Bounds on optimal cost for a replacement problem with partial observations

This paper characterizes the structure of optimal strategies for a replacement problem for two special cases of observation quality. It is shown that when the state of the system is either completely observed or completely unobserved at every decision epoch by the controller, reasonable assumptions are sufficient for the existence of optimal replacement strategies composed of policies having a generalized, control-limit form. These structural results are of particular interest since the optimal cost functions for the two special cases represent bounds on the optimal cost function for the general partially observed case, significant computational simplification can result for the two special cases due to their optimal strategy structure, and optimal strategies possessing a control-limit structure do not necessarily exist for the general partially observed case.     

A methodology for studying the dynamics of extended logistic systems

An extended logistic system is a well-defined configuration of equipment, modules, inventories, and repair and replacement facilities modeling a complex, repairable system with on-going repair. The design of such systems has been based largely on the static tools of inventory theory and reliability theory, i.e., on steady-state distributions and on associated means and variances. Such static tools suppress the scale of real lime and ignore system persistence time in up-states and persistence time in down-states. A reasonably simple dynamic methodology is presented, focusing on system failure time as a more meaningful objective function for system-design tradeoff studies. In the presence of good reliability, it is shown that different candidates for system failure time effectively merge to yield an unambiguous, single system failure time. Examples illustrating the importance of dynamic information for system design are given.     

Estimating the economic impact of the 1973 Navy base closing: Models,tests, and an ex post evaluation of the forecasting performance

In 1973 the Defense Department made plans to close many Navy bases in the United States. Hardest hit was Rhode Island which would suffer a loss of 45.61% of the total cutback of 42,812 jobs. This paper describes two models which were built to forecast the severity of the economic impact in Rhode Island: one used the reduced form equation approach, and the other the simultaneous equations system approach. Tests on multicollinearity, specification, and serial correlation were conducted. An ex post evaluation of these two models' performance in forecasting then concludes the paper.     

Optimization in mixed-integer space with a single linear bound

The search for an optimal point in a mixed-integer space with a single linear bound may be significantly reduced by a procedure resembling the Lagrangian technique. This procedure uses the coefficients of the linear bound to generate a set of necessary conditions that may eliminate most of the space from further consideration. Enumerative or other techniques can then locate the optimum with greater efficiency. Several methods are presented for applying this theory to separable and quadratic objectives. In the maximization of a separable concave function, the resulting average range of the variables is approximately equal to the maximum (integer) coefficient of the constraint equation.     

An approach to the allocation of common costs of multi-mission systems

Many Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak-load pricing as developed by Marcel Boiteux. The basic principle is that the long-run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission-specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.     

Tolerance intervals for univariate distributions

A review of univariate tolerance intervals is presented from an application-oriented point of view. Both β-content and β-expectation intervals are defined and considered. Standard problems are discussed for the distribution-free case and with various distributional assumptions (normal, gamma, Poisson) which occur most frequently in practice. The determination of sample size is emphasized. A number of examples are used to illustrate the types of problems which permit solutions with the excellent tables now available.     

Constructing bimatrix games with special properties

This work is concerned primarily with presenting techniques for constructing bimatrix games with predetermined equilibrium points. Some partial results on Nash-solvability are also given.     

The payment scheduling problem

Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.     

Cyclic best first search: Using contours to guide branch‐and‐bound algorithms

The cyclic best‐first search (CBFS) strategy is a recent search strategy that has been successfully applied to branch‐and‐bound algorithms in a number of different settings. CBFS is a modification of best‐first search (BFS) that places search tree subproblems into contours which are collections of subproblems grouped in some way, and repeatedly cycles through all non‐empty contours, selecting one subproblem to explore from each. In this article, the theoretical properties of CBFS are analyzed for the first time. CBFS is proved to be a generalization of all other search strategies by using a contour definition that explores the same sequence of subproblems as any other search strategy. Further, a bound is proved between the number of subproblems explored by BFS and the number of children generated by CBFS, given a fixed branching strategy and set of pruning rules. Finally, a discussion of heuristic contour‐labeling functions is provided, and proof‐of‐concept computational results for mixed‐integer programming problems from the MIPLIB 2010 database are shown. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 64–82, 2017