stage of Clausewitz’s thinking. We exemplify the utility, illustrate the underpinnings and appreciate the potential of this criterion. We argue that the criterion offers the prospect of a shared, coherent, fully consistent and faithful rendering of Clausewitz’s theory of war.     

Proliferation and critical risk

Does proliferation increase the risk of war between new nuclear powers? Two schools of thought ‐ proliferation pessimists and optimists ‐ offer very different answers. The former stress the first‐strike danger of nuclear‐armed ballistic missiles and the resulting crisis instability as a cause of preemptive war. The latter stress the caution‐inducing effects of nuclear warheads and fear of retaliation as a check on would‐be attackers.

To bridge the gap between these two schools, Daniel Ellsberg's concept of critical risk is used to show how the likelihood of war changes as new nuclear powers enlarge and improve their missile forces. Ellsberg's framework suggests that the danger of war is low between recent proliferators but rises as nuclear stockpiles grow, thereby changing the payoffs associated with striking first or striking second and increasing the danger of war due to accidents, miscalculations, and uncontrollable interactions between rival nuclear forces.

Ellsberg's framework also suggests that the transition from weaponization to secure second strike force is likely to be long and difficult, in part because short‐range missiles like India's Prithvi are better suited to strike first than to strike second, and in part because negative control procedures reduce the value of striking second, thereby increasing the attraction of a preemptive strike.     

The Iraq Survey Group: From Weapons of Mass Destruction to Counterinsurgency

The discovery and elimination of Iraq's alleged weapons of mass destruction (WMD) was a focal point of the Coalition's strategy and operations in the aftermath of Operation ‘Iraqi Freedom’. Despite the failure of the WMD mission to meet expectations after almost two years of intensive operations, the Iraq Survey Group (ISG) was able to integrate multinational and multi-agency forces to provide detailed intelligence regarding the history of Iraq's WMD programs and to assist in the battle against insurgents. The ISG's experience raises the question of whether a standing intelligence force could become a key component in future counterproliferation and counterterrorism efforts around the world.1 ¹The views expressed in this paper are those of the author and do not reflect the official policy or position of the Defense Intelligence Agency, the Dept. of Defense, or the US Government. View all notes