Combining cost-based and rule-based knowledge in complex resource allocation problems

A major challenge in the formulation of optimization models for large-scale, complex operational problems is that some data are impossible or uneconomical to collect, producing a cost model that suffers from incomplete information. As a result, even an optimal solution may be "wrong" in the sense that it is solving the wrong problem. In many operational settings, knowledgeable experts will already know. at least approximately, how a model should behave, and can express this knowledge in the form of low dimensional patterns: "high powered locomotives should pull intermodal trains" (because they need to move quickly) or "loaded C-141s should not be flown into Saudi Arabia" (for maintenance reasons). Unlike the literature on inverse optimization which uses observed actions to train the parameters of a cost model, we used exogenous patterns to guide the behavior of a model using a proximal point term that penalizes deviations from these patterns. Under the assumption that the patterns are derived from rational behaviors, we establish the conditions under which incorporating patterns will reduce actual costs rather than just the engineered costs. The effectiveness of the approach is demonstrated in a controlled, laboratory setting using data from a major railroad.