We study the problem of online resource allocation, where multiple customers arrive sequentially and the seller must irrevocably allocate resources to each incoming customer while also facing a procurement cost for the total allocation. Assuming resource procurement follows an a priori known marginally increasing cost function, the objective is to maximize the reward obtained from fulfilling the customers' requests sans the cumulative procurement cost. We analyze the competitive ratio of a primal-dual algorithm in this setting, and develop an optimization framework for synthesizing a surrogate function for the procurement cost function to be used by the algorithm, in order to improve the competitive ratio of the primal-dual algorithm. Our first design method focuses on polynomial procurement cost functions and uses the optimal surrogate function to provide a more refined bound than the state of the art. Our second design method uses quasiconvex optimization to find optimal design parameters for a general class of procurement cost functions. Numerical examples are used to illustrate the design techniques. We conclude by extending the analysis to devise a posted pricing mechanism in which the algorithm does not require the customers' preferences to be revealed.
Flemish Institute for Technological Research（弗拉芒技术研究院）
In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-aris…
This paper studies the problem of procuring diverse resources in a forward market to cover a set $\bf{E}$ of uncertain demand signals $\bf{e}$. We consider two scenarios: (a) $\bf{e}$ is revealed all at once by an oracle (b) $\bf{e}$ reveals itself causally. Each scenario induces an optimal procurement cost. The ratio between these two costs is defined as the {\em price of causality}. It captures the additional cost of not knowing the future values of the uncertain demand signal. We consider two application contexts: procuring energy reserves from a forward capacity market, and purchasing virt…
The large shares of wind power generation in electricity markets motivate higher levels of operating reserves. However, current reserve sizing practices fail to account for important topological aspects that might hinder their deployment, thus resulting in high operating costs. Zonal reserve procurement mitigates such inefficiencies, however, the way the zones are defined is still open to interpretation. This paper challenges the efficiency of predetermined zonal setups that neglect the location of stochastic power production in the system, as well as the availability, cost and accessibility o…
Motivated by the application of energy storage management in electricity markets, this paper considers the problem of online linear programming with inventory management constraints. Specifically, a decision maker should satisfy some units of an asset as her demand, either form a market with time-varying price or from her own inventory. The decision maker is presented a price in slot-by-slot manner, and must immediately decide the purchased amount with the current price to cover the demand or to store in inventory for covering the future demand. The inventory has a limited capacity and its cri…
We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.
This paper studies the SI1SI2S spreading model of two competing behaviors over a bilayer network. We address the problem of determining resource allocation strategies which design a spreading network so as to ensure the extinction of a selected process. Our discussion begins by extending the SI1SI2S model to edge-dependent infection and node-dependent recovery parameters with generalized graph topologies, which builds upon prior work that studies the homogeneous case. We then find conditions under which the mean-field approximation of a chosen epidemic process stabilizes to extinction exponent…
We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint. The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step. Of particular interest are classic experiment design problems in the online setting, with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially. We analyze two greedy primal-dual algorithms and provide bounds on their competitive ratios. Our analysis re…
The significant presence of demand charges in electric bills motivates large-load customers to utilize energy storage to reduce the peak procurement from the grid. We herein study the problem of energy storage allocation for peak minimization, under the online setting where irrevocable decisions are sequentially made without knowing future demands. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. We apply the CR-Pursuit framework and address the challenges …
Monotone Allocations without Single-Crossing: When to Bunch and When to Jump
Instituto Nacional de Matemática Pura e Aplicada（巴西国家纯数学和应用数学研究所）；Graduate School of Economics, Getúlio Vargas Foundation（格特利奥·瓦加斯基金会经济研究生院）；Faculdade de Ciências Econômicas, UERJ（里约热内卢州立大学经济科学学院）；Ibmec（伊梅克斯）
Cainiao Network（菜鸟网络）；City University of Hong Kong（香港城市大学）；University of Science and Technology of China（中国科学技术大学）
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the two-sided constraints affect the prospects of resource consumption more severely. As a result, only limited violations of constraints or pessimistic competitive bounds could be guaranteed. To tackle the challenge, we define a measure of feasibility $ξ^*$ to evaluate the hardness of this problem, and estimate this measurement by an optimization routine with theoret…
