The validity of assumptions underlying current uses of Lanchester attrition rates

This study examines critically the various assumptions, results, and concepts that exist to date in the literature and scientific community concerning the relationships among the Lanchester, stochastic Lanchester, and the general renewal models of combat. Many of the prevailing understandings are shown to be erroneous.     

Application of perturbation analysis to a class of periodic review (s,S) inventory systems

In this article we apply perturbation analysis (PA), combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s, S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. We first develop the general form of four different estimators of the gradient for the finite-horizon case, and prove that they are unbiased. We next consider the problem of implementing our estimators, and develop efficient methodologies for the infinite-horizon case. For the case of exponentially distributed demand interarrival times, we implement our estimators using a single sample path. Generally distributed interarrival times are modeled as phase-type distributions, and the implementation of this more general case requires a number of additional off-line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. We conclude by reporting the results of simulation experiments. The results provide further validity of our methodology and also indicate that our estimators have very low variance. © 1994 John Wiley & Sons, Inc.     

Cost allocation in continuous-review inventory models

A centralized inventory system serves a number of stores with common ownership, and thus reliable and timely information sharing. Each of them pays a share of the inventory cost, and the reward structure leaves the owners of individual stores rewarded for their individual performance. Appropriate selection of a cost allocation method is important if such a centralized system is to last. In this work we propose three necessary criteria—stability (core of a related cooperative game), justifiability (consistency of benefits with costs), and polynomial computability. For a concrete example we demonstrate that common allocation procedures may not meet all three tests, and we present a method that that meets all three criteria. This kind of cost allocation analysis helps the common management to evaluate the trade-offs in choosing an allocation scheme for the cost of inventory centralization. © 1996 John Wiley & Sons, Inc.     

Modeling the fatigue life of longitudinal elements

Functional equations enable us to arrive at a simple consensus model for fatigue life of longitudinal elements based on engineering principles. The model is then applied to two representative data sets. By the application of proportional hazards techniques and subsequent likelihood analysis, simple parsimonious Weibull models are derived. Inter alia attention is given to the desirability of deriving models exhibiting plausible asymptotic independence. © 1996 John Wiley & Sons, Inc.     

Makespan minimization for m parallel identical processors

We introduce an algorithm, called TMO (Two-Machine Optimal Scheduling) which minimizes the makespan for two identical processors. TMO employs lexicographic search in conjunction with the longest-processing time sequence to derive an optimal schedule. For the m identical parallel processors problem, we propose an improvement algorithm, which improves the seed solution obtained by any existing heuristic. The improvement algorithm, called Extended TMO, breaks the original m-machine problem into a set of two-machine problems and solves them repeatedly by the TMO. A simulation study is performed to evaluate the effectiveness of the proposed algorithms by comparing it against three existing heuristics: LPT (Graham, [11]), MULTIFIT (Coffman, Garey, and Johnson, [6]), and RMG (Lee and Massey, [17]). The simulation results show that: for the two processors case, the TMO performs significantly better than LPT, MULTIFIT, and RMG, and it generally takes considerably less CPU time than MULTIFIT and RMG. For the general parallel processors case, the Extended TMO algorithm is shown to be capable of greatly improving any seed solution. © 1995 John Wiley & Sons, Inc.     

A general axiomatization of additive measurement with applications

Necessary and sufficient conditions are specified for a general theory of additive measurement that presumes very little set-theoretic structure. The theory is illustrated for numerical representations in extensive, conjoint, difference, threshold, expected utility, probability, ambiguity, and subset measurement. © 1992 John Wiley & Sons, Inc.     

Economic design of X¯ control charts for two manufacturing process models

Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.     

Nature of renyi's entropy and associated divergence function

Nature of Renyi's entropy and associated divergence function is discussed in terms of concave (convex) and pseudoconcave (pseudoconvex) functions.