Stochastic production–distribution planning with transportation mode-dependent lead times
研究了工厂在随机需求下同时决定生产和运输方式的问题，提出一种基于滚动时域和树搜索的启发式算法，在中等规模实例上平均差距低于0.1%，速度比CPLEX快316倍。
Plants and distribution centers often deliver their products to numerous customers spread over a vast territory and can thus rely on a combination of different transportation modes (such as road, air, rail, and maritime) to make their deliveries. 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 production and transportation decisions, which include the selection of the transportation modes to use for shipping products 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 and finite time horizon during which customers face a stochastic demand. As such, this problem is an extension of the stochastic lot sizing problem. In each time period, the plant has to make production and transportation decisions before the demand is revealed. We solve the resulting multi-stage problem approximately in 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 guide 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. The tree-search framework and the guide heuristic are evaluated on medium-size instances and compared to CPLEX. The guide heuristic proves to be able to select solutions with an average gap below 0.1% compared to the best one while being 316 times faster than CPLEX on average. The presented results highlight the challenges that complex stochastic lot-sizing problems pose for general-purpose commercial solvers. The performance of the proposed framework underscores the necessity of developing tailored meta-heuristic architectures and efficient sub-problem formulations to navigate the computational complexity of multi-stage optimization under uncertainty.