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Modelling and solving resource allocation problems via a dynamic programming approach

INTERNATIONAL JOURNAL OF CONTROL 2021年第6期94卷 1544-1555页

作者： Forootani, Ali Tipaldi, Massimo Zarch, Majid Ghaniee Liuzza, Davide Glielmo, Luigi Univ Sannio Dept Engn I-82100 Benevento Italy Univ Sci & Technol Dept Elect Engn Tehran Iran

In this paper, resource allocation problems are formulated via a set of parallel birth-death processes (BDP). This way, we can model the fact that resources can be allocated to customers at different prices, and that customers can hold them as long as they like. More specifically, a discretisation approach is applied to model resource allocation problems as a set of discrete-time BDPs, which are then integrated into one Markov decision process. The stochastic dynamics of the resulting system are also investigated. As a result, revenue management becomes a stochastic decision-making problem, where price managers can propose suitable prices to the allocation requests such that the maximum expected total revenue is obtained at the end of a predefined finite time horizon. Stochastic Dynamic Programming is employed to solve the related optimisation problem with the support of an ad-hoc Matlab-based application. Several simulations are performed to prove the effectiveness of the proposed model and the optimisation approach.

关键词： resource allocation problems stochastic dynamic programming Markov chain Markov decision process birth-death process

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A multi-objective evolutionary algorithm to exploit the similarities of resource allocation problems

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JOURNAL OF SCHEDULING 2008年第6期11卷 405-419页

作者： Datta, Dilip Fonseca, Carlos M. Deb, Kalyanmoy Natl Inst Technol Silchar Dept Mech Engn Silchar 788010 India Univ Algarve DEEI Fac Ciencias & Tecnol P-8005139 Faro Portugal Indian Inst Technol Dept Mech Engn Kanpur 208016 Uttar Pradesh India

The complexity of a resource allocation problem (RAP) is usually NP-complete, which makes an exact method inadequate to handle RAPs, and encourages heuristic techniques to this class of problems for obtaining approximate solutions in polynomial time. Different heuristic techniques have already been investigated for handling various RAPs. However, since the properties of an RAP can help in characterizing other RAPs, instead of individual solution techniques, the similarities of different RAPs might be exploited for developing a common solution technique for them. Two RAPs of quite different nature, namely university class timetabling and land-use management, are considered here for such a study. The similarities between the problems are first explored, and then a common multi-objective evolutionary algorithm (a kind of heuristic techniques) for them is developed by exploiting those similarities. The algorithm is problem-dependent to some extent and can easily be extended to other similar RAPs. In the present work, the algorithm is applied to two real instances of the considered problems, and its properties are derived from the obtained results.

关键词： Multi-objective optimization Evolutionary algorithm resource allocation problems Class timetabling Land-use management

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A Multi-Agent Architecture for a Web-based DSS Application to resource allocation problems in a Flow-Shop Manufacturing System

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JOURNAL OF DECISION SYSTEMS 2011年第4期20卷 443-466页

作者： Taghezout, Noria Bessedik, Imene Adla, Abdelkader Univ Oran Dept Comp Sci Oran Algeria

This paper proposes an agent-based architecture for a Web-based DSS. The basic research consideration is that Internet facilitates access to data, information, and knowledge sources available online. The proposed DSS mainly includes five components: Analyzer Agent (AA), Proposal Agent (PrA), resource agent (RA), Production Agent (PA), and Coordinator Agent (CA). In particular, the agents are used to collect information and generate alternatives that would allow the user to focus on significant solutions. They communicate through the JADE platform, and exploit the potential advantages of Web 2.0 tools and Web services in carrying out their different tasks. We also present in this work the coordination protocol that supports the distributed and decentralized task achievement. The functions of each component are discussed and a corresponding prototype system is developed. Finally, some simple scenarios are given for the purpose of illustrating the feasibility of our approach.

关键词： Coordinator Agent (CA) Decision Support System (DSS) Multi-Agent Systems (MAS) resource allocation problems Web 2.0 Web-based DSS

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The Online Best Reply Algorithm for resource allocation problems 12th

The Online Best Reply Algorithm for Resource Allocation Prob...

