Schedule reliability is a crucial metric for measuring liner container shipping service. Due to the inherent uncertainties at sea and ports, schedule delays and unreliable on-time performance have long plagued shipping companies. In practice, the heterogeneity of container vessels also creates challenges for deployment and schedule optimization. To address the problem, we develop a two-step approach with two programming sub-models. In the first step, we tackle the challenges of ship deployment and scheduling by considering heterogeneous vessels and capturing the interarrival time between adjacent ports of call. In the second step, we use the conditional value-at-risk (CVaR) to address the uncertainty risk avoidance in schedule design. To solve the stochastic programming models, we employ a solution framework based on the outer linear approximation method and the risk measure method, where CVaR is specified as the risk measure. We illustrate the application of our model on a case study concerning a real route operated by COSCO Shipping Lines. The results show that the total cost of liner shipping service with heterogeneous fleet on the route can be reduce by 4.77% compared with homogeneous fleet. And the cost of risk with the reliable schedule can be decreased by 8.04% compared with the ideal schedule. The research conclusions can provide some useful decision-making references for shipping companies to deploy heterogeneous vessels and design reliable schedules.

班期可靠性是衡量班轮集装箱运输服务的一个重要指标。由于海上和港口固有的不确定性，船期延误和准点率不可靠长期以来一直困扰着航运公司。在实践中，集装箱船的异构性也给部署和船期优化带来了挑战。为了解决这个问题，我们开发了一种具有两个编程子模型的两步方法。第一步，我们通过考虑异构船舶并捕获相邻停靠港之间的到达间隔时间来解决船舶部署和调度的挑战。第二步，我们使用条件风险价值（CVaR）来解决进度设计中的不确定性风险规避问题。为了求解随机规划模型，我们采用基于外部线性逼近法和风险测度法的解决方案框架，其中CVaR被指定为风险测度。我们通过中远海运集运运营的实际航线的案例研究来说明我们的模型的应用。结果表明，航线上异构船队的班轮运输服务总成本比同类船队可降低4.77%。可靠进度的风险成本比理想进度可降低8.04%。研究结论可为航运公司部署异构船舶、设计可靠的班期提供有益的决策参考。