Defence and attack of systems with variable attacker system structure detection probability

A system consists of identical elements. The cumulative performance of these elements should meet a demand. The defender applies three types of defensive actions to reduce a damage associated with system performance reduction caused by an external attack: deploying separated redundant genuine system elements, deploying false elements, and protecting genuine elements. If the attacker cannot distinguish between genuine and false elements, he chooses a number of elements to attack and then selects the elements at random, distributing his resources equally across these elements. By obtaining intelligence data, the attacker can get full information about the system structure and identify false and unprotected genuine elements. The defender estimates the probability that the attacker can identify all system elements. This paper analyses the influence of this probability in a non-cooperative two-period minmax game between the defender and the attacker.     

False targets efficiency in defense strategy

The paper analyzes the efficiency of deploying false targets as part of a defense strategy. It is assumed that the defender has a single object that can be destroyed by the attacker. The defender distributes its resource between deploying false targets and protecting the object from outside attacks. The attacker cannot distinguish the false targets from the defended object (genuine target). Therefore the attacker has no preferences for attacking one target rather than another target. The defender decides how many false targets to deploy whereas the attacker decides how many targets to attack. The article assumes that both the defender and attacker have complete information and full rationality. The optimal number of false targets and the attacked targets are obtained for the case of fixed and variable resources of the defender and the attacker as solutions of a non-cooperative game between the two agents.     

Permanence of general stage-structured consumer–resource models

Much of the existing stage-structured consumer–resource models ignore the permanence. In this paper, we consider the permanence for a series of staged-structured consumer–resource models with the function response of so-called “prey-dependence”(resource-dependence) type. We show that the systems are permanent, if and only if the adult consumer's recruitment rate at the peak of resource abundance is more than its death rate. Our results indicate that the large consumer's maturation time delay will directly lead to its extinction. Furthermore, our arguments for the main results give a light for permanence in the general stage-structured consumer–resource systems.     

The structure of optimal solutions for harvesting a renewable resource

We consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy. Recommendations for Resource Managers :

• We have rigorously explored a standard optimal harvesting model and its steady states.
• We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution).
• With some modifications, similar results hold for a finite planning horizon.
• Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

     

Parallel systems under two sequential attacks with imperfect detection of the first attack outcome

The paper compares the efficiency of single and double attack against a system consisting of identical parallel elements. An attacker maximizes the system vulnerability (probability of total destruction). In order to destroy the system, the attacker distributes its constrained resource optimally across two attacks and chooses the number of elements to be attacked in the first attack. The attacker observes which elements are destroyed and not destroyed in the first attack and allocates its remaining resource into attacking the remaining elements in the second attack. The paper considers two types of identification errors: wrong identification of a destroyed element as not destroyed, and wrong identification of a not destroyed element as destroyed. First, the influence of the identification error probabilities on the optimal attack strategy against a system with a fixed number of elements is analysed. Thereafter, a minmax two-period game between the attacker and the defender is considered, in which the defender in the first period distributes its constrained resource between deploying redundant elements and protecting them against the attack in the second period. It is shown how the identification error probabilities affect the defence strategy.     

Separation in homogeneous systems with independent identical elements

The paper considers strategic defense and attack of a system which can be separated into independent identical homogeneous parallel elements. The defender distributes its resource between separation of the elements and their protection from outside attacks. The attacker distributes its effort evenly among all attacked elements. The vulnerability of each element is determined by a contest success function between the attacker and the defender. The defender can choose a subset of the elements to defend. The attacker does not know which elements are protected and can choose a number of randomly chosen elements to attack. Separation efficiency conditions are formulated dependent on the defender’s and attacker’s budgets, separation costs, contest intensity, and system demand. An algorithm for determining the optimal number of protected elements is suggested for the case when both the defender and the attacker can choose the number of protected and attacked elements freely. The article considers both the cases without and with performance redundancy. Illustrative numerical examples are presented.     

Mixed-integer linear programming for resource leveling problems

We consider project scheduling problems subject to general temporal constraints, where the utilization of a set of renewable resources has to be smoothed over a prescribed planning horizon. In particular, we consider the classical resource leveling problem, where the variation in resource utilization during project execution is to be minimized, and the so-called “overload problem”, where costs are incurred if a given resource-utilization threshold is exceeded. For both problems, we present new mixed-integer linear model formulations and domain-reducing preprocessing techniques. In order to strengthen the models, lower and upper bounds for resource requirements at particular points in time, as well as effective cutting planes, are outlined. We use CPLEX 12.1 to solve medium-scale instances, as well as instances of the well-known test set devised by Kolisch et al. (1999). Instances with up to 50 activities and tight project deadlines are solved to optimality for the first time.     

