# Multi-objective optimisation of ship scheduling from different stakeholders’ perspectives

This section extends the model in Section 7.6 in several aspects: (i) additional uncertainty at sea is considered; (ii) additional CO2 emissions of ships at ports are considered; (iii) shipping lines can take either of two operational strategies: a constant sailing speed and a flexible sailing speed; (iv) a wider range of KPIs are defined from different stakeholders’ perspectives, e.g. from shipping line, shipper, terminal operator, and society.

The purpose is to examine how the ship schedule and planned speed would be designed differently from different stakeholders’ viewpoints, and how a compromise could be achieved for multiple stakeholders. This would give a more complete picture in terms of the impact of ship scheduling on various performance indicators. Similar to Section 7.6, the MOGA is applied to address the ship schedule optimisation problem. This section is partially based on Song et al. (2017).

## The dynamic system considering additional uncertainty at sea

Apart from the uncertainty at ports, we now consider additional uncertainty at sea. Hence, in addition to the notation defined in Section 7.6.1, the following notations are introduced to model the dynamic system appropriately:

*y-{.* the random variable describing the uncertain time in the sea leg from the ith portcall to the (1 + l)th portcall. *f _{p}:* the vessel’s FC in tonnes per hour at berth in port.

Consider the ship deployment, ship scheduling, and planned maximum speed optimisation problem for a shipping service route. The decision variables are the same as that in Section 7.6, i.e. *{n„,s _{v},* T,

*:i =*1, 2,N}. The vessel actual arrival and departure times are given by

where *Yijc* should be regarded as the realised sample of the random variable /{.} is an indicator function, which takes 1 if the condition in {} is true, and 0 otherwise.

If the shipping line adopts a constant speed strategy, then the actual sailing speed is determined by

If the shipping line adopts a flexible speed strategy, then the actual sailing speed is determined by

The constant speed strategy represents the situations that shipping lines concentrate on cost-saving without caring about the schedule reliability, whereas the flexible speed strategy (which is assumed in Section 7.6) represents the situations that shipping lines are willing to catch up the schedule if the vessels are delayed, but only speeding up to a pre-specified planned speed.

7.7.2 *KPIsfrom different stakeholders’ perspectives*

Three broad categories of KPIs are considered: cost, reliability, and emission. The cost category includes two KPIs taking from the ocean carrier’s and the shipper’s perspective, respectively. The ocean carrier’s cost is defined by the annual total ship-operating cost *[ J**Carrier Cost **f* consisting of two components: the FC cost of all ships deployed in the service route to sail the planned voyages over a year (assume 365 days in a year), and the charter hire for all ships in the service to sail the planned voyages. Here, we assumed that the planned number of voyages over a year has to be completed, even though the total voyages may exceed one year due to the uncertainties at sea and at ports.

Specifically, the ship charter hire cost is determined by the product of three elements: the number of ships deployed in the service route *n,„* the number of voyages over a year 365 / (7и^), and the expected total voyage time in days *t ^{a}N+i /* (24L). Thus,

The shipper’s cost *(J**shipper Cost)* includes the inventory holding cost for the cargos in transition on top of the ocean carrier’s cost. With the assumption of 70% of ship load factor, each laden container (TEU) carrying $27,331 value of cargos, and the annual inventory carrying cost being 35%, the annual total ship-operating cost plus in-transit inventory holding cost is given by,

The reliability category includes three KPIs. The first KPI is to measure service unreliability that is defined as the probability that the ship arrives at a portcall later than the planned arrival time plus the arrival time window *{JDelay Probis* which is the same as the service unreliability in Section 7.6. This KPI may be regarded as the reliability KPI taking from ocean carriers’ perspective because ocean carriers or shipping consultants often declare their service reliability in such way. For example, sea-intelligence defines ship reliability as the probability that the ship arrives at the port before the published schedule plus one calendar day.

The second KPI to measure service reliability is the average amount of delays per portcall. Note that the length of delays will significantly affect the shipper’s operations and inventory management. On the one hand, it increases the cargo transit time which increases the cycle inventory cost; on the other hand, it increases the variance of the transit time, which leads to higher safety stock. In that sense, this KPI can be regarded as a service reliability indicator taking from the shippers’ (or the freight forwarders’) perspective. The mathematical definition of the second KPI *(J**Delay Amount)* i^{s} given by

The third KPI to measure service reliability is the standard deviation of the ship arrival variation. This KPI may be regarded as a service reliability indicator taking from the terminal operator’s perspective. This is based on the argument that small deviation from the ship arrival schedule may be accommodated by terminal operators without changing the berth allocation plan (e.g. Dalian port has purposely designed several-hour buffer time into the berth plan), whereas a large deviation will significantly affect the berth allocation planning and terminal resource planning. Nevertheless, it should be pointed out that the standard deviation indicator is also important to shippers since it is highly related to the safety stock level and the arrangement of hinterland transportation of the containers. The third KPI *(Js _{l(}j d_{ci}?) *of service reliability is given as follows in which the standard deviation of the ship lateness takes the maximum for all portcalls in all voyages in the planning horizon,

The emission category includes two performance indicators. The first KPI is the annual total ССЬ emissions from all the ships in the service route * (Jsea со?)* during the sailing time at sea. The second KPI is the annual total CO2 emissions from all the ships in the service route (

*) during the sailing time at sea plus during berthing time at ports. As the ship’s berthing time is often beyond the control of ocean carriers, shipping companies may use the emissions from ships at sea to claim their emission performance. In that sense, the first KPI of emission may be regarded as taking from the ocean carrier’s perspective. This KPI is the same as the one used in Section 7.6. The second emission KPI includes the emissions from the ships both at sea and at port, which can be regarded as from the society’s perspective (that takes a systematic viewpoint). Note that the emission is proportional to the FC. We have:*

**Jroial со?**The simulation-based MOGA presented in Section 7.6 can be applied to optimise these multiple KPIs simultaneously or individually. The results would also reveal how the ship scheduling decisions would respond to various KPIs. Moreover, the best individual KPI solution in the final set of the MOGA procedure can be regarded as the result of a single-objective optimisation approach by giving the highest priority to the selected KPI and lower priority to other KPIs. In the next section, we provide a case study to apply MOGA and discuss the findings and implications of the results.