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We study the problem of online resource allocation, where multiple customersarrive sequentially and the seller must irrevocably allocate resources to eachincoming customer while also facing a procurement cost for the totalallocation. Assuming resource procurement follows an a priori known marginallyincreasing cost function, the objective is to maximize the reward obtained fromfulfilling the customers' requests sans the cumulative procurement cost. Weanalyze the competitive ratio of a primal-dual algorithm in this setting, anddevelop an optimization framework for synthesizing a surrogate function for theprocurement cost function to be used by the algorithm, in order to improve thecompetitive ratio of the primal-dual algorithm. Our first design method focuseson polynomial procurement cost functions and uses the optimal surrogatefunction to provide a more refined bound than the state of the art. Our seconddesign method uses quasiconvex optimization to find optimal design parametersfor a general class of procurement cost functions. Numerical examples are usedto illustrate the design techniques. We conclude by extending the analysis todevise a posted pricing mechanism in which the algorithm does not require thecustomers' preferences to be revealed.

Function Design for Improved Competitive Ratio in Online Resource Allocation with Procurement Costs