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In the resource allocation problem (RAP), the goal is to divide a given amount of a resource over a set of activities while minimizing the cost of this allocation and possibly satisfying constraints on allocations to subsets of the activities. Most solution approaches for the RAP and its extensions allow each activity to have its own cost function. However, in many applications, often the structure of the objective function is the same for each activity, and the difference between the cost functions lies in different parameter choices, such as, for example, the multiplicative factors. In this article, we introduce a new class of objective functions that captures a significant number of the objectives occurring in studied applications. These objectives are characterized by a shared structure of the cost function depending on two input parameters. We show that, given the two input parameters, there exists a solution to the RAP that is optimal for any choice of the shared structure. As a consequence, this problem reduces to the quadratic RAP, making available the vast amount of solution approaches and algorithms for the latter problem. We show the impact of our reduction result on several applications, and in particular, we improve the best-known worst-case complexity bound of two problems in vessel routing and processor scheduling from [Formula: see text] to [Formula: see text]. Summary of Contribution: The resource allocation problem (RAP) with submodular constraints and its special cases are classic problems in operations research. Because these problems are studied in many different scientific disciplines, many conceptual insights, structural properties, and solution approaches have been reinvented and rediscovered many times. The goal of this article is to reduce the amount of future reinventions and rediscoveries by bringing together these different perspectives on RAPs in a way that is accessible to researchers with different backgrounds. The article serves as an exposition on RAPs and on their wide applicability in many areas, including telecommunications, energy, and logistics. In particular, we provide tools and examples that can be used to formulate and solve problems in these areas as RAPs. To accomplish this, we make three concrete contributions. First, we provide a survey on algorithms and complexity results for RAPs and discuss several recent advances in these areas. Second, we show that many objectives for RAPs can be reduced to a (simpler) quadratic objective function, which makes available the extensive collection of fast and efficient algorithms for quadratic RAPs to solve these problems. Third, we discuss the impact that RAPs and the aforementioned reduction result can make in several application areas.

The increasing penetration of electric vehicles (EVs) requires the development of smart charging strategies that accommodate the increasing load of these EVs on the distribution grid. Many existing charging strategies assume that an EV is allowed to charge at any rate up to a given maximum rate. However, in practice, charging at low rates is inefficient and often even impossible. Therefore, this paper presents an efficient algorithm for scheduling an EV within a decentralized energy management system that allows only charging above a given threshold. We show that the resulting optimal EV schedule is characterized by an activation level and a fill-level. Moreover, based on this result, we derive an online approach that does not require predictions of uncontrollable loads as input, but merely a prediction of these two characterizing values. Simulation results show that the online algorithm is robust against prediction errors in these values and can produce near-optimal online solutions.

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Due to the large increase in electric vehicles (EVs), smart charging strategies are required in order for the distribution grid to accommodate all these EVs. Many charging strategies either assume that future loads are known in advance, or use predictions of these loads as input. However, accurate prediction of uncontrollable load is very difficult. Online valleyfilling algorithms circumvent this problem by determining the charging profile based on a prediction of the fill-level: a single parameter that characterizes the optimal EV schedule. This paper presents a simple, but accurate, method to predict this fill-level. We show that near-optimal charging profiles with an optimality gap of less than 1% can be realized when our method is used to predict the input level for the online valley-filling approach. Furthermore, our method is very fast and thus suitable for use in decentralized energy management systems that employ the online valley-filling approach.

In this paper, we present a method to forecast the spread of SARS-CoV-2 across regions with a focus on the role of mobility. Mobility has previously been shown to play a significant role in the spread of the virus, particularly between regions. Here, we investigate under which epidemiological circumstances incorporating mobility into transmission models yields improvements in the accuracy of forecasting, where we take the situation in The Netherlands during and after the first wave of transmission in 2020 as a case study. We assess the quality of forecasting on the detailed level of municipalities, instead of on a nationwide level. To model transmissions, we use a simple mobility-enhanced SEIR compartmental model with subpopulations corresponding to the Dutch municipalities. We use commuter information to quantify mobility, and develop a method based on maximum likelihood estimation to determine the other relevant parameters. We show that taking inter-regional mobility into account generally leads to an improvement in forecast quality. However, at times when policies are in place that aim to reduce contacts or travel, this improvement is very small. By contrast, the improvement becomes larger when municipalities have a relatively large amount of incoming mobility compared with the number of inhabitants.

We study a convex quadratic nonseparable resource allocation problem that arises in the area of decentralized energy management (DEM), where unbalance in electricity networks has to be minimized. In this problem, the given resource is allocated over a set of activities that is divided into subsets, and a cost is assigned to the overall allocated amount of resources to activities within the same subset. We derive two efficient algorithms with [Formula: see text] worst-case time complexity to solve this problem. For the special case where all subsets have the same size, one of these algorithms even runs in linear time given the subset size. Both algorithms are inspired by well-studied breakpoint search methods for separable convex resource allocation problems. Numerical evaluations on both real and synthetic data confirm the theoretical efficiency of both algorithms and demonstrate their suitability for integration in DEM systems.

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