Statistical Analysis as an Adjunct to Historical Research: Identification of the Likely Manufacturers of British Pattern 1907 Bayonets Supplied by the Birmingham Small Arms Company to the Siamese Government in 1920

In 1920, the Birmingham Small Arms Company supplied 10,000 Pattern 1907 bayonets to the government of Siam to accompany an order for rifles. The original maker of these bayonets was unknown, but historical research indicates that the Wilkinson Sword Co. Ltd. was a primary maker. The weights of some surviving Pattern 1907 bayonets, including twelve bayonets from the 10,000 described above, produced by the six makers in the UK before and during the Great War (1914–1918) period were available. A statistical analysis of the data was performed to compare with the historical research. The results strongly supported that the Wilkinson Sword Co. Ltd. was a primary maker. They were also sufficient to exclude from this batch of twelve bayonets the Royal Small Arms Factory (Enfield) and Vickers Ltd. as manufacturers. The statistical evidence for the presence of bayonets made by J.A. Chapman Ltd., R. Mole & Sons and Sanderson Bros. was weaker than that for the Wilkinson Sword Co. Ltd., but was nevertheless supportive of that hypothesis. Overall, the analysis was consistent with the supply to Siam of commingled bayonets from British government stores. It was noted that the bayonets for the Siam contract fell into a relatively narrow weight range, but the reason for this could not be determined.     

Inventory rotation policies for slow moving items

In this article we present a stochastic model for determining inventory rotation policies for a retail firm which must stock many hundreds of distinctive items having uncertain heterogeneous sales patterns. The model develops explicit decision rules for determining (1) the length of time that an item should remain in inventory before the decision is made on whether or not to rotate the item out of inventory and (2) the minimum sales level necessary for retaining the item in inventory. Two inventory rotation policies are developed, the first of which maximizes cumulative expected sales over a finite planning horizon and the second of which maximizes cumulative expected profit. We also consider the statistical behavior of items having uncertain, discrete, and heterogeneous sales patterns using a two-period prediction methodology where period 1 is used to accumulate information on individual sales rates and this knowledge is then used, in a Bayesian context, to make sales predictions for period 2. This methodology assumes that over an arbitrary time interval sales for each item are Poisson with unknown but stationary mean sales rates and the mean sales rates are distributed gamma across all items. We also report the application of the model to a retail firm which stocks many hundreds of distinctive unframed poster art titles. The application provides some useful insights into the behavior of the model as well as some interesting aspects pertaining to the implementation of the results in a “real-world” situation.     

Robustness of the normal approximation of lead-time demand in a distribution setting

Previous studies criticize the general use of the normal approximation of lead-time demand on the grounds that it can lead to serious errors in safety stock. We reexamine this issue for the distribution of fast-moving finished goods. We first determine the optimal reorder points and quantities by using the classical normal-approximation method and a theoretically correct procedure. We then evaluate the misspecification error of the normal approximation solution with respect to safety stock, logistics-system costs, total costs (logistics costs, including acquisition costs), and fill rates. The results provide evidence that the normal approximation is robust with respect to both cost and service for seven major industry groups. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 165–186, 1997     

An inventory model of incentives for on-time delivery in just-in-time purchasing contracts

This article formulates an analytic model of just-in-time purchasing contracts and compares the minimum cost solution with the cost attainable through vertical integration. The models use standard inventory theory cost parameters and decision variables. The results quantify the increase in cost of buying an item rather than making it. Optimal incentives are characterized when JIT purchasing contracts are used. When JIT purchasing is implemented, buffer inventories are typically reduced. This inventory reduction makes on-time delivery critical to the buyer; yet timeliness is controlled by the supplier. As an incentive to provide on-time delivery, the buyer offers the supplier a bonus for on-time delivery. The supplier chooses a flow time allowance based upon the bonus offered. First- and second-order conditions are characterized in general, and examples are provided for exponentially and uniformly distributed flow times. The delivery timeliness obtainable in a vertically integrated firm is determined and compared with timeliness obtainable between separate firms. This comparison indicates that buyers who choose to purchase materials from a separate firm are more likely to experience late deliveries. The relationship between the value of the bonus and the proportion of on-time deliveries is also considered. The bonus required to achieve the same probability of on-time delivery as under vertical integration is also determined. © 1993 John Wiley & Sons, Inc.     

Landmarks in defense literature

Some Principles of Maritime Strategy. Julian S. Corbett. Longmans, London, 1911     

Distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables

In this paper the exact distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables is given.     

A saddle-point theorem for a class of infinite games

In this paper, the existence of a saddle point for two-person zero-sum infinite games of a special type is proved. The games have continuous bilinear payoff functions and strategy sets which are convex, noncompact subsets of an infinite-dimensional vector space. The closures of the strategy sets are, however, compact. The payoff functions satisfy conditions which allow the use of dominance arguments to show that points in the closure of a strategy set are dominated by or are strategically equivalent to points in the strategy set itself. Combining the dominance arguments with a well-known existence theorem produces the main result of the paper. The class of games treated is an extension of a class studied by J. D. Matheson, who obtained explicit solutions for the saddle points by using necessary conditions.