As mentioned in §5.1, the fundamental (fixed) model features included in the model configura- tion component cannot always accommodate all types of MLE response selection situations or necessarily conform to operator judgment or preferences. In this section, a number of examples of such situations, as well as ways of representing them in the mathematical modelling process, are briefly described. Unlike the features found in the cutting plane sub-component, features of the model adaptation sub-component are not necessarily configured as a function of time stages. In other words, the operator may sometimes wish to implement changes in the model formu- lation independently of the occurrence of disturbances. The features of this sub-component are typically achieved by a temporary constraint relaxation, a specification of temporary hard constraints or a modification of MLE response selection sets.
5.3.1 Combined assignments
It has been assumed up to this point that a VOI may only be scheduled for interception by at most one MLE resource. As stated in Characteristic 10 of §4.1.2, however, certain threatening MLE situations may require the use of multiple MLE resources in order to successfully neutralise them. Henceforth, define the notion of a combined assignment as the strategic unification of multiple MLE resources with respect to the interception of one or more specific VOIs. Combined assignments may be implemented whenever a strong requirement is present to neutralise the threats embodied in certain VOIs as efficiently as possible (in order, for instance, to reduce the risk of infeasible encounters or reduce the expected service times of these VOIs). Two examples of combined assignments are presented in this section, namely converged assignments, where multiple MLE resources are scheduled to intercept a single VOI for a once-off event, and convoyed assignments, where multiple MLE resources are scheduled to travel along a visitation route together. Combined assignments are assumed to be capable of neutralising a threat more effectively than single MLE resources, contributing towards preventing the risk of infeasible encounters, improving counter-threat performances and delivering shorter service times, as the converging subset combines the manpower and other resources from several MLE resources.
Converged assignments
Converged assignments deal with once-off events that are typically deemed very threatening, and require the use of multiple MLE resources in order to increase the chances of successfully neutralising the threat involved. This process is conducted in a “drop everything you are doing” attitude where, following the start of the time stage triggered by a VOI, the operator allocates a subset of MLE resources to converge on that VOI from their current locations. Each of these MLE resources is therefore re-scheduled along a route containing a single, common VOI; that is, they are immediately sent to the VOI involved without visiting any other VOIs previously assigned to them. Interestingly, if an operator would, for instance, prefer that an MLE resource
5.3. The model adaptation sub-component 99
completes servicing a VOI it may currently be busy investigating, intercept another specific VOI prior to investigating the involved VOI or investigate other VOIs after investigating the involved VOI, then he may, in addition to the sets presented in this section, make use of the sets described in §5.2.2.
Suppose i∗ ∈ Vτe is a VOI which causes the operator to subjectively trigger a disturbance requesting a converged assignment situation, and define the set Vr
i∗τ ⊆ Vr to contain the subset
of MLE resources scheduled by the operator to converge to VOI i∗ during time stage τ . By definition, it follows that Vkτe = {i∗} for all k ∈ Vir∗τ. The basic idea behind the concept of converged assignments in MLE response selection operations is illustrated graphically in Figure 5.4. Vr Vr i∗τ Ve τ i∗
Figure 5.4: Graphical representation of a converged assignment scenario.
In order to incorporate the above-mentioned visitation requirements, the set of constraints x0ki∗kτ = 1, k∈ V
r i∗τ
may (temporarily) be included in the mathematical modelling process at the beginning of time stage τ . In addition, the constraint set (4.2.4) in §4.2.4, which states that no more than one MLE resource may visit a VOI, should temporarily be relaxed at the beginning of time stage τ , replacing it by X k∈Vr k /∈Vr i∗τ yikτ ≤ 1, i∈ Vτe.
In cases of more than one converged assignment during any given time stage, it is assumed that each such assignment involves its own VOIs and subset of MLE resources; that is, if i∗, j∗ ∈ Ve
τ, j∗ 6= i∗ are VOIs involved in respective situations of converged assignments, then
Vir∗τ ∩ Vjr∗τ =∅.
Convoyed assignments
In convoyed assignments, multiple MLE resources are required to travel together along a route induced by one or more VOIs. These MLE resources are required to begin their route at a
pre-specified common location, and together intercept the VOIs assigned to them. One way of implementing such a requirement is to include certain instance constraints in the model formulation and redefine certain fundamental constraints and parameters. Undertaking this task is, however, not trivial, and is expected to add considerable complexity to the model formulation. A simpler and more efficient approach is to redefine the set of MLE resources Vr
so as to temporarily combine a certain subset of MLE resources as one entry. Hence, define the set Vr
cτ = {1, . . . , |Vcτr |} ⊆ Vr to contain MLE resources that the operator
wishes to configure in a convoyed assignment during time stage τ , and redefine the fleet set
Vr = Vr τ ={1, . . . , Vcτr , . . . , m + 1− |Vcτr |}, if|Vcτr | ≤ m − 2 Vr τ ={1, Vcτr }, if|Vcτr | = m − 1 Vr τ =Vcτr , if|Vcτr | = m
for this situation as the updated set of MLE resources during time stage τ . Note that, in this case, although Vr and Vr
τ are formulated differently, they have the exact same composition of
MLE resources. Furthermore, the MLE resources involved in such a set are assumed to be in an idle state while they converge towards one another at the start of their route (some pre-defined point in space), and the disturbance is triggered as soon as these MLE resources are grouped and ready to set out along their convoy route.
