A general model for accelerated life testing with time‐dependent covariates

This paper introduces a general or “distribution‐free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution‐free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time‐dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time‐dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time‐dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 303–321, 1999     

Volume discount decisions: Wealth maximization or EOQ approach?

A recent paper finds that when volume discounts are available, in some cases, reliance on the Economic Order Quantity (EOQ) model can induce purchasers to make wealth reducing decisions, and the Present Value (PV) approach should be preferred. While this finding is theoretically correct, the magnitudes of wealth reductions suggested by the paper's numerical examples seem to be questionable. Furthermore, the paper also finds that, in some other cases, a purchaser using the EOQ approach realizes a net increase in current wealth compared to a purchaser using the PV approach. Logic suggests that such a finding cannot be correct, since by its very definition, it is the PV approach that seeks to maximize the current wealth. We offer an alternative frame of comparison and a modified model to show that, under the paper's assumptions, the EOQ approach can never realize a net increase in current wealth compared to the current wealth generated by the PV approach. On the other hand, we also show that when typical values of the relevant parameters prevail, the additional costs imposed by the EOQ approach are not significant. Finally, we suggest that insofar as the PV approach requires greater administrative costs to implement, it may even be counterproductive to the goal of wealth maximization. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 377–389, 1998     

Parallel machine replacement

We consider the parallel replacement problem in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance costs motivate replacements, and the fixed replacement cost provides incentive for replacing machines of different ages together in “clusters.” We prove two intuitive results for this problem. First, it is never optimal to split a cluster of like-aged machines, and second, it is never optimal to replace newer clusters before older clusters. By incorporating these two results into an algorithmic approach, we vastly reduce the amount of computation required to identify an optimal replacement policy.     

Setting military reenlistment bonuses

The United States military frequently has difficulty retaining enlisted personnel beyond their initial enlistment. A bonus program within each service, called a Selective Reenlistment Bonus (SRB) program, seeks to enhance reenlistments and thus reduce personnel shortages in critical military occupational specialties (MOSs). The amount of bonus is set by assigning “SRB multipliers” to each MOS. We develop a nonlinear integer program to select multipliers which minimize a function of deviations from desired reenlistment targets. A Lagrangian relaxation of a linearized version of the integer program is used to obtain lower bounds and feasible solutions. The best feasible solution, discovered in a coordinate search of the Lagrangian function, is heuristically improved by apportioning unexpended funds. For large problems a heuristic variable reduction is employed to speed model solution. U.S. Army data and requirements for FY87 yield a 0-1 integer program with 12,992 binary variables and 273 constraints, which is solved within 0.00002% of optimality on an IBM 3033AP in less than 1.7 seconds. More general models with up to 463,000 binary variables are solved, on average, to within 0.009% of optimality in less than 1.8 minutes. The U.S. Marine Corps has used a simpler version of this model since 1986. © 1993 John Wiley & Sons, Inc.     

A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system

The system under study is a single item, two‐echelon production‐inventory system consisting of a capacitated production facility, a central warehouse, and M regional distribution centers that satisfy stochastic demand. Our objective is to determine a system base‐stock level which minimizes the long run average system cost per period. Central to the approach are (1) an inventory allocation model and associated convex cost function designed to allocate a given amount of system inventory across locations, and (2) a characterization of the amount of available system inventory using the inventory shortfall random variable. An exact model must consider the possibility that inventories may be imbalanced in a given period. By assuming inventory imbalances cannot occur, we develop an approximation model from which we obtain a lower bound on the per period expected cost. Through an extensive simulation study, we analyze the quality of our approximation, which on average performed within 0.50% of the lower bound. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 377–398, 2000     

Selecting T for a periodic review inventory model with staggered deliveries

Consider a single‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one audits the current stock level and decides on deliveries for the next T periods, thus incurring a fixed audit cost and—when one schedules deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy that satisfy the average cost criterion. The current article extends an earlier treatment of this problem, which assumed that the fixed order cost is automatically incurred once every T periods. We characterize an optimal ordering policy when T is fixed, prove that an optimal review period T** exists, and develop a global search algorithm for its computation. We also study the behavior of four approximations to T** based on the assumption that the fixed order cost is incurred during every cycle. Analytic results from a companion article (where μ/σ is large) and extensive computational experiments with normal and gamma demand test problems suggest these approximations and associated heuristic policies perform well when μ/σ ≥ 2. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 329–352, 2000     

A Markovian model for process setup and improvement

We examine the setup and improvement policies for a production process with multiple performance states. Assume that the production process deteriorates randomly over time, following a Markovian process with known transition probabilities. In order to reduce the production cost incurred because of process deterioration, the process is inspected at the end of each period. Then one of three actions may be taken: do nothing, perform routine process setup, or perform routine setup and process improvement. The routine setup operation returns the process to its best performance state, whereas the process improvement action may reduce future production and setup costs and improve the process-state transition probabilities. A discounted Markovian model is formulated to find the strategy that minimizes the total cost of operating the production process. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 383–400, 1997     

A heuristic algorithm for determining replacement policies in k-out-of-n systems

The authors study a discrete-time, infinite-horizon, dynamic programming model for the replacement of components in a binary k-out-of-n failure system. (The system fails when k or more of its n components fail.) Costs are incurred when the system fails and when failed components are replaced. The objective is to minimize the long-run expected average undiscounted cost per period. A companion article develops a branch-and-bound algorithm for computing optimal policies. Extensive computational experiments find it effective for k to be small or near n; however, difficulties are encountered when n ≥ 30 and 10 ≤ k ≤ n − 4. This article presents a simple, intuitive heuristic rule for determining a replacement policy whose memory storage and computation time requirements are O(n − k) and O(n(n − k) + k), respectively. This heuristic is based on a plausible formula for ranking components in order of their usefulness. The authors provide sufficient conditions for it to be optimal and undertake computational experiments that suggest that it handles parallel systems (k = n) effectively and, further, that its effectiveness increases as k moves away from n. In our test problems, the mean relative errors are under 5% when n ≤ 100 and under 2% when k ≤ n − 3 and n ≤ 50. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 273–286, 1997.     

Mimetic and normative isomorphism in the establishment and maintenance of independent air forces

Why do countries have air forces? Organizational alternatives, such as maintaining separate air arms for the army and navy, have become quite rare. The conventional narrative advanced by advocates of independent air forces stress that the primacy of airpower in modern warfare mandates centralized control of most military aviation. In this view, political–military uncertainty has driven mimetic isomorphism – pressure on national governments to organize as others organize so as to fight or deter war just as effectively. However, working from a set of 56 countries that were politically independent within a few years of the establishment of the first ever independent air force (the Royal Air Force) in 1918, and continuing through nearly the present, there is no clear pattern of external military pressure prompting this particular reorganization. Rather, from anecdotal evidence, the cause has more likely been normative isomorphism – a professional craving to look as others look to foster political or personal legitimacy. For whatever reason, though, choices of structures tend to lead to specific choices of policies. Thus, the result suggests that defense ministries looking for more effective or less costly organizational schemas may reasonably consider alternatives to the tripartite army–navy–air force structure.