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12th International Symposium on Algorithmic Game Theory (SAGT)

作者： Klimm, Max Schmand, Daniel Toennis, Andreas HU Berlin Operat Res Berlin Germany Goethe Univ Frankfurt Inst Comp Sci Frankfurt Germany Univ Bonn Dept Comp Sci Bonn Germany

ISBN: (纸本)9783030304737;9783030304720

We study the performance of a best reply algorithm for online resource allocation problems with a diseconomy of scale. In an online resource allocation problem, we are given a set of resources and a set of requests that arrive in an online manner. Each request consists of a set of feasible allocations and an allocation is a set of resources. The total cost of an allocation vector is given by the sum of the resources' costs, where each resource's cost depends on the total load on the resource under the allocation vector. We analyze the natural online procedure where each request is allocated greedily to a feasible set of resources that minimizes the individual cost of that particular request. In the literature, this algorithm is also known as a one-round walk in congestion games starting from the empty state. For unweighted resource allocation problems with polynomial cost functions with maximum degree d, upper bounds on the competitive ratio of this greedy algorithm were known only for the special cases d is an element of {1, 2, 3}. In this paper, we show a general upper bound on the competitive ratio of d(d/W(1.2d - 1/d+1))(d+1) for the unweighted case where W denotes the Lambert-W function on R->= 0. For the weighted case, we show that the competitive ratio of the greedy algorithm is bounded from above by (d/W(d/d+1))(d+1).

关键词： Online algorithms resource allocation problems Congestion games

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Integration of decision levels in operating room scheduling problems: Systematic review and proposition of a decision support framework

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COMPUTERS & OPERATIONS RESEARCH 2025年 180卷

作者： de Melo, Igor Eduardo Santos Fogliatto, Flavio Sanson Univ Fed Rio Grande do Sul Ind Engn Dept Ave Osvaldo Aranha 995th Floor BR-90035190 Porto Alegre Brazil

resource allocation problems are a significant subset of optimization problems widely present in the healthcare industry. Notably, the Operating Room Scheduling Problem (ORSP) is prominent in literature due to its substantial cost and revenue implications. ORSP is structured into three hierarchical decision levels: strategic, tactical and operational, with higher-level decisions influencing subsequent ones. While most studies focus on single decision levels, there has been a growing interest in integrated models, as these offer a more holistic view and often result in better outcomes, despite their complexity of resolution. Although various literature reviews have explored different aspects of ORSP, few have focused on models integrating multiple decision levels. This study addresses that gap by systematically reviewing the literature focusing on contributions presenting mathematical programming models and optimization algorithms that simultaneously address multiple decision levels of the ORSP. Following the PRISMA 2020 protocol, the review spans works published until October 2024, totaling 46 articles. It outlines objectives, characteristics, solution approaches, and identifies gaps in literature. Additionally, a decision framework summarizing the identified integration levels is proposed.

关键词： resource allocation problems Operating room planning and scheduling Multiple decision level integration Mathematical programming models Systematic literature review

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resource optimisation using bandwidth-power product for multiple-input multiple-output orthogonal frequency-division multiplexing access system in cognitive radio networks

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IET COMMUNICATIONS 2015年第14期9卷 1710-1720页

作者： Chen, Bo Zhao, Minjian Zhang, Lei Lei, Ming Zhejiang Univ Dept Informat Sci & Elect Engn Hangzhou 310027 Peoples R China

This study investigates resource allocation problems for a point-to-point multi-carrier multiple-input multiple-output cognitive radio network. Different from conventional resource optimisation problems, a joint power and bandwidth resource optimisation framework using the novel optimisation metric, namely bandwidth-power product, is developed. Besides, rate requirement of the secondary system is satisfied, and the interferences introduced to the primary users (PUs) are below threshold of tolerance. The optimal source precoding matrix is designed and two methods, namely the project-channel singular value decomposition (SVD) and direct-channel SVD methods, are applied to satisfy interference power constraints for PUs. Then the unified power and channel allocation problem is derived and found to be a mixed-integer programming problem. Hence, a sub-optimal and tractable algorithm with low complexity is proposed. The innovative idea is to determine the channel resource budget by selecting the best channels, where the criterion for evaluating the quality of channel is detailed discussed. Then the power optimisation subproblem and channel allocation subproblem can be performed independently using the Lagrange-duality theory and Gauss-Newton method, respectively. The simulation results show significant improvement in spectral efficiency by using this framework compared to classical power optimisation framework using the waterfilling scheme.

