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(BUSM) must construct a schedule that simultaneously assigns residents to five types of call shifts, spanning three different hospitals, over a 365-day planning horizon. We show how user expertise and heuristic approaches alone fail to find acceptable solutions to this complex combinatorial problem; likewise, mathematical programming techniques alone are inadequate, largely because they lack a clearly definable objective function. However, by combining both approaches, we were able to find high-quality solutions in a very short time. The resulting schedule, which BUSM uses currently, has yielded substantial benefits; the solution quality has improved, and the effort required to develop the solution has been reduced.

Small package delivery is a multi-billion dollar industry with complex planning decisions required to efficiently utilize costly resources and meet tight time requirements. The planning process is typically decomposed into sequential sub-problems to establish tractability. This decomposition can greatly degrade solution quality. In this paper, we therefore consider the integration of two closely related key sub-problems: load matching and routing and equipment balancing. First, we identify critical challenges faced in trying to solve these problems. Then, we present a novel modeling approach to address these challenges. Finally, we conclude with computational results from UPS, the world's largest package delivery company, demonstrating an improvement of approximately 5% over their existing methods for solving this pair of problems.