We consider a coal mine that extracts raw coal by a set of coal mining equipment (CME), separates out multiple products by a set of coal washing equipment, and delivers the products through a fleet of trains over a multi-period horizon. The equipment requires a daily preventive maintenance (PM) and each CME is subject to random failures and repairs. We study a joint PM, production, and delivery problem that determines when to perform the PM and how to manage coal production and delivery in each period, to minimize the expected total cost. We formulate a multi-period stochastic optimization model that delicately integrates the static PM decisions with the adaptive production-delivery decisions, which is extremely difficult to solve due to CME’s decision-dependent operating status. We propose a novel two-phase solution approach to overcome this difficulty. Phase 1 firstly determines the PM decisions using a scenario-based variable neighborhood search algorithm. Using the PM solution and the resultant set of scenarios as input parameters, Phase 2 adaptively determines the production-delivery decisions using a forward-looking algorithm in a rolling horizon manner. We show numerically that our approach consistently produces good-quality and robust solutions while preserving tractability for varying problem instances.

我们考虑一个煤矿，它通过一套煤炭开采设备（CME）提取原煤，通过一套洗煤设备分离出多种产品，并通过一组列车在多个时期内交付产品。设备需要进行日常预防性维护 (PM)，并且每个 CME 都会发生随机故障和维修。我们研究联合 PM、生产和交付问题，确定何时执行 PM 以及如何管理每个时期的煤炭生产和交付，以最小化预期总成本。我们制定了一个多周期随机优化模型，将静态 PM 决策与自适应生产交付决策巧妙地结合起来，由于 CME 依赖于决策的运行状态，这一问题很难解决。我们提出了一种新颖的两阶段解决方案来克服这一困难。第 1 阶段首先使用基于场景的变量邻域搜索算法确定 PM 决策。使用 PM 解决方案和由此产生的场景集作为输入参数，第二阶段使用前瞻性算法以滚动方式自适应地确定生产交付决策。我们以数字方式表明，我们的方法始终能够产生优质且稳健的解决方案，同时保持对不同问题实例的易处理性。