Dr Anastasios Tsoularis

This paper examines optimal predation by a predator preying upon two types of prey, modes and mimics. Models are unpalatable prey and mimics are palatable prey resembling the models so as to derive some protection from predation. This biological phenomenon is known in Ecology as Batesian mimicry. An optimal control problem in continuous time is formulated with the sole objective to maximize the net energetic benefit to the predator from predation in the presence of evolving prey populations. The constrained optimal control is bang-bang with the scalar control taken as the probability of attacking prey. Conditions for the existence of singular controls are obtained.

In Ecology, the term mimicry describes a situation in which one type of species, the mimic, shares common external features with another type of species, the model with the sole purpose of confusing potential predators. In Batesian mimicry, named after Henry Walter Bates, the English naturalist, the mimics, which are palatable to predators, send similar signals to model species, which are unpalatable. His theory of mimicry postulates that predators tend to avoid nauseous (in smell or taste) models and the mimics derive some form of protection by resembling the models. This theory carries the assumption that models are more abundant than mimics so that predators can learn to avoid them. In this work a stochastic optimal control problem for optimal predation is presented. The objective is to maximize the predator's net energetic benefit. Mimic consumption is beneficial (positive) whereas model consumption is detrimental (negative).

In this paper I propose a reinforcement learning model for a predator preying upon two types of prey, the unpalatable (noxious) models, and the palatable mimics. The latter type of prey resembles the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. Essentially the predator is treated as a learning automaton adopting a simple reinforcement learning strategy in order to increase its consumption of palatable prey and reduce the consumption of unpalatable ones. The populations of both mimics and models are assumed to grow logistically. © 2007 Springer Science+Business Media B.V.

This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings.

This article considers the deterministic optimal control problem of profit maximization for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the inventor, product order rate and price are derived using the maximum principle. Bounds on the maximum price possible are also derived.

© 2018, The Author(s). Inventory for an item is being replenished at a constant rate whilst simultaneously being depleted by demand growing randomly and in relation to the inventory level. A stochastic differential equation is put forward to model this situation with solutions to it derived when analytically possible. Probabilities of reaching designated a priori inventory levels from some initial level are considered. Finally, the existence of stable inventory states is investigated by solving the Fokker–Planck equation for the diffusion process at the steady state. Investigation of the stability properties of the Fokker–Planck equation reveals that a judicious choice of control strategy allows the inventory level to remain in a stable regime.

In this paper, a mathematical model of random encounters between a predator and two types of prey is presented. One type of prey (model) is noxious to the predator whilst the other is palatable (mimic). The mimics resemble the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. The populations of both mimics and models are assumed to grow logistically. The effect of learning and population growth on prey attacks is examined via simulations.

The population dynamics for predator and prey environments have been studied extensively, and several major mathematical models have been introduced to quantify this. The situation becomes more complex, however, when the prey incorporates preservation strategies for survival. One of the most interesting approaches here is the use of mimicry of prey which are unacceptable to the predator, to avoid being consumed. Here we develop a Markov chain model of interactions between a predator and a prey population comprising unpalatable models, general mimics and specific mimics. This incorporates a simple stochastic procedure for the predator, enabling modifiable behavior to be modeled. We calculate equilibrium consumption probabilities and introduce a fitness measure for each type of prey. Finally, by taking into account the population size of each type of prey, we extend the previously reported notion of a predator benefit function for this more complex situation and provide various mathematical forms of optimal benefit for the predator under selected scenarios of biological importance.

In this article, the focus is on modelling the predation of Batesian mimics using reinforcement learning methodology. Essentially, it is proposed that the predator be modelled as a learning automaton aided by reinforcement algorithms to select palatable prey for consumption and avoid unpalatable ones. A tentative connection between reinforcement learning and the theory of dynamic programming and optimal control is also considered. The paper concludes by offering some ideas for future research in this area. © 2009 Inderscience Enterprises Ltd.

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case. Copyright © 2014 Inderscience Enterprises Ltd.