Individual <Emphasis Type="Italic">versus</Emphasis> overarching protection against strategic attacks

This article considers a system consisting of elements that can be protected and attacked individually and collectively. To destroy the system, the attacker must always penetrate/destroy the collective (overarching) protection. In the case of the parallel system, it also must destroy all elements, whereas in the case of the series system, it must destroy at least one element. Both the attacker and the defender have limited resources and can distribute these freely between the two types of protection. The attacker chooses the resource distribution and the number of attacked elements to maximize the system destruction probability. The defender chooses the resource distribution and the number of protected elements to minimize the system destruction probability. The bi-contest minmax game is formulated and its analytical solutions are presented and analysed. The asymptotical analysis of the solutions is presented. The influence of the game parameters on the optimal defence and attack strategies is discussed.     

Investigation of one-dimensional problem of resource distribution on an infinite time interval

Two controlled nonlinear dynamic models of resource distribution are considered in the case of an infinite horizon. Both of the models are studied on the basis of a known theoretical result that can only be applied without any constraints to the first problem. For both of the models, optimal solutions are found and their optimality is proved.     

Parallel systems under two sequential attacks with contest intensity variation

Single and double attacks against a system of parallel elements are analyzed. The vulnerability of each element depends on an attacker-defender contest success function. The contest intensity may change from the first to the second attack as determined by a contest intensity variation factor. The defender allocates its resource between deploying elements to provide redundancy, and protecting each element. The attacker allocates its resource optimally across the two attacks, may attack a subset of the elements in the first attack, observes which elements are destroyed in the first attack, and attacks all surviving elements in the second attack. A minmax two period game is analyzed where the defender moves first and the attacker moves second. The paper shows how the contest intensity variation factor affects the defense and attack strategies.     

Multi-mode resource constrained multi-project scheduling and resource portfolio problem

This paper introduces a multi-project problem environment which involves multiple projects with assigned due dates; activities that have alternative resource usage modes; a resource dedication policy that does not allow sharing of resources among projects throughout the planning horizon; and a total budget. Three issues arise when investigating this multi-project environment. First, the total budget should be distributed among different resource types to determine the general resource capacities, which correspond to the total amount for each renewable resource to be dedicated to the projects. With the general resource capacities at hand, the next issue is to determine the amounts of resources to be dedicated to the individual projects. The dedication of resources reduces the scheduling of the projects’ activities to a multi-mode resource constrained project scheduling problem (MRCPSP) for each individual project. Finally, the last issue is the efficient solution of the resulting MRCPSPs. In this paper, this multi-project environment is modeled in an integrated fashion and designated as the resource portfolio problem. A two-phase and a monolithic genetic algorithm are proposed as two solution approaches, each of which employs a new improvement move designated as the combinatorial auction for resource portfolio and the combinatorial auction for resource dedication. A computational study using test problems demonstrated the effectiveness of the solution approach proposed.     

Information resource planning for a health-care system using an AHP-based goal programming method

This paper presents a goal programming (GP) model which aids in allocating a health-care system's information resources pertinent to strategic planning. The model is developed based on the data obtained from a major health-care system in the United States. The overall objective is to design and evaluate a model for effective information resource planning in a health-care system. The proposed model: (1) utilizes a GP approach to reflect the multiple, conflicting goals of the health-care system; (2) employs a GP solution process to reflect multi-dimensional aspects of the resource allocation planning; and (3) allows for some degree of flexibility of decision-making with respect to resource allocation. The goals are decomposed and prioritized with respect to the corresponding criteria using the analytic hierarchy process (AHP). The model result is derived and discussed. This GP model facilitates decision-making planning process and managerial policy in health-care information resources planning and similar planning settings.     

Single machine scheduling with resource allocation and learning effect considering the rate-modifying activity

This paper addresses a single machine scheduling problem in which the actual job processing times are determined by resource allocation function, its position in a sequence and a rate-modifying activity simultaneously. We discuss two objective functions with two resource allocation functions under the consideration of a rate-modifying activity. We show that the problems are solvable in O(n⁴)$O(n^4)$ time for a linear resource allocation function and are solvable in O(n²logn)$O(n^2\mathit{logn})$ time for a convex resource allocation function.     

