Fair task allocation in transportation

Traditionally, optimization of task allocation problems considered only the costs involved in the allocation. However, there has been in recent years more attention to cases where cost should not always be the sole consideration (Campbell et al. 2008). There are circumstances when other criteria need to be taken into account as well during the decision making process. Fairness has been considered as one of the important additional criteria in many application domains (Ogryczak et al. 2005, Gopinathan and Li 2011, Bertsimas et al. 2012). Although there is no common definition for the term, there are two fairness criteria that are often used in the literature: the Nash bargaining criterion and the Rawlsian maximin criterion. The former is based on Nash's four axioms of pareto optimality, independency of irrelevant alternatives, symmetry, and invariance to affine transformations or equivalent utility representations (Nash 1950). The latter is based on Rawls' two principles of justice (Rawls 1971). Rawls' maximin criterion maximizes the welfare level of the worst-off group member and has therefore been used in allocation problems (Jaffe 1981, Kumar and Kleinberg 2000).