Many engineering tasks can be formulated as dynamic optimization or open-loop optimal control problems, where we search a priori for the input profiles to a dynamic system that optimize a given performance measure over a certain time period. Further, many systems of interest in the chemical processing industries experience significant discontinuities during transients of interest in process design and operation. This paper discusses three classes of dynamic optimization problems with discontinuities:  path-constrained problems, hybrid discrete/continuous problems, and mixed-integer dynamic optimization problems. In particular, progress toward a general numerical technology for the solution of large-scale discontinuous dynamic optimization problems is discussed.

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When a customer orders online, an online retailer assigns the order to one or more of its warehouses and/or drop-shippers to minimize procurement and transportation costs based on the available current information. However, this assignment is necessarily myopic because it cannot account for any subsequent customer orders or future inventory replenishment. We examine the benefits of periodically reevaluating these real-time assignments. We construct near-optimal heuristics for the reassignment for a large set of customer orders to minimize the total number of shipments. Finally, we present evidence of significant saving opportunities by testing the heuristics on order data from a major online retailer.online retailing, online order fulfillment, local search heuristics

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