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Introduction
Linear programming techniques assume that the data used is perfect. In particular, when activating these features, you are assuming that the objective function and constraint coefficients are correct, rather than the best estimates available. If this assumption does not hold, the solutions found may be sub-optimal.
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Solvers use arc-node networks as their inputs. Source creates arc-node networks automatically for each time-step from the node-link network in the Schematic Editorthe Schematic Editor. There may be differences between the solution found by the solver ("as predicted") and flows as modelled during the flow phase ("as released"). The flow distribution phase resolves these differences by considering the ordering phase as having provided a minimum target to aim for. The optimum flow for each arc is determined by the netLP so that water will flow along the least cost pathway.
To choose network linear programming as the ordering algorithm, choose Edit » Scenario Options Ordering Algorithm. This opens the Ordering Algorithm section of Scenario Options (Figure 1). To configure netLP, choose Iterative solution to network linear program, this will make the rest of the display active and allow you to configure options for netLP.
Figure 1. Enabling ordering
About costs
The solvers use a scheme of costs to determine optimal flows. Costs can range from -1.1E13 through to +1.1E13. The larger the cost, the greater the disincentive for water to flow along an arc. Conversely, the smaller the cost, the greater the incentive for water to flow along an arc. For example, in the above list of solver priorities, satisfying evaporative and transmission losses have the lowest cost, and therefore the highest incentive, in any model. The question of relative costs becomes relevant when defining cost functions for storages that are being operated in harmony.
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*side constraints have not yet been fully implemented and tested in Source
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To configure optimised ordering, begin by choosing Edit » Ordering Network Costs... or click Configure Ordering on the Ordering toolbar and choose Network Costs.... This opens the Network costs dialog (Figure 1).
Figure 1. Network costs (summary)
Creating cost functions
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Figure 2. Network Costs (Storage Break Points)
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| Although you can define storage breakpoints for storage A in terms of storage B, you should avoid doing so because it can lead to infeasible solutions. |
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A more formal specification of the cost calculation is:
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Recall that negative costs are incentives. Accordingly, in this table, the greatest incentive is to retain any water in the bottom-most 10% of the capacity of the storage (for carry-over to the next time-step), followed by the water in the next 40% of the capacity of the storage. By interleaving base costs and increment values, releases from multiple storages can be controlled quite precisely to maintain a desired balance.
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Figure 3. Carryover Arc Costs vs Storage Volume
Applying cost functions
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Figure 4. Network costs (Storage targets)
You can also import storage targets from a .CSV file. The format of the file is shown in Table 3. Note that the column ordering in the .CSV file does not match the display in Figure 4.
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Figure 5. Network costs (Demand priorities)
You can control the order in which shortfalls are satisfied. The Priority column in Figure 5 shows which demand component of the model has will receive water via its shortfall arcs.
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| Note: In a netLP system, refer to Operating targets when setting up a storage node. |
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Troubleshooting It is possible to visualise the arc-node networks that are generated by Source using third party software. For more information please see: Troubleshooting and Debugging