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| Indices and sets |
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| Set of nodes |
| Set of origin railway stations, |
| Set of intermodal transfer hubs, where containers are transferred from train services to ship services, |
| Set of destinations including railway stations and destination ports, |
| Set of arcs |
| Set of outward arcs of node i, |
| Set of inward arcs of node i, |
| Set of container demands |
| Set of transportation services including train services and ship services |
| Set of services with origin node i, |
| Set of services with destination node i, |
| Set of train services, |
| Set of ship services, |
| Origin of container demand p, |
| Destination of container demand p, |
| A node in sea-rail intermodal network, |
| A transportation link, |
| A container demand, |
| Two transportation services, |
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| Input parameters |
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| The volume of container demand p measured in Twenty-foot Equivalent Units, which is a random variable (TEUs) |
| Due time when container demand p must arrive at its destination, i.e. the latest delivery time (hours) |
| Travel time of service s, which is a random variable (hours) |
| Travel time of arc a, which is a random variable (hours) |
| Transfer time at node i, which is a random variable (hours) |
| Fixed cost (locomotives, crew, etc.) for operating a train service (if the service is provided) (US/train service) |
| Fixed cost for operating a ship service (US/ship service) |
| Unit cost for transporting one container on arc a (US/TEU) |
| Unit transfer cost for loading, unloading and transporting operations between two consecutive services at node i (US/TEUs) |
| Unit penalty cost for late delivery (US/TEU/day) |
| Capacity of service s (TEUs) |
| Capacity of arc a (TEUs) |
| Transfer capacity of node i (TEUs) |
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| Auxiliary variables |
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| The number of containers transported via service s (TEUs) |
| The number of containers on arc a (TEUs) |
| A binary variable, equal to 1 if arc a is on the route of service s, and 0 otherwise |
| A binary variable, equal to 1 if container demand p is delayed, and 0 otherwise |
| A large enough number |
| A random vector including all random variables, |
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| Decision variables |
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| A binary variable, equal to 1 if the service s is operated; 0 otherwise |
| A binary variable, equal to 1 if the trains service is used for container demand p; 0 otherwise |
| A binary variable, equal to 1 if the ship service is used for container demand p; 0 otherwise |
| A binary variable, equal to 1 if the container demand p is transported on arc a; 0 otherwise |
| A binary variable, equal to 1 if the container demand p is transferred at node i; 0 otherwise |
| Service frequency of service s, i.e. the number of service s operated within the planning horizon |
| A vector that consists of all first stage decision variables, |
| A vector that consists of all second stage decision variables, |
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