Degeneracy in inventory models

In order‐quantity reorder‐point formulations for inventory items where backordering is allowed, some of the more common ways to prevent excessive stockouts in an optimal solution are to impose either a cost per unit short, a cost per stockout occasion, or a target fill rate. We show that these popular formulations, both exact and approximate, can become “degenerate” even with quite plausible parameters. By degeneracy we mean any situation in which the formulation either cannot be solved, leads to nonsensical “optimal” solutions, or becomes equivalent to something substantially simpler. We explain the reasons for the degeneracies, yielding new insight into these models, and we provide practical advice for inventory managers. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 686–705, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10037     

Scheduling prowler training

The U.S. Navy Prowler aircraft is designed for electronic surveillance and countermeasures. In this paper, we describe the problem of scheduling Prowler crew training, and we present two integer programming models to solve it. The first model maximizes the number of aviators trained above 75% in each mission area, subject to the available number of flights, over a single month. The second model distinguishes peacetime from mobilization, and minimizes the number of flights done in mobilization subject to the available number of flights in peacetime. Our models distinguish different types of crew and allow more than one qualification to be earned on a given flight. We give numerical results using real data, comparing our results to the actual readiness of a squadron. We found that crew readiness of Prowler squadrons can be increased by 10%, simply by better scheduling. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 289–305, 2003.     

More military base closure? Considering the alternatives*

Despite multiple base closing rounds, the United States Department of Defense still has excess base capacity, and thus President Trump and high-level Defense Department officials are calling for more base closure through the Base Realignment and Closure (BRAC) process. However, another BRAC may not be the optimal solution, because simple base closure is not an efficient way to reduce surplus base capacity. Thus, Defense Department officials should consider other methods to reduce surplus capacity, including reduction in base size, leasing excess base property, or transferring it to another government agency for a variety of alternative uses. The surplus capacity issue also offers an opportunity to DOD to reassess base utilization, to update base requirements with current and future force structure. While BRAC focuses on American military bases, the process and alternatives also have international applications.     

On optimal aiming to hit a linear target

Typically weapon systems have an inherent systematic error and a random error for each round, centered around its mean point of impact. The systematic error is common to all aimings. Assume such a system for which there is a preassigned amount of ammunition of n rounds to engage a given target simultaneously, and which is capable of administering their fire with individual aiming points (allowing “offsets”). The objective is to determine the best aiming points for the system so as to maximize the probability of hitting the target by at least one of the n rounds. In this paper we focus on the special case where the target is linear (one‐dimensional) and there are no random errors. We prove that as long as the aiming error is symmetrically distributed and possesses one mode at zero, the optimal aiming is independent of the particular error distribution, and we specify the optimal aiming points. Possible extensions are further discussed, as well as civilian applications in manufacturing, radio‐electronics, and detection. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 323–333, 1999     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

See the light: Optimization of put-to-light order picking systems

Put-to-light order picking systems invert the basic logic of conventional picker-to-parts systems. Instead of successively visiting the storage positions of the stock keeping units (SKUs) when collecting picking orders, an order picker accompanies successive bins each containing multiple items of a specific SKU along a lane of subsequent orders. Whenever the picker passes an order requiring the current SKU, which is indicated by a light signal, she puts the requested number of items into the bin associated with the order. Such an order picking system is well-suited if the assortment is not overly large and all orders demand similar SKUs, so that it is mainly applied in distribution centers of brick-and-mortar retail chains. This paper evaluates four different setups of put-to-light systems, which, during operations, require the solution of different storage assignment and SKU sequencing problems. We formulate these problems, prove computational complexity, and suggest suited solution algorithms. By applying these algorithms in a comprehensive computational study, we benchmark the impact of the four different setups on picking performance. In this way, warehouse managers receive decision support on how to set up their put-to-light systems.     

The Enfield Lock Barrel Mill of 1815 and Moves to Replace Musket Barrel Grinding by Turning c1780 to c1840

In 1841 Henry Wilkinson in his book Engines of War and William Greener in The Science of Gunnery describe a range of methods then in use for shaping the outside of gun barrels after the barrel forging process, ranging from manual off-hand grinding to the use of precision machines. In the same year G. & J. Rennie published the design of their state-of-the-art lathe that was capable of turning complex and dished barrel forms. This built upon the earlier work of both Henry Nock and John Jones. In the early years of the 19th century both Britain, at Enfield and other locations, and the USA, at Harpers Ferry and Springfield, began to introduce barrel-turning technology. This paper uses measurements taken from a significant number of military barrels made by several makers, and also newly exposed information about Henry Nock and the Enfield Factory of 1815, to understand better the technologies that were applied to military flintlock barrel finishing from the 1780s to the 1840s, and particularly during the major wars of 1793–1815, when high output was paramount. Measurements both of barrel form and out-of-roundness are presented. These allow the interpretation of the techniques being used by different makers at different locations, and raise questions about the purpose and achievement of the complex dished barrel forms found on British military flintlock muskets. This approach also allows us to better describe the earliest factory on the Enfield site, one of the most significant sites in the wider history of UK manufacturing.