A family of games on 1,∞)2 with payoff a function of y/x

A two-parameter class of games on 1,∞)² is studied. The games may be regarded as analogs of Silverman games, having continuous payoff function in place of a step function of y/x. This change is motivated by a desire to move toward a model for competitive situations where the penalty for overspending increases with the amount of overspending. There are some similarities to games with bell-shaped kernel. For most of the region considered in the plane of the two parameters there are solutions of finite type, which are obtained explicitly. There are, however, pockets in this plane where no optimal strategies have been found and possibly where none of finite type exist.     

The U.S. versus the Soviet incentive models

This paper is concerned with models of the use of performance incentives in the Soviet Union and United States. The principal analytical result is an extension of an analysis of the methods whereby Soviet planners make the decision about production targets a variable under control of the producer, who is the only one possessing a knowledge of the uncertain condition of production. It is shown that this device can be viewed as a classical inventory problem. There is also an examination of the “U.S. incentive program” referring to multi-incentive contracts in which the profits received by the private producers are related to performance, outcome and cost. The analysis describes how this device can be extended to solve the target output selection problem of the Soviet planning system.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

Markov chain with taboo states and reliability

A computationally feasible matrix method is presented to find the first-passage probabilities in a Markov chain where a set of states is taboo during transit. This concept has been used to evaluate the reliability of a system whose changes in strength can be thought of as a Markov chain, while the environment in which it is functioning generates stresses which can also be envisaged as another Markov chain.     

“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

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.     

Comparison of rank aggregation methods based on inherent ability

Ranking is a common task for selecting and evaluating alternatives. In the past few decades, combining rankings results from various sources into a consensus ranking has become an increasingly active research topic. In this study, we focus on the evaluation of rank aggregation methods. We first develop an experimental data generation method, which can provide ground truth ranking for alternatives based on their “inherent ability.” This experimental data generation method can generate the required individual synthetic rankings with adjustable accuracy and length. We propose characterizing the effectiveness of rank aggregation methods by calculating the Kendall tau distance between the aggregated ranking and the ground truth ranking. We then compare four classical rank aggregation methods and present some useful findings on the relative performances of the four methods. The results reveal that both the accuracy and length of individual rankings have a remarkable effect on the comparison results between rank aggregation methods. Our methods and results may be helpful to both researchers and decision‐makers.     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

Turkey’s strategic choice: buy or make weapons?

Turkey has been investing in its national defence industrial base since the 1980s. As with other developing countries, Turkey’s motivations for investing in national defence industries can be boiled down to the pursuit of defence autarky, economic benefits and international prestige. However, after 40 years of investment, Turkey is unable to reach the primary goals of defence industrialisation. We argue that three factors are important to understanding Turkey’s persistence in these primary goals. First, Turkey believes that there is an overall improvement in its defence industrial capabilities and the goal of autarky is still reachable. Second, increased defence exports support the belief that Turkish defence industries have become sustainable and the trend will continue in the future. The third reason, perhaps most important of all, has to do with the domestic political gains of defence industrialisation: the AKP uses defence industry and indigenous weapon systems for prestige and, therefore, garners broader support.