# Logistics and Operations Analysis for the Military

• Shelemyahu Zacks
Chapter
Part of the Statistics for Industry, Technology, and Engineering book series (SITE)

## Abstract

As described in Sect. of the Introduction, we present in this chapter theoretical contributions made in the areas of inventory control, readiness evaluation of big military units, and reliability of items entering a wear out phase. The inventory control study served the needs of naval applications in the 60s and the 70s. Inventory systems today are based on computer control and on fast delivery. What is described here might not be applicable in modern times, but might be of historical interest. We start with one-echelon inventory system and then proceed to two-echelon systems. Before we start with the inventory control theory, we introduce the scenario. The stock of the customer (a ship or a submarine) consists of a large number of items. Each item requires its specific demand analysis. The theory presented in this chapter discusses a special case of discrete variables, which present the number of items consumed between replenishments. The theory for continuous demand variables (fluids) can be modified appropriately.

## References

1. Barzily, Z., Marlow, W. H., & Zacks, S. (1979). Survey of approaches to readiness. Naval Research Logistics Quarterly, 26, 21–31.
2. Breir, S. S., Zacks, S., & Marlow, W. H. (1986). An application of empirical Bayes techniques to the simultaneous estimation of many probabilities. Naval Research Logistics Quarterly, 33, 77–90.
3. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society, B, 39, 1–38.
4. James, W., & Stein, C. (1960). Estimation with quadratic loss. In Proceedings of Fourth Berkeley Symposium on Mathematical Statistics and Probability (vol. 1). Berkely: Statistics Laboratories of the University of California.Google Scholar
5. Johnson, N. L., & Kotz, S. (1969). Distributions in statistics: Discrete distributions. Boston: Houghton and Mifflin.
6. Morris, C. (1983). Parametric empirical Bayes inference: Theory and applications. Journal of the American Statistical Association, 78, 47–54.
7. Zacks, S. (1969a). Bayes sequential design of stock levels. Naval Research Logistics Quarterly, 16, 143–155.
8. Zacks, S. (1969b). Bayes sequential design of fixed samples from finite populations. Journal of the American Statistical Association, 64, 1342–1349.
9. Zacks, S. (1974). On the optimality of the Bayes prediction policy in two-echelon multi-station inventory systems. Naval Research Logistics Quarterly, 21, 569–574.
10. Zacks, S. (1984). Estimating the shift to wear-out of systems having Exponential-Weibull life distributions. Operations Research, 32, 741–749.
11. Zacks, S. (1988), A simulation study of the efficiency of Empirical Bayes’ estimators of multiple correlated probability vectors. Naval Research Logistics Quarterly, 35, 237–246.
12. Zacks, S. (2014). Problems and examples in mathematical statistics. New York: Wiley.
13. Zacks, S., & Fennel, J. (1972). Bayes adaptive control of two-echelon inventory systems, I: Development for a special case of one-station lower echelon and Monte Carlo evaluation. Naval Research Logistics Quarterly, 19, 15–28.
14. Zacks, S., & Fennel, J. (1973). Distribution of adjusted stock levels under statistical adaptive control procedures for inventory systems. Journal of the American Statistical Association, 68, 88–91.
15. Zacks, S., & Fennel, J. (1974). Bayes adaptive control of two-echelon inventory systems, II: The multi-station case. Naval Research Logistics Quarterly, 21, 575–593.
16. Zacks, S., Marlow, W. H., & Breir, S. S. (1985). Statistical analysis of very high-dimensional data sets of hierarchically structured binary random variables with missing data and application to Marine Corps readiness evaluations. Naval Research Logistics Quarterly, 32, 467–490.