On a Reduction for a Class of Resource Allocation Problems

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