Software rejuvenation and resource reservation policies for optimizing server resource availability using cyclic nonhomogeneous Markov chains

Software rejuvenation is modeled in a client–server system, which provides resources to priority classes of users. To assure availability, resource reservation policies are adopted for the higher priority classes. In addition software rejuvenation is proposed to optimize resource availability. The system is modeled by a cyclic nonhomogeneous Markov chain to capture the variation of the arrival and service rates during a day period. An optimization problem is solved based on a similar previous work and given the optimal resource reservation policy obtained by its solution, rejuvenation is performed and the optimal rejuvenation policy is determined. As a measure of resource availability the blocking probability of each priority class is used. Performability indicators expressing the total cost are also derived, with respect to the optimal resource reservation and optimal rejuvenation policies, to examine whether rejuvenation benefits the system in terms of cost. To derive the blocking probabilities, the limiting probability distribution is computed using explicit generalized approximate inverse preconditioning for solving efficiently sparse linear systems of algebraic equations. Copyright © 2012 John Wiley & Sons, Ltd.     

A genetic approach for strategic resource allocation planning

Enterprises often implement a measurement system to monitor their march towards their strategic goals. Although this way it is possible to assess the progress of each goal, there is no structured way to reconsider resource allocation to those goals and to plan an optimal (or near optimal) allocation scheme. In this study we propose a genetic approach to match each goal with an autonomous entity (agent) with a specific resource sharing behavior. The overall performance is evaluated through a set of functions and genetic algorithms are used to eventuate in approximate optimal behavior’s schemes. To outline the strategic goals of the enterprise we used the balanced scorecard method. Letting agents deploy their sharing behavior over simulation time, we measure the scorecard’s performance and detect distinguished behaviors, namely recommendations for resource allocation.     

NATURAL RESOURCE ECONOMICS UNDER UNCERTAINTY: EFFECT OF FUTURES MARKETS

The effects of hedging and time-dependent price and geological uncertainty on the behavior of a firm exploiting a nonrenewable natural resource are derived. Contrasts in behavior with and without hedging and uncertainty are identified and discussed. Much of the analysis centers on the firm's implicit value of its in situ reserves, marginal user cost. The main result is that time-dependent uncertainty lowers the implicit value of reserves. Hedging ameliorates this effect somewhat. Under some conditions even with risk reducing hedging, the firm tilts its extraction and development paths toward the present and may also shorten its decision-making time horizon.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal resource allocation program in a two-sector economic model with a Cobb-Douglas production function

We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canonical form by a scaling of the phase variables and time. We prove the optimality of the extremal solution constructed on the basis of the maximum principle. The solution of the boundary value problem of the maximum principle is constructed in closed form for three cases of location of the initial plant state.     

Optimal defence of single object with imperfect false targets

The paper considers an object exposed to external intentional attacks. The defender distributes its resource between deploying false targets and protecting the object. The false targets are not perfect and there is a nonzero probability that a false target can be detected by the attacker. Once the attacker has detected a certain number of false targets, it ignores them and chooses such number of undetected targets to attack that maximizes the probability of the object destruction. The defender decides how many false targets to deploy in order to minimize the probability of the object destruction assuming that the attacker uses the most harmful strategy to attack. The optimal number of false targets and the optimal number of attacked targets are obtained for the case of single and multiple types of the false targets. A methodology of finding the optimal defence strategy under uncertain contest intensity is suggested.     

Optimal resource allocation in a two-sector economic model with singular regimes

The article considers the problem of resource allocation in a two-sector economic model with a nonlinear production function of a special type. The main mathematical apparatus is Pontryagin’s maximum principle, i.e., the theorem on necessary conditions of optimality. It is shown that in the given problem the maximum principle provides a necessary and sufficient condition of optimality. A possible singular solution of the problem is found. An extremum solution is constructed in explicit form under various assumptions about the initial values. A “sufficiently long” planning horizon is assumed. An alternative approach is described, which does not use the maximum principle and instead investigates the integral representation of the optimand functional. The detailed theoretical investigation of the problem is accompanied by numerous illustrations.