Model objectives

A selection from the following set of objectives is proposed to inform the formulation of MLE response strategies in the centralised paradigm:

I Maximise the combined visitation score of VOIs scheduled to be intercepted and investi- gated, weighted by (a) the probabilities of these VOIs being various types of threats from a pre-specified list of relevant threats and (b) the priorities assigned by the coastal nation with respect to neutralising the threat types from this list.

II Minimise the combined time delay score of VOIs scheduled to be intercepted, weighted in the same manner as in Objective I above.

III Minimise the total operating costs incurred by the dispatch of active MLE resources, including (a) their set-up costs, (b) their travelling costs while in an active state and (c) their trajectory deviation costs.

IV Minimise the so-called incapacity score of MLE resources obtained from the accumulated risk of infeasible encounters between active MLE resources and the VOIs scheduled for interception on their routes, weighted in the same manner as in Objective I above as well as with an estimated opportunity cost resulting from the inability of the MLE resources to neutralise these VOIs.

Mathematically, these objectives may respectively be formulated as follows: I Maximise X i∈Ve τ X k∈Vr yikτ X h∈H QhWkhpihτ, II Minimise X i∈Ve τ tiτ X k∈Vr yikτ X h∈H pihτQh, III Minimise X k∈Vr Υs_kτ+ Υt_kτ + Υp_kτ
, and IV Minimise X i∈Ve τ X k∈Vr yikτ X h∈H δkhpihτCikhτe ,

where in Objective III

Υs_kτ = γkτCks X j∈Ve τ x0kτjkτ, Υt_kτ = Γk X i=0kτ i∈Ve τ X j∈Vτ j6=0kτ xijkτdijkτ and Υp_kτ = C_kd(1_{− x}0kτJk(τ−1)kτ) X j∈Ve τ j6=Jk(τ−1) x0kτjkτ.

Objective I refers to the significance of the expected benefits associated with the successful interception and neutralisation of various types of threats at sea, as discussed in _{§4.1.6. It} is assumed that the level of threat posed by a VOI at sea is directly proportional to both the probability that the VOI is actually a threat of a specific type and the importance of neutralising such a type of threat. Pursuit of this objective is expected to increase the probability of assigning suitable or highly appropriate MLE resources to intercept VOIs that are expected to embody highly dangerous threats. This objective is expressed as a linear combination of the probabilities of VOIs being the types of threats mentioned in _{§4.1.4 and the priority scores associated with} neutralising threats of these types.

The second objective above refers to the total time that elapses between the detection and interception of the VOIs at sea that are scheduled for interception. It is assumed that taking long to intercept a VOI (i.e. incurring a long MLE response time) impacts negatively on the overall success of MLE operations. More specifically, a longer response time is expected to increase the chance that tracking operators of the VOI fail or that the VOI exits the EEZ before interception takes place. This objective is expressed as a linear combination of the probabilities of VOIs being the types of threats mentioned in §4.1.4, the priority scores associated with neutralising threats

4.2. Model configuration in the centralised paradigm 81

of these types and the expected response times of the MLE resources assigned to investigate the VOIs. Pursuit of this objective is therefore expected to result in seemingly more threatening VOIs being serviced more rapidly.

Objective III refers to the costliness of committing MLE resources to investigating VOIs at sea. As mentioned previously, it is assumed that an MLE resource incurs a fixed set-up cost every time it is dispatched from a base and a variable operating cost which depends on the overall distance travelled on a mission at sea. Furthermore, it is assumed that an active MLE resource incurs a certain cost associated with the manoeuvres required when changing routes at the start of a problem instance. In the mathematical formulation of this objective,

Objective IV above relates to the possibility of infeasible encounters between MLE resources and VOIs. Such encounters should, of course, be avoided in MLE resource assignment operations, if possible, as they result in wasted travel costs and unnecessary VOI servicing delays. The objective is expressed as a linear combination of the probabilities of VOIs embodying certain types of threats and the estimated costs associated with infeasible assignments.

Objectives I and II share a certain degree of inter-dependency. It should, however, be observed that these two objectives complement each other in a manner that would not be possible if they were to be pursued in isolation. On the one hand, solely adopting Objective I may lead to increased levels of interception of those VOIs expected to embody highly dangerous threats, but will not account for the urgency factor involved when planning the trips of the MLE resources assigned to carry out these interceptions. On the other hand, solely adopting Objective II will lead to the situation where no VOIs are actually intercepted (the situation of a zero delay score) and would analogously benefit Objective III as well.

Additionally, Objectives I and IV share a certain degree of inter-dependency, as the visitation score is expected to discourage the assignment of MLE resources for the interception of VOIs embodying types of threats which they are strictly incapable of neutralising. Because the nature of a VOI is, however, typically not known in advance with certainty, there may be a (typically relatively small) probability that the VOI embodies a certain type of threat which cannot be neutralised by certain MLE resources. Because the visitation score will afford more weight to the scores with higher probabilities, these small probability terms may, in fact, not have a significant impact on the overall visitation score, thus prompting the suggestion of Objective IV above. There are two main scenarios in which this objective is anticipated to be especially relevant. It may be the case that the costs associated with infeasible encounters are high (e.g. as a result of a large jurisdiction area, limitations in terms of the number and/or strength of MLE resources, the presence of numerous types of threats to deal with, or poor threat evaluation performances). In such a case Objective IV will promote a minimisation of the probability of infeasible encounters which may not be avoided when only implementing Objective I (which does not directly account for the lost opportunity as a result of infeasible encounters). The operator may indeed be interested in selecting solutions which embody low risks of producing infeasible encounters, while also achieving good visitation scores. Secondly, although the operator may choose to implement Objective I in the model, he may lean more towards implementing solutions which incur low operating costs (see Objective III).

Because Objective IV also deals with costs to some extent, these two objectives may be perceived as correlated. In other words, if the operator has strong preferences for implementing solutions with low operating costs, then he will also prefer to implement solutions with low risks of infeasible encounters, so as to minimise the overall economical implications of both objectives.