Mathematical modeling in economics became central to economic theory during the decade of the Second World War. The leading figure in that period was Paul Anthony Samuelson whose 1947 book, Foundations of Economic Analysis, formalized the problem of dynamic analysis in economics. In this brief chapter some seminal applications of differential equations in economic growth, capital and business trade cycles are outlined in deterministic setting. Chaos and bifurcations in economic dynamics are not considered. Explicit analytical solutions are presented only in relatively straightforward cases and in more complicated cases a path to the solution is outlined. Differential equations in modern dynamic economic modeling are extensions and modifications of these classical works. Finally we would like to stress that the differential equations presented in this chapter are of the “stand-alone” type in that they were solely introduced to model economic growth and trade cycles. Partial differential equations such as those which arise in related fields, like Bioeconomics and Differential Games, from optimizing the Hamiltonian of the problem, and stochastic differential equations of Finance and Macroeconomics are not considered here.

With the advent and maturity of the internet, reverse electronic auctions (e-auctions) are now an important mechanism for public and private sector organisations, in the procurement of goods and services. Here, a novel link is made between reverse electronic auctions (e-auctions) and its potential impact on organisational agility, a link not previously developed in the literature. In this paper, we justify this relationship from a theoretical perspective. We investigate how information and internet technology impacts procurement, by an analysis and evaluation of the literature. E-auctions are reviewed and organisational agility defined; the advantages of agile management are also identified and the role that e-auctions can play in achieving this, discussed. Strategies for re-aligning reverse e-auctions in support of organisational agility are proposed and the advantages of this process discussed. Recommendations for future practice that will maximise the chances of realising agile systems management are also presented. Finally, areas for further research are identified.

In this paper, we utilize a reinforcement learning model for a specialist predator preying upon two types of prey, the noxious models, which are abundant, and the palatable mimics, which are much rarer, in accord with the concept of Batesian mimicry. The latter type of prey resembles the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. We treat the predator as a slow learning automaton adopting a simple reinforcement learning strategy in order to increase its consumption of palatable prey and reduce the consumption of unpalatable ones. We assume a logistic growth for both models and mimics.

In this paper we propose a mathematical learning model for the feeding behaviour of a specialist predator operating in a random environment occupied by two types of prey, palatable mimics and unpalatable models, and a generalist predator with additional alternative prey at its disposal. A well known linear reinforcement learning algorithm and its special cases are considered for updating the probabilities of the two actions, eat prey or ignore prey. Each action elicits a probabilistic response from the environment that can be favorable or unfavourable. To assess the performance of the predator a payoff function is constructed that captures the energetic benefit from consuming acceptable prey, the energetic cost from consuming unacceptable prey, and lost benefit from ignoring acceptable prey. Conditions for an improving predator payoff are also explicitly formulated. © 2005 Elsevier Inc. All rights reserved.

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions. A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting. © 2002 Elsevier Science Inc. All rights reserved.

The Internet has reached a stage of maturity where its innovative adoption and implementation can be a source of competitive advantage. Supply chains are one of the areas that has reportedly benefited greatly, achieving optimisation through low cost, high efficiency use of the Internet, almost seamlessly linking global supply chains into e-supply networks. This field is still in its academic and practical infancy, and there is a need for more empirical research to build a robust theoretical foundation, which advances our knowledge and understanding. Here, the main aims and objectives are to highlight the importance of information flows in e-supply chains/networks, and the need for their standardisation to facilitate integration, legality, security, and efficiency of operations. This chapter contributes to the field by recommending a three-stage framework enabling this process through the development of standardised Internet technology platforms (e-platforms), integration requirements and classification of information flows.

This paper presents a stochastic automaton approach to stock ordering for retailers of time-limited goods, in the modern supply chain network. The rationale applied is that by ordering in small quantities frequently, overstocking will be reduced, capital liquidity improved and wastage limited. A consequence for the complete supply chain is that such an approach could substantially minimise the reactive bullwhip effect, leading to more efficient utilisation, production and agility throughout the chain. Such agility and flexibility can only be achieved by full integration of stock inventory monitoring technologies (such as RFID) with enterprise integration systems (such as ERP) connected to suppliers, mediated by the internet. We undertake a comparative simulation study of stock ordering using a stochastic automaton and a naïve traditional approach. This shows that stochastic ordering, prompted by a stochastic automaton, exhibits characteristic properties that are a prerequisite for reducing the bullwhip effect, thus enabling agile inventory management.