Max-min resource allocation

A problem is considered of the allocation of resources so as to maximize the minimum return from several activities. Optimality conditions are given for the case of a single resource, and are used to derive a solution algorithm. Problems with several resources cannot be solved by resourcewise optimization. Concave return functions are treated approximately by linear programming, and optimality or almost optimality of any feasible solution to such a problem can be evaluated by the solution of a linear programming problem. The evaluation measure is extended to certain feasible solutions of problems which have continuous, but not necessarily concave, return functions. A numerical example is given.     

Fuzzy resource management analysis

Traditionally, the efficient and productive delivery of services is a major goal of public institutions. This is especially true in the law enforcement industry. Here, the management of a set of dynamic resources (police patrol personnel) is central to the delivery of services. In the past there have been two major perspectives towards the management of low enforcement resources: first, ignoring all patterns in demands resources are distributed equally across time and space. Second, resources are deployed according to the proportionate distribution of demands. In both of these models the resources are manipulated or controlled according to an algorithm derived independently from demand patterns. These models are highly vulnerable to shifts in demand patterns and can be strategically inefficient and tactically unstable. In this paper a new algorithmic process is defined for the strategic and tactical evaluation of resource needs for police patrolling which combines deployment and control strategies, and simulates combinations of the strategies for comparative analysis. It was discovered that the degree of reliance upon the analysis of future resource usage and the accuracy of the projection of the future demands had a significant impact on the performance of the methodologies studied. This process can be used to draw general conclusions about patrolling systems.     

Optimal resource allocation in presidential primaries

A model for the optimal allocation of resources in presidential primaries is described, under the assumption that two candidates seek to maximize their expected delegate vote in a sequential game that allows for momentum transfer from earlier to later contests. Specifically, the model assumes that the probability that a voter in a primary state votes for a particular candidate is a function of both the resources that candidate and his opponent allocate to that primary and their performances in the immediately preceding primary - and indirectly on all earlier primaries. Given that the candidates make equal (optimal) allocations to each primary, a local maximum, which heavily emphasizes the earlier primaries, is found. Several modifications in the basic model are discussed. Preliminary financial expenditure data are used to test the basic model for the 1976 primaries, and some cursory comparisons with 1980 are made. Possible normative implications of changes in the primary rules are briefly considered, particularly with respect to inequities the present rules seem to engender.     

Product development resource allocation with foresight

Shortening project duration is critical to product development project success in many industries. As a primary driver of progress and an effective management tool, resource allocation among development activities can strongly influence project duration. Effective allocation is difficult due to the inherent closed loop flow of development work and the dynamic demand patterns of work backlogs. The Resource Allocation Policy Matrix is proposed as a means of describing resource allocation policies in dynamic systems. Simple system dynamics and control theoretic models of resource allocation in a product development context are developed. The control theory model is used to specify a foresighted policy, which is tested with the system dynamics model. The benefits of foresight are found to reduce with increasing complexity. Process concurrence is found to potentially reverse the impact of foresight on project duration. The model structure is used to explain these results and future research topics are discussed.     

Minmax regret linear resource allocation problems

For minmax regret versions of some basic resource allocation problems with linear cost functions and uncertain coefficients (interval-data case), we present efficient (polynomial and pseudopolynomial) algorithms. As a by-product, we obtain an algorithm for the interval data minmax regret continuous knapsack problem.     

Centralized resource allocation with stochastic data

Data Envelopment Analysis (DEA) is a technique based on mathematical programming for evaluating the efficiency of homogeneous Decision Making Units (DMUs). In this technique inefficient DMUs are projected on to the frontier which constructed by the best performers. Centralized Resource Allocation (CRA) is a method in which all DMUs are projected on to the efficient frontier through solving just one DEA model. The intent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA) in order to allocate centralized resources where inputs and outputs are stochastic. The concept discussed throughout this paper is illustrated using the aforementioned example.     

Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.     

Approximation algorithms for dynamic resource allocation

We consider a problem of allocating limited quantities of M types of resources among N independent activities that evolve over T epochs. In each epoch, we assign to each activity a task which consumes resources, generates utility, and determines the subsequent state of the activity. We study the complexity of, and approximation algorithms for, maximizing average utility.     

Optimal resource allocation across related channels

In this paper, we consider resource allocation strategies of a limited resource across two related channels in a multi-period setting. We study a stochastic control problem where the objective is to determine the optimal limited resource allocation policy across two related channels and optimal transshipment policy between these two channels. We characterize some structural results of the optimal resource allocation policy and show that it is determined by three monotone curves.     

Solution of a resource allocation game

Translated from Vychislitel'nye Sistemy i Voprosy Prinyatiya Reshenii, pp. 180–183, 1991.     

Centralized resource allocation for enhanced Russell models

This paper proposes a centralized resource allocation (CRA) model for the enhanced Russell model. All the DMUs can be easily projected onto the efficient frontier by solving only one model. This projection can be made by transforming the proposed model to a linear programming problem. In this paper, instead of non-radially increasing or decreasing the inputs or outputs individually, we increase or decrease non-radially all of the inputs and outputs at the same time. By solving a single model, we can provide targets for all DMUs. By the proposed approximation, different targets can be found for all DMUs, as compared to those obtained by the previous approximations. The proposed model can be developed to CRA models. Finally, an applied example emphasizes the importance of the proposed model.     

Interactive model-based search with reactive resource allocation

We revisit the interactive model-based approach to global optimization proposed in Wang and Garcia (J Glob Optim 61(3):479–495, 2015) in which parallel threads independently execute a model-based search method and periodically interact through a simple acceptance-rejection rule aimed at preventing duplication of search efforts. In that paper it was assumed that each thread successfully identifies a locally optimal solution every time the acceptance-rejection rule is implemented. Under this stylized model of computational time, the rate of convergence to a globally optimal solution was shown to increase exponentially in the number of threads. In practice however, the computational time required to identify a locally optimal solution varies greatly. Therefore, when the acceptance-rejection rule is implemented, several threads may fail to identify a locally optimal solution. This situation calls for reallocation of computational resources in order to speed up the identification of local optima when one or more threads repeatedly fail to do so. In this paper we consider an implementation of the interactive model-based approach that accounts for real time, that is, it takes into account the possibility that several threads may fail to identify a locally optimal solution whenever the acceptance-rejection rule is implemented. We propose a modified acceptance-rejection rule that alternates between enforcing diverse search (in order to prevent duplication) and reallocation of computational effort (in order to speed up the identification of local optima). We show that the rate of convergence in real-time increases with the number of threads. This result formalizes the idea that in parallel computing, exploitation and exploration can be complementary provided relatively simple rules for interaction are implemented. We report the results from extensive numerical experiments which are illustrate the theoretical analysis of performance.     

Optimality conditions in a resource allocation problem

Translated from Vychislitel'nye Kompleksy i Modelirovanie Slozhnykh Sistem, pp. 138–141, Moscow State University, 1989.     

On swarm-level resource allocation in BitTorrent communities

BitTorrent is a peer-to-peer computer network protocol for sharing content in an efficient and scalable way. Modeling and analysis of the popular private BitTorrent communities has become an active area of research. In these communities users are strongly incentivized to contribute their resources, i.e., to share their files. In BitTorrent terminology, users who have finished downloading files and stay online to share these files with others in the network are called seeders. The combination of seeders and downloaders of a file is called a swarm. In this paper we examine and evaluate the efficiency of the resource allocation of seeders in multiple swarms. This is formulated as an integer linear fractional programming problem. The evaluation is done on traces representing two existing BitTorrent communities. We find that in communities, particularly with low users-to-files ratio (which is typically the case), there is room for improvement.     

