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Plants and distribution centers often deliver their products to numerous customers spread over a vast territory and can thus rely on a combination of air, road, rail, and maritime transportation. These means of transportation have different costs but also different lead times, and there is thus a fundamental trade-off to be considered: a shorter lead time typically comes at a higher cost but offers more flexibility to react quickly to changes in demand. Hence, the plant faces the complex problem of making simultaneous pro duction and transportation decisions, which include the selection of the transportation modes to use for shipping the goods to different customers. The objective is often to minimize the expected cost of production, transportation, inventory, and lost sales. We consider this problem in a setting with a discrete finite time horizon during which customers face a stochastic demand. In each time period, the plant has to make production and transportation decisions before the demand is revealed.

The resulting dynamic multi-stage problem is solved approximately with a rolling horizon framework that relies on a static-dynamic representation of the problem. To efficiently solve this static-dynamic problem, we present a tree-search heuristic based on Anytime Column Search and Limited Discrepancy Search. For the node selection strategy, we develop a heuristic that aggregates all the considered scenarios to quickly improve the current solution with respect to the set-up decisions of the current tree-search node.