Late Medieval Lance Use: Mounted Combat and Martial Arts in Western Europe from the 14th to the 16th Century

Despite the lance’s status and the amount of attention the couched lance has received in historiography, study of its martial art has been neglected. The various lance types and techniques used by western European cavalry have only recently begun to receive scholarly attention. Additionally, Medieval European lance use has too often been studied in isolation, without an adequate understanding of the idiosyncratic and asymmetrical dynamics of mounted combat. Although the charge with the couched lance was a valid tactic, it was only one of many. Light and heavy lances were used in one hand or two to trip, block, unhorse, and wrestle. These techniques were governed by the harsh laws of distance, speed, impact, iron, and asymmetry. By utilizing the surviving Fechtbücher and several Peninsular and Near Eastern sources, a brief foray into the diverse techniques of lance use and their purposes has been attempted here.     

Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019     

Optimal maintenance models for systems subject to failure–A Review

This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.     

Order-preserving allocation of jobs to two machines

In this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.     

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.     

Adaptive forecasting of the size of a work force subject to random withdrawals

Adaptive forecasting procedures are developed for predicting the size of a work force which is subject to random withdrawals. The procedures are illustrated using Marine Corps data in which four stages of service for incoming cohorts are distinguished. Using these data, three forecasting procedures—conditional maximum likelihood estimation of prediction intervals; tolerance intervals; and Bayes prediction intervals—are compared.     

Determining the most vital link in a flow network

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.     

A two-echelon multi-station inventory model for navy applications

The two inventory echelons under consideration are the depot, D, and k tender ships E₁, …, E_k. The tender ships supply the demand for certain parts of operational boats (the customers). The statistical model assumes that the total monthly demands at the k tenders are stationary independent Poisson random variables, with unknown means λ₁, …, λ_k. The stock levels on the tenders, at the heginning of each month, can be adjusted either by ordering more units from the depot, or by shipping bach to the depot an excess stock. There is no traffic of stock between tenders which is not via the depot. The lead time from the depot to the tenders is at most 1 month. The lead time for orders of the depot from the manufacturer is L months. The loss function due to erroneous decision js comprised of linear functions of the extra monthly stocks, and linear functions of shortages at the tenders and at the depot over the N months. A Bayes sequential decision process is set up for the optimal adjustment levels and orders of the two echelons. The Dynamic Programming recursive functions are given for a planning horizon of N months.     

Resource allocation for transportation

A linear programming formulation is described that will permit the optimal assignment of transportation resources (vehicles) and movement requirements to a network consisting of a set of designated origins, ports of embarkation, enroute bases, ports of debarkation, and destinations to achieve a prescribed schedule of arrivals.     

A finite algorithm for concave minimization over a polyhedron

We present a new algorithm for solving the problem of minimizing a nonseparable concave function over a polyhedron. The algorithm is of the branch-and-bound type. It finds a globally optimal extreme point solution for this problem in a finite number of steps. One of the major advantages of the algorithm is that the linear programming subproblems solved during the branch-and-bound search each have the same feasible region. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some preliminary computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several bilinear programming problems with the code.