More than one case of convoyed assignments may occur during any given time stage, in which case it is assumed that each involves its own subset of MLE resources and visits its own subset of VOIs as in any of the other visitation routes); that is, if Vr
c1τ ⊆ V
r and Vr c2τ ⊆ V
r are two
MLE resource sets used in convoyed assignments during time stage τ , thenVr c1τ ∩ V
r c2τ =∅.
Possible implementation
The major challenge associated with combined assignments lies in (rapidly) reassessing certain critical fixed and dynamic parameters at the beginning of the time stage. For example, the expected service time of the VOI involved in a converged assignment scenario has to be evaluated in case one of the MLE resources involved is assigned to a route containing another VOI to be visited after having intercepted and serviced the VOI involved in the converged assignment, as the delay time associated with this other VOI has to be evaluated during the solution search process. Moreover, the counter-threat performances, expected service times, and travel speeds of a group of MLE resources configured to the same route in a convoyed assignment process should also be re-evaluated accordingly, which is certainly not a simple task.
5.3.2 Non-operational MLE resources
In some cases, an active MLE resource may experience technical problems while on a mission, causing it no longer to be able to carry on with its visitation route5. Active MLE resources expe-
riencing such technical problems while in an active state are then classified as non-operational. The current problem instance must then be resolved while prohibiting the problematic MLE resource from operating in an active state. Note that in the case where an idle MLE resource inVr were to experience such technical problems, it would not affect the current MLE response
5Such a situation is not to be confused with MLE resources undergoing maintenance or repairs; these MLE
resources are currently not part of the setVr and are, by definition, therefore neither active nor idle, but unavail-
5.3. The model adaptation sub-component 101
selection process, and it is the responsibility of the idle MLE resources DSS to deal with it accordingly.
One way of accommodating this scenario is to redefine the set of MLE resources by excluding the non-operational MLE resource, say k, from the set of MLE resources Vr
τ, by performing
the substitution Vr
τ ← Vτr\k, until the MLE resource is functional again. Another way of
accommodating this feature is simply to include the constraint X
j∈Ve τ
x0
kjkτ = 0
in the mathematical modelling process at the beginning of every time stage τ (while maintaining k ∈ Vr
τ), from the time that the MLE resource is classified as non-operational until it is functional
again.
5.3.3 Capacity restrictions
In certain situations, it may be the case that an MLE resource is no longer able to continue along its initial route after having intercepted one or more VOIs embodying certain types of threats, and is subsequently required to return to a base prior to servicing any further VOIs. Situations of this type are referred to as capacity restrictions. Such situations may not necessarily be predictable in advance as the natures of VOI interception (even ones known in advance and embodying the same type of threat) may differ significantly from one to another. Suppose that an MLE resource, say ˜k, is experiencing a capacity restriction situation. Then, the constraint
X
b∈Vb x0
˜
kb˜kτ = 1
may (temporarily) be included in the mathematical modelling process at the beginning of time stage τ in order to accommodate this situation.
5.3.4 Deployable bases
It has been assumed, up to this point, that the set of bases is fixed (or at least updated indepen- dently of MLE response selection operations, such as, for example, as a result of the construction of a new coastal base) and that their locations are also fixed in space. Some coastal nations may, however, possess deployable bases (See Characteristic 15 in §4.1.2), typically in the form of very large vessels with very high autonomy levels that may strategically be moved in space. Areas at sea that are relatively far away from the coastline and/or in which a relatively high concentration of VOIs are known to appear are examples of strategic candidate locations for de- ployable bases. These bases provide the same basic services to a certain subset of MLE resources as coastal bases do between missions, such as fuel replenishment, basic maintenance, crew shift changes and possibly stationing). Deployable bases may be treated like any other bases in Vb,
with the exception that the number of MLE resources allowed to use such facilities is typically more restricted.
Due to their mobility, however, deployable base locations have to be updated at the beginning of every time stage. Moreover, if a deployable base has significantly moved in space over a relatively long, disturbance-free period of time, an operator may trigger a new time stage in order to resolve the current MLE response selection problem, as certain routes may no longer be distance or time feasible (particularly if the distance from an MLE resource to its pre-assigned end-of-route deployable base has increased significantly).