Abstract
We develop an optimization model to provide a fair allocation of multiple resources to multiple users. All resources might not be suitable to all users. We develop a notion of fairness, and then provide a general class of functions achieving it. Next, we develop more restricted notions of fairness—special cases of which exist in literature. Finally, we distinguish between scarce and abundant resources, and show that if a resource is abundant, all users seeking it achieve the maximum possible coverage.
Highlights
We study the problem of allocating different kinds of substitutable resources to different populations seeking them
We develop an optimization model to provide a fair allocation of multiple resources to multiple users
Our aim is to allocate resources in a fair manner, a term we make precise below, and we develop a class of optimization models that achieve specific notions of fairness
Summary
We study the problem of allocating different kinds of substitutable resources to different populations seeking them. This work finds applications in resource allocation problems that have been studied in specific settings; see, e.g., distribution of coal among power companies [2], several military and defense examples [11], multiperiod manufacturing of high-tech products [12], wireless networks [9], healthcare [6], education [3], and conservation of threatened species [8]. Special cases of this general problem include the so-called waterfilling algorithm; see, e.g., [13]. As with Aristotle’s equity principle, our models serve to answer the question: how should allocation decisions be conducted when resources are due to users with pre-existing claims?
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