Optimal capacity expansion

We consider the problem of temporal expansion of the capacity of, say, a plant or road given estimates of its desired usage (demand). The basic problem is: given a sequence of predicted demands for N time periods, determine the optimal investment decision in each period to minimize a linear investment cost and a strictly convex cost of capacity. The relationship between capacity and the investment decisions is assumed to be linear, but time varying. Constraints on both the individual decisions and on the sum of the decisions are considered. An algorithm for solving this problem is derived.     

Statistical tests for exponential service from m/g/1 waiting-time data

From an original motivation in quantitative inventory modeling, we develop methods for testing the hypothesis that the service times of an M/G/1 queue are exponentially distributed, given a sequence of observations of customer line and/or system waits. The approaches are mostly extensions of the well-known exponential goodness-of-fit test popularized by Gnedenko, which results from the observation that the sum of a random exponential sample is Erlang distributed and thus that the quotient of two independent exponential sample means is F distributed.     

The mixed ordering policy in periodic review stochastic multi-commodity inventory systems

In multi-commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two-commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K₁, or K₂, where max (K₁, K₂) ≤ K ≤ K₁ + K₂, This paper considers a two-commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.     

Institutions,information, and commitment: the role of democracy in conflict

This paper explores the hypothesis that both the preexisting quality of democracy in a polity at the onset of conflict and the quality of democracy expected to emerge in the aftermath influence the likelihood of civil war. An empirical investigation of the hypothesis presents a challenge due to concerns of endogeneity and selection: the post-conflict level of democracy is endogenous to the pre-conflict level. Further, for a given time period, either a number of countries have not experienced civil war; or if they did, did not resolve the conflict. We overcome this selection bias by implementing a three-step extension to the Heckman procedure using an unbalanced cross-country panel of 77 countries over the period 1971–2005. Consistent with our hypothesis, we find that a standard deviation improvement in the existing level of democracy reduces the probability of civil war by approximately 9 percentage points and a corresponding improvement in expected post-conflict democratization increases the probability of conflict by approximately 48 percentage points.     

Challenges of measuring progress in Afghanistan using violence trends: the effects of aggregation,military operations,seasonality, weather,and other causal factors

Measuring nationwide progress of counterinsurgency operations in Afghanistan using violence trends is difficult due to several factors: aggregation of data to the national level may obfuscate disparate local trends; the observed seasonality in violence makes comparisons difficult and may obscure progress; and short-term spikes or troughs – attributable to weather, military operations and tempo, or holiday periods – heavily influence simple averaging schemes. Despite these challenges, proper understanding of violence statistics is critical to estimating the effectiveness of military forces added during a surge or redeployed as part of transition. This article explores methods for analyzing observed violence trends to identify causal factors, to provide a comparable baseline, and to inform assessments at appropriate levels of aggregation. One methodology for seasonal adjustment of violence data is discussed and shown to provide a logical baseline for examining trends. An ordinary least squares regression model is developed and implemented using time-series violence data.     

Single machine parallel batch scheduling subject to precedence constraints

We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP‐hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n²) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Value added analysis for army equipment modernization

This paper describes the Value Added Analysis methodology which is used as part of the U.S. Army's Planning, Programming, Budgeting, and Execution System to assist the Army leadership in evaluating and prioritizing competing weapon system alternatives during the process of building the Army budget. The Value Added Analysis concept uses a family of models to estimate an alternative system's contribution to the Army's effectiveness using a multiattribute value hierarchy. A mathematical optimization model is then used to simultaneously determine an alternative's cost‐benefit and to identify an optimal mix of weapon systems for inclusion in the Army budget. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 233–253, 1999     

The parallel machine min-max weighted absolute lateness scheduling problem

Given a set of jobs, a processing time and a weight for each job, several parallel and identical machines, and a common due date that is not too early to constrain the scheduling decision, we want to find an optimal job schedule so as to minimize the maximum weighted absolute lateness. We show that this problem is NP-complete even for the single-machine case, and is strongly NP-complete for the general case. We present a polynomial time heuristic for this problem and analyze its worst-case performance. Empirical testing of the heuristic is reported, and the results suggest that the performance is asymptotically optimal as the number of jobs tends to infinity. © 1994 John Wiley & Sons, Inc.