Note: The economic manufacturing lot-sizing problem with imperfect production processes: Bounds and optimal solutions

In this paper, we consider the economic production quantity problem in the presence of imperfect processes. In the literature, the time to shift from the in-control state to the out-of-control state is assumed to be exponentially distributed. In this study, we consider general time to shift distributions and provide distribution-based and distribution-free bounds on the optimal cost. For the exponential case, we compare the optimal solutions to approximate solutions proposed in the literature. A numerical example is used to illustrate the analysis presented and to conduct a sensitivity analysis in order to see the effect of the input parameters on the various solutions to the problem. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 423–433, 1998     

Note: Dynamic lot sizing for a finite rate input process

The basic single-product dynamic lot-sizing problem involves determining the optimal batch production schedule to meet a deterministic, discrete-in-time, varying demand pattern subject to linear setup and stockholding costs. The most widely known procedure for deriving the optimal solution is the Wagner-Whitin algorithm, although many other approaches have subsequently been developed for tackling the same problem. The objective of this note is to show how these procedures can readily be adapted when the input is a finite rate production process. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 221–228, 1997     

The reliability of multicomponent systems subject to cannibalization

A reliability model for multicomponent multistate systems is presented. This is a generalization of a model previously studied by Hirsch, Meisner, and Boll. In the earlier model, when a failure occurs for which no replacement spare is available, the locations using the same type of part as that having failed are “cannibalized” so as to allocate the shortages to locations where they are least detrimental to system performance. Here, we permit certain restrictions to be imposed upon the cannibalization procedure, and develop effective techniques for relating the probability laws governing the level of system performance to the system structure, cannibalization policy, kit of spare parts, and part reliabilities.     

Combination setwise-Bonferroni-type bounds

We consider three classes of lower bounds to P(c) = P (X₁ ≤ c₁,…, X_n ≤ c); Bonferroni-type bounds, product-type bounds and setwise bounds. Setwise probability inequalities are shown to be a compromise between product-type and Bonferroni-type probability inequalities. Bonferroni-type inequalities always hold. Product-type inequalities require positive dependence conditions, but are superior to the Bonferroni-type and setwise bounds when these conditions are satisfied. Setwise inequalities require less stringent positive dependence bound conditions than the product-type bounds. Neither setwise nor Bonferroni-type bounds dominate the other. Optimized setwise bounds are developed. Results pertaining to the nesting of setwise bounds are obtained. Combination setwise-Bonferroni-type bounds are developed in which high dimensional setwise bounds are applied and second and third order Bonferroni-type bounds are applied within each subvector of the setwise bounds. These new combination bounds, which are applicable for associated random variables, are shown to be superior to Bonferroni-type and setwise bounds for moving averages and runs probabilities. Recently proposed upper bounds to P(c) are reviewed. The lower and upper bounds are tabulated for various classes of multivariate normal distributions with banded covariance matrices. The bounds are shown to be surprisingly accurate and are much easier to compute than the inclusion-exclusion bounds. A strategy for employing the bounds is developed. © 1996 John Wiley & Sons, Inc.     

Excess procurement strategies by a dominant buyer under constrained supply

Supply chains are often characterized by the presence of a dominant buyer purchasing from a supplier with limited capacity. We study such a situation where a single supplier sells capacity to an established and more powerful buyer and also to a relatively less powerful buyer. The more powerful buyer enjoys the first right to book her capacity requirements at supplier's end, and then the common supplier fulfills the requirement of the less powerful buyer. We find that when the supplier's capacity is either too low (below the lower threshold) or too high (above the higher threshold), there is no excess procurement as compared to the case when supplier has infinite capacity. When the supplier's capacity is between these two thresholds, the more powerful buyer purchases an excess amount in comparison to the infinite capacity case.     

Contrasting the Impacts of Combat and Humanitarian Assistance/Disaster Relief Missions on the Mental Health of Military Service Members

Abstract

We study the differential impacts of combat and humanitarian assistance/disaster relief (HA/DR) missions on the mental health of U.S. Marine Corps members. The deployment experiences of any individual Marine are plausibly random conditional on the observable characteristics which are used to assign Marines into units. Leveraging this exogenous variation, we compare the incidence of post-traumatic stress disorder (PTSD) and suicide deaths among Marines who deployed to either Operation Enduring Freedom/Operation Iraqi Freedom (OEF/OIF) or HA/DR missions between 2001 and 2011. We find that the hazard of PTSD is close to eight times higher among Marines returning from OEF/OIF compared to those never deployed, and just 1.33 times higher among those returning from HA/DR (and never participated in OEF/OIF). Those returning from OEF/OIF missions are 1.81 times more likely than those never deployed to die by suicide when they were still active duty, and the hazard increases to almost 3 after they have left the military. In contrast, we find no difference in the hazards of suicide death between those that deployed to only HA/DR missions and non-deployed Marines.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

Vector processing approach to constrained network problems

Modification of algorithms designed for scalar computing, to take advantage of vector processing, raises several challenges. This article presents the vectorization of the primal simplex based network algorithm and results in a 50% improvement in computational time. One of the major contributors to this improvement is the matching of the size of the pricing candidate list to the vector register size. The side constraints are relaxed into a single surrogate constraint. The single constraint network algorithm is vectorized and used as the basis for solving large-scale constrained network problems. Computational experiments are presented which illustrate the vectorization of the network code as well as the ability of the surrogate constraint approach to deal with large constrained network problems.