Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.

Optimal Resource Partitioning in a Military Conflict based on Lanchester Attrition Models

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts. The Lanchester attrition model is used to develop the dynamical equations governing the variation in force strength. Three different allocation schemes - Time-Zero-Allocation (TZA), Allocate-Assess-Reallocate (AAR), and Continuous Constant Allocation (CCA) - are considered and the optimal solutions are obtained in each case. Numerical examples are given to support the analytical results.

Optimal Resource Partitioning in a Military Conflict based on Lanchester Attrition Models

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts. The Lanchester attrition model is used to develop the dynamical equations governing the variation in force strength. Three different allocation schemes - Time-Zero-Allocation (TZA), Allocate-Assess-Reallocate (AAR), and Continuous Constant Allocation (CCA) - are considered and the optimal solutions are obtained in each case. Numerical examples are given to support the analytical results.

Optimal resource partitioning in conflicts based on Lanchester (n, 1) attrition model

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary from n different fronts. The problem of optimally partitioning the defending forces against the attacking forces is addressed. The Lanchester square law model is used to develop the dynamical equations governing the variation in force strength. Two different allocation schemes-Time-ZeroAllocation (TZA) and Continuous Constant Allocation (CCA) are considered and the optimal solutions for both are obtained analytically. These results generalize other results available in the literature. Numerical examples are given to support the analytical results.

Worker piping triggers hissing for coordinated colony defence in the dwarf honeybee Apis florea

Defending a large social insect colony containing several thousands of workers requires the simultaneous action of many individuals. Ideally this action involves communication between the workers, enabling coordinated action and a fast response. The Asian dwarf honeybee, Apis florea, is a small honeybee with an open nesting habit and a comparatively small colony size, features that leave them particularly exposed to predators. We describe here a novel defence response of these bees in which the emission of an initial warning signal from one individual (“piping”) is followed 0.3 to 0.7 seconds later by a general response from a large number of bees (“hissing”). Piping is audible to the human ear, with a fundamental frequency of 384 ± 31Hz and lasting for 0.82 ± 0.35 seconds. Hissing is a broad band, noisy signal, clearly audible to the human observer and produced by slight but visible movements of the bees' wings. Hissing begins in individuals close to the piping bee, spreads rapidly to neighbours and results in an impressive coordinated crescendo occasionally involving the entire colony. Piping and hissing are accompanied by a marked decrease, or even cessation, of worker activities such as forager dancing and departures from the colony. We show that whereas hissing of the colony can be elicited without piping, the sequential and correlated piping and hissing response is specific to the presence of potential predators close to the colony. We suggest that the combined audio-visual effect of the hissing might deter small predators, while the cessation of flight activity could decrease the risk of predation by birds and insects which prey selectively on flying bees.