Random Reactor Supply-Based Exchange

This section describes the resource exchange generation for the case where reactors are supplying used fuel to supporting facilities. The primary goal is to discern what are the possible options that parameterize a given instance of such an exchange in order to test the underlying formulation under different scalings of these parameters.

A supply group corresponds to a supply of reactor used fuel item which represent assembly-like objects. In general, supply groups will be generated in much the same way that demand groups are generated in the reactor request case, except that the the number and commodity of their supply nodes is known at solution time. Supply constraints are also simpler. Each unit coefficient is unity and the supply value is set to the assembly mass, however their total number is much larger, as there is one per assembly.

A request group corresponds to a supporting facility’s request for used reactor fuel. Accordingly, a request group may be comprised of multiple commodity demands (e.g., fast/thermal reactor fuels A and B), where each commodity is represented by a node. Demand constraints will mirror the supply constraints of the reactor request exchange in that the demand constraint values are not necessarily related (e.g. process versus inventory constraints).

number of commodities

The number of commodities associated with the exchange.

Distribution Candidacy

None

Theoretical Basis

The number of commodities is a fundamental parameter for resource exchange.

number of suppliers

The number of reactors being modeled.

Distribution Candidacy

None

Theoretical Basis

The number of suppliers is a fundamental parameter for resource exchange.

assemblies per supplier

How many items to model a supplier providing. Nominally, a small number (1, 2) corresponds to a ^batch^-type fueling system whereas a large number corresponds to an assembly-type fueling system. Each assembly corresponds to a node in the exchange graph. .

It is likely that this parameter will be sampled bimodally – in small numbers (i.e., 1 - 3) to model batch-type reactors and in large numbers (40 - 65). The large number scaling is indicative of a range for an AP1000 operating in a 4-batch mode (i.e., 157 / 4) to a ^Typical XL Plant^ running in 3-batch mode (i.e., 193 / 3) (see http://www.nrc.gov/reactors/new-reactors/design-cert/ap1000/dcd/Tier%202/Chapter%204/4-1_r14.pdf).

Distribution Candidacy

Possibly a integral distribution around an average.

Theoretical Basis

The number of assemblies per supplier is directly proportional to the total number of supply nodes. Therefore, scaling all supply simultaneous simply results in a larger problem size. Medium-scale problem sizes are handled by medium-scale number of assemblies.

commodities per supplier

The number of commodities in a supplier’s assembly group.

Distribution Candidacy

A reasonable range is [1, 4]. Two distributions are required to assign commodities to suppliers:

• the number of commodities
• the commodities themselves

Initial attempts for the number of commodities will use an integral value future attempts may use an integral distribuition centered on that value. Initial attempts for commodity selection will include a flat distribution and future attempts may include preferential distributions (e.g., for cases where UOX, MOX, and ThOX are possible commodities, but UOX and MOX have a higher usage probability than ThOX).

Theoretical Basis

Reactors may expel more than one commodity type given their input commodity types, and simulations will determine the variation and distribution of these commodity types.

assembly commodity

Given that a supplier has a number of assemblies and a number of commodities, assemblies must be assigned commodities.

Distribution Candidacy

Two primary distributions are considered, given the number and type of commodities of which a reactor’s assembly group is comprised. The first is a flat distribution, i.e., assemblies have an equal probability of being assigned any commodity in the pool. The second is a preferred distribution (e.g., decaying exponential), which models a situation in which reactors have a preference over their commodity types and have achieved their preference to some degree of satisfaction.

Theoretical Basis

Simulations mechanics will determine the actual distribution of assembly commodities for an arbitrary reactor, however, the above distributions model two distinct use cases: cases in which reactors have no preference over their commodity type and the case in which they do.

exclusion probability

The probability that a given supply will be exclusive (i.e., models a quantized assembly).

Distribution Candidacy

Possibly a distribution around an average, but unlikely.

Theoretical Basis

This parameter is directly related to the assembly modeling fidelity required by a given reactor model. A value of 0 implies minimum fidelity, a value of 1 implies maximum fidelity, and it is conceiveable with module mixing that this level of fidelity may exist on a spectrum.

number of supply constraints

Trivially defined as the number of assemblies.

supply constraint values

Defined as the mass of the supplied assembly. The average mass for an assembly is normalized to unity without loss of generality.

Distribution Candidacy

Either unity for all assemblies, or a distribution as a function of commodity and supplier around unity. The former will be analyzed first with a possible future investigation of the latter.

Theoretical Basis

It is not clear how modelers will choose assembly mass size. A naive approach is to assume all assemblies have the same size. A more sophisticated, and much more complicated, approach assumes that size is a function of reactor type (i.e., supplier) and commodity type.

number of requesters

The number of requesters. A requester may request more than one commodity. By definition, there must be at least one requester per commodity. If there are more requesters than commodities, the additional requesters are randomly assigned base commodities.

Distribution Candidacy

None

Theoretical Basis

The number of requesters is a fundamental parameter for resource exchange.

fraction of multicommodity requesters

The fraction of requesters that request more than one commodity.

Distribution Candidacy

Possibly a distribution around an average.

Theoretical Basis

An example might include a fast reactor fuel requester that requests multiple types of fast reactor fuel defined as different commodities.

number of commodities per requester

The average number of commodities that a multicommodity requester supplies.

Distribution Candidacy

Primarily two cases of interest exist. The first assumes a relatively even distribution of requesters per commodity. The second assumes that the distribution peaks at some commodity, while some are minimally satisfied. The former case will be investigated first.

Theoretical Basis

A used fuel requester may request more than one commodity, e.g., a fast reactor fuel requester may offer two types of fast reactor fuel which are istopically similar but treated as separate commodities.

number of request constraints

A requester may have an arbitrary number of request constraints that may or may not be related. A estimated reasonable range to model is [1, 4].

Distribution Candidacy

Requesters can either all be modeled as having the same number of constraints or a distribution can be sampled around an average. In effect, both sample a spectrum of total requester constraints, where the former represents a few special cases of the latter, where the distribution is uniformly sampled around integral values.

Theoretical Basis

A requester may have more than one constraint on their request.

request constraint values

As previously mentioned, request constraints need not be related. Classic examples provided so far are inventory constraints (i.e., a requester may have only so much room for new resources) and a processing constraint (i.e., it will only take as much as it can process, which may be an arbitrary function of resource quality).

An identical approach to the reactor request supply constraints and values will be taken.

Distribution Candidacy

See reactor request supply constraints and values.

Theoretical Basis

See reactor request supply constraints and values.

unit capacity/demand coefficient values

An identical approach to the reactor request case will be taken.

preference coefficient values

An identical approach to the reactor request case will be taken.

connection probability

An identical approach to the reactor request case will be taken.