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Optimization models generally aim for efficiency by maximizing total benefitor minimizing cost. Yet a trade-off between fairness and efficiency is animportant element of many practical decisions. We propose a principled andpractical method for balancing these two criteria in an optimization model.Following a critical assessment of existing schemes, we define a set of socialwelfare functions (SWFs) that combine Rawlsian leximax fairness andutilitarianism and overcome some of the weaknesses of previous approaches. Inparticular, we regulate the equity/efficiency trade-off with a single parameterthat has a meaningful interpretation in practical contexts. We formulate theSWFs using mixed integer constraints and sequentially maximize them subject toconstraints that define the problem at hand. After providing practicalstep-by-step instructions for implementation, we demonstrate the method onproblems of realistic size involving healthcare resource allocation anddisaster preparation. The solution times are modest, ranging from a fraction ofa second to 18 seconds for a given value of the trade-off parameter.

Balancing Fairness and Efficiency in an Optimization Model