Optimal resource allocation for security in reliability systems

Recent results have used game theory to explore the nature of optimal investments in the security of simple series and parallel systems. However, it is clearly important in practice to extend these simple security models to more complicated system structures with both parallel and series subsystems (and, eventually, to more general networked systems). The purpose of this paper is to begin to address this challenge. While achieving fully general results is likely to be difficult, and may require heuristic approaches, we are able to find closed-form results for systems with moderately general structures, under the assumption that the cost of an attack against any given component increases linearly in the amount of defensive investment in that component. These results have interesting and sometimes counterintuitive implications for the nature of optimal investments in security.     

Identifying Pareto-optimal settlements for two-party resource allocation negotiations

We explore models to identify Pareto-optimal outcomes in two-party multiple program resource allocation post-settlement settlement negotiations. The approximation of the contract curve, that is the set of Pareto-optimal outcomes, is also discussed. We consider the case where the parties split a shared hard resource. An application of the models to a resource allocation problem in a Finnish university is also discussed.     

A single-resource allocation problem with Poisson resource requirements

We consider a stochastic resource allocation problem that generalizes the knapsack problem to account for random item weights that follow a Poisson distribution. When the sum of realized weights exceeds capacity, a penalty cost is incurred. We wish to select the items that maximize expected profit. We provide an effective solution method and illustrate the advantages of this approach via computational experiments.     

A dynamic approach to multiple-objective resource allocation problem

A new approach using dynamic programming is developed for solving the multiple-objective resource allocation problem. There are two key issues being addressed in this approach. The first one is to develop a methodology of fuzzy evaluation and fuzzy optimization for multiple-objective systems. The procedure of getting the marginal evaluation for each objective and aggregating them synthetically into a global evaluation is presented in this paper. The second one is to design a dynamic optimization algorithm by incorporating the method of fuzzy evaluation and fuzzy optimization with the conventional dynamic programming technique. A characteristic feature of the approach presented is that various objectives are synthetically considered by the fuzzy systematic technique instead of the frequently employed weighted-average method. Numeric examples are also given to clarify the developed approach and to demonstrate its effectiveness.     

A lexicographic minimax algorithm for multiperiod resource allocation

Resource allocation problems are typically formulated as mathematical programs with some special structure that facilitates the development of efficient algorithms. We consider a multiperiod problem in which excess resources in one period can be used in subsequent periods. The objective minimizes lexicographically the nonincreasingly sorted vector of weighted deviations of cumulative activity levels from cumulative demands. To this end, we first develop a new minimax algorithm that minimizes the largest weighted deviation among all cumulative activity levels. The minimax algorithm handles resource constraints, ordering constraints, and lower and upper bounds. At each iteration, it fixes certain variables at their lower bounds, and sets groups of other variables equal to each other as long as no lower bounds are violated. The algorithm takes advantage of the problem's special structure; e.g., each term in the objective is a linear decreasing function of only one variable. This algorithm solves large problems very fast, orders of magnitude faster than well known linear programming packages. (The latter are, of course, not designed to solve such minimax problems efficiently.) The lexicographic procedure repeatedly employs the minimax algorithm described above to solve problems, each of the same format but with smaller dimension.     

A generalized DEA model for centralized resource allocation

In this paper, we introduced a new generalized centralized resource allocation model which extends Lozano and Villa’s and Asmild et al.’s models to a more general case. In order to uncover the sources of such total input contraction in the generalized centralized resource allocation model, we applied the structural efficiency to further decompose it into three components: the aggregate technical efficiency, the aggregate allocative efficiency and re-transferable efficiency components. The proposed models are not only flexible enough for the central decision-maker to adjust the inputs and outputs to achieve the total input contraction but also identify the sources of such total input contraction, thereby giving rise to an important interpretation and understanding of the generalized centralized resource allocation model. Finally, an empirical example is used to illustrate the approach.