The problem of allocating a pool of cross-trained workers across multiple departments, units, or work centers is important for both manufacturing and service environments. Within the context of services, such as hospital nursing, the problem has commonly been formulated as a nonlinear assignment problem with an operationally-oriented objective function that focuses on the maximization of service utility as a function of deviations from target staffing levels in the departments. However, service managers might also deem it appropriate to consider human resource-oriented goals, such as accommodating worker preferences, avoiding decay of skill productivity, or the provision of training. We present a bicriterion formulation of the nonlinear worker assignment problem that incorporates both operational and human resource objective criteria. An algorithm for generating the entire Pareto efficient set associated with the bicriterion model is subsequently presented. A small numerical example is used to illustrate the bicriterion model and algorithm. A second example based on a test problem from the literature is also contained in the paper, and a third example is provided in an online supplement. In addition, a simulation experiment was conducted to evaluate the sensitivity of the algorithm to a variety of environmental characteristics. 
A bicriterion algorithm for the allocation of cross-trained workers based on operational and human resource objectives