We study an online resource allocation problem under uncertainty about demand and about the reward of each type of demand (agents) for the resource. Even though dealing with demand uncertainty in resource allocation problems has been the topic of many papers in the literature, the challenge of not knowing rewards has been barely explored. The lack of knowledge about agents' rewards is inspired by the problem of allocating units of a new resource (e.g., newly developed vaccines or drugs) with unknown effectiveness/value. For such settings, we assume that we can \emph{test} the market before the…
The goal of this paper is to develop a generic framework for converting modern optimization algorithms into mechanisms where inputs come from self-interested agents. We focus on aggregating preferences from $n$ players in a context without money. Special cases of this setting include voting, allocation of items by lottery, and matching. Our key technical contribution is a new meta-algorithm we call \apex (Adaptive Pricing Equalizing Externalities). The framework is sufficiently general to be combined with any optimization algorithm that is based on local search. We outline an agenda for studyi…
Resource allocation plays a central role in many networked systems such as smart grids, communication networks and urban transportation systems. In these systems, many constraints have physical meaning and having feasible allocation is often vital to avoid system breakdown. Hence, algorithms with asymptotic feasibility guarantees are often insufficient since it is impractical to run algorithms for an infinite number of rounds. This paper proposes a distributed feasible method (DFM) for safe resource allocation based on barrier functions. In DFM, every iterate is feasible and thus safe to imple…
Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic feasibility guarantees for the iterates, since overallocation of resources easily causes systems to break down. In this paper, we develop a distributed resource reallocation algorithm where every iteration produces a feasible allocation. The algorithm is fully distributed in the sense that nodes communicate only with neighbors over a given communication network.…
The high proportions of demand charges in electric bills motivate large-power customers to leverage energy storage for reducing the peak procurement from the outer grid. Given limited energy storage, we expect to maximize the peak-demand reduction in an online fashion, challenged by the highly uncertain demands and renewable injections, the non-cumulative nature of peak consumption, and the coupling of online decisions. In this paper, we propose an optimal online algorithm that achieves the best competitive ratio, following the idea of maintaining a constant ratio between the online and the op…
Demand dispatch is the science of extracting virtual energy storage through the automatic control of deferrable loads to provide balancing or regulation services to the grid, while maintaining consumer-end quality of service (QoS). The control of a large collection of heterogeneous loads is in part a resource allocation problem, since different classes of loads are valuable for different services. The goal of this paper is to unveil the structure of the optimal solution to the resource allocation problem and to investigate short term market implications. It is found that the marginal cost for …
In this paper, we study multi-agent systems with decentralized resource allocations. Agents have local demand and resource supply, and are interconnected through a network designed to support sharing of the local resource; and the network has no external resource supply. It is known from classical welfare economics theory that by pricing the flow of resource, balance between the demand and supply is possible. Agents decide on the consumed resource, and perhaps further the traded resource as well, to maximize their payoffs considering both the utility of the consumption, and the income from the…
We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibriu…
In the Nordic region, many interconnectors are formed by HVDC links, as Scandinavia, Continental Europe and the Baltic region are non-synchronous AC systems. This paper presents two cost benefit analyses on the utilization of HVDC interconnectors in the Nordic countries: in the first we investigate the utilization of HVDC interconnectors for reserve procurement and, in the second, we assess the implementation of implicit grid losses on HVDC interconnectors in the day-ahead market. The first analysis is motivated by real events in 2018 where the inertia of the Nordic system dropped below a crit…
Online optimization covers problems such as online resource allocation, online bipartite matching, adwords (a central problem in e-commerce and advertising), and adwords with separable concave returns. We analyze the worst case competitive ratio of two primal-dual algorithms for a class of online convex (conic) optimization problems that contains the previous examples as special cases defined on the positive orthant. We derive a sufficient condition on the objective function that guarantees a constant worst case competitive ratio (greater than or equal to $\frac{1}{2}$) for monotone objective …
