The machine sequencing problem – review and extensions

The deterministic sequencing problem is reviewed from the points of view of variety, models, context, methodology, and current state of the art. The relationship between the theory of sequencing and other areas of control is illustrated with the relationship of sequencing to inventory. The “cyclical EMQ (Economical Manufacturing Quantities)” problem is discussed and new formulations are presented which promise a computationally feasible resolution of this outstanding problem.     

Geometry of the total time on test transform

Total time on test (TTT) plots provide a useful graphical method for tentative identification of failure distribution models. Identification is based on properties of the TTT transform. New properties of the TTT transform distribution are obtained. These results are useful to the user of TTT plots. Although IFR (DFR) distributions are particularly easy to identify from TTT plots, the user must exercise caution relative to identification of IFR A (DFRA) distributions.     

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.     

Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.     

Bounds on parallel-processing of queues with multiple-phase jobs

Currently, both the hardware and software designs of many large computing systems aim at improved system performance through exploitation of parallelism in multiprocessor systems. In studying these systems, mathematical modelling and analysis constitute an important step towards providing design tools that can be used in building such systems. With this view the present paper describes a queueing model of a multiprocessor system operating in a job-shop environment in which arriving jobs consist of a random number of segments (sub-jobs). Two service disciplines are considered: one assumes that the sub-jobs of a given job are capable of parallel operation on different processors while the other assumes that the same sub-jobs must be operated in a strictly serial sequ'snce. The results (in particular, the mean number in the system and waiting time in queue) obtained for these two disciplines are shown to be bounds for more general job structures.     

The US NATO and military burden sharing: post-Cold War accomplishments and future prospects

NATO burden sharing has become an especially timely issue in the past several years as a result of a number of factors, including Russian annexation of Crimea and destabilization of eastern Ukraine in 2014. This article argues that alliance unity among the great democracies of Europe and North America is indispensable to peace and stability on the Eurasian continent. A fractured NATO, and especially, a large divide in purposes or commitments as between the United States and its European security partners, invites aggression and the possibility of inadvertent escalation. Past successes and failures in US-involved multinational peace and stability operations, within and outside of Europe, show that mission accomplishment requires give and take, including the occasional acceptance of unequal costs and benefits among the members, in order to achieve peace and security objectives.     

Finding saddle points on polyhedra: Solving certain continuous minimax problems

This article reviews procedures for computing saddle points of certain continuous concave-convex functions defined on polyhedra and investigates how certain parameters and payoff functions influence equilibrium solutions. The discussion centers on two widely studied applications: missile defense and market-share attraction games. In both settings, each player allocates a limited resource, called effort, among a finite number of alternatives. Equilibrium solutions to these two-person games are particularly easy to compute under a proportional effectiveness hypothesis, either in closed form or in a finite number of steps. One of the more interesting qualitative properties we establish is the identification of conditions under which the maximizing player can ignore the values of the alternatives in determining allocation decisions. © 1996 John Wiley & Sons, Inc.     

Lot sizing when yields increase during the production run

We investigate the problem of determining lot sizes for multiple items when the expected percentage of acceptable output increases with the duration of the production run, usually due to adjustments made during the early part of the production run. Such problems arise in metal stamping, textile finishing processes, and a variety of other industries. The goal is to minimize the total cost of production, inventory holding costs, and setup costs (where applicable). We develop a heuristic procedure based on a Lagrangian relaxation that differs from relaxations used in earlier studies. We use various properties of the objective function to guide the adjustment of the initial solution from the relaxation toward feasibility. Computational results indicate that, on the average, the heuristic produces solutions within 4.9% of the lower bound obtained from the Lagrangian relaxation. © 1996 John Wiley & Sons, Inc.