关键词： resource allocation MIMO communication frequency division multiple access cognitive radio singular value decomposition integer programming bandwidth-power product multiple-input multiple-output orthogonal frequency-division multiplexing access system resource allocation problems point-to-point multi-carrier multiple-input multiple-output cognitive radio network joint power and bandwidth resource optimisation framework optimisation metric primary users optimal source precoding matrix project-channel singular value decomposition SVD mixed-integer programming problem Lagrange-duality theory Gauss-Newton method

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Revenue management policies for the truck rental industry

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2012年第1期48卷 202-214页

作者： Guerriero, Francesca Miglionico, Giovanna Olivito, Filomena Univ Calabria Dept Elect Informat & Syst I-87036 Arcavacata Di Rende Italy

In this paper, we consider the problem of managing a fleet of trucks with different capacity to serve the requests of different customers that arise randomly over time. The problem is formulated via dynamic programming. Linear programming approximations of the problem are presented and their solutions are exploited to develop partitioned booking limits and bid prices policies. The numerical experiments show that the proposed policies can be profitably used in supporting the decision maker. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： resource allocation problems Dynamic programming Revenue management Booking limits Bid prices

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A FUZZY DYNAMIC APPROACH TO THE MULTICRITERION resource-allocation PROBLEM

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FUZZY SETS AND SYSTEMS 1995年第2期69卷 115-124页

作者： HUSSEIN, ML ABOSINNA, MA MENOUFIA UNIV FAC ENGNDEPT MATHSHIBIN AL KAWMEGYPT

In this paper, a new approach using fuzzy dynamic programming is proposed for solving the multiple criteria resource allocation problems, It has been concluded that solutions obtained by this approach are always efficient, hence an ''optimal'' compromise solution can be introduced. A characteristic feature of the presented approach is that the objective function (scalarization) can be taken into account by using fuzzy set notations. A numerical example is given to clarify the developed approach.

关键词： FUZZY SET THEORY MULTIPLE CRITERIA FUZZY DYNAMIC PROGRAMMING resource allocation problems EFFICIENT SOLUTIONS

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Random Coordinate Descent Algorithms for Multi-Agent Convex Optimization Over Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第8期58卷 2001-2012页

作者： Necoara, Ion Univ Politehn Bucuresti Dept Automat Control & Syst Engn Bucharest 060042 Romania

In this paper, we develop randomized block-coordinate descent methods for minimizing multi-agent convex optimization problems with linearly coupled constraints over networks and prove that they obtain in expectation an accurate solution in at most O(1/lambda(2)(Q)epsilon) iterations, where lambda(2)(Q) is the second smallest eigenvalue of a matrix Q that is defined in terms of the probabilities and the number of blocks. However, the computational complexity per iteration of our methods is much simpler than the one of a method based on full gradient information and each iteration can be computed in a completely distributed way. We focus on how to choose the probabilities to make these randomized algorithms to converge as fast as possible and we arrive at solving a sparse SDP. Analysis for rate of convergence in probability is also provided. For strongly convex functions our distributed algorithms converge linearly. We also extend the main algorithm to a more general random coordinate descent method and to problems with more general linearly coupled constraints. Preliminary numerical tests confirm that on very large optimization problems our method is much more numerically efficient than methods based on full gradient.

关键词： Distributed control linearly coupled constraints random coordinate descent rate of convergence resource allocation problems smooth convex optimization

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Allocating resources via price management systems: a dynamic programming-based approach

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INTERNATIONAL JOURNAL OF CONTROL 2021年第8期94卷 2123-2143页

作者： Forootani, Ali Liuzza, Davide Tipaldi, Massimo Glielmo, Luigi Univ Sannio Dept Engn Piazza Roma 21 I-82100 Benevento Italy ENEA Fus & Nucl Safety Dept Frascati Rome Italy

In this paper, a novel model for price management systems in resource allocation problems is proposed. Stochastic customer requests for resource allocations and releases are modelled as constrained parallel Birth-Death Processes (BDP). We address both instant (i.e. the customer requires a resource to be allocated immediately) and advance (i.e. the customer books a resource for future use) reservation requests, the latter with both bounded and unbounded time interval options. Algorithms based on Dynamic Programming (DP) principles are proposed for the calculation of suitable price profiles. At the core of such algorithms, there is the resolution of stochastic optimisation problems. In particular, the maximisation of the expected total revenue is formulated via a constrained Stochastic Dynamic Programming (SDP) approach, which becomes time-variant in case of advance reservation requests. Approximate Dynamic Programming (ADP) techniques are adopted in case of large state spaces. Simulations are performed to show the effectiveness of the proposed models and the related algorithms.

关键词： Price management systems resource allocation problems stochastic dynamic programming Markov decision process approximate dynamic programming

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