Very important to note. No unit can be operational if water flows are below its minimum level. Take

Unit $4$ ; if the water flow rate is $1\mathrm{.}95[k\frac{g}{s}],$ then the unit will shut down and produce zero cooling for

that interval. Further importance, the unit cannot utilise more than its maximum flow rate rating. If

$10\mathrm{.}0[k\frac{g}{s}]$ water is available for Unit $4,$ it can only draw $69[kW]$ electrical power for the compressor

and provide $693\mathrm{.}5=241\mathrm{.}5[kW]$ of air cooling.

What is provided

You will receive an Excel file with a six$-$hourly averaged water flow data set over a time period. The

flows within the six$-$hour intervals may be assumed to be constant, i$.$e$.,$ no variance within any six$-$

hour interval. The profiles is a typical representation of waterflows that can be expected during any

time of the year when production occurs at the mine and labelled Data$1.$

What is required

You are required to set up four LP models. Models I to III must be solved for and Model IV only need to be formulated. You will therefore have a maximum of four optimisation models on paper and three being coded.

$1.$ Model I: you must solve for the single best $($optimal$)$ unit to be used under water profile Data $1.$ The objective must be to maximise accumulated air cooling over time $($equivalent to the highest average$).$ Times when sufficient water is available the unit may provide air cooling and for the times when sufficient water is not available, the unit must be switched off and provide zero air cooling. For each time step the air$-$cooling rates of the optimally selected unit must be written to the Excel file under the provided column in the $$Results$$ tab. Make sure to indicate in Row $2$ of the sheet what unit your model solved for, i$.$e$.$ Unit $1,2,3$ or $4.$

$2.$ Model II: you must solve for the single best $($optimal$)$ unit to be used under water profile Data $1.$ The objective must be to maximise accumulated air cooling over time $($equivalent to the highest average$).$ Times when sufficient water is available the unit may provide air cooling and for the times when sufficient water is not available, the unit must be switched off and provide zero air cooling. When the unit is switched off, it must remain switched off for at least three time$-$steps $($i$.$e$.18$ hours: time period unit switches off and at least the two following time periods.$).$ For each time step the air$-$cooling rates of the optimally selected unit must be written to the Excel file under the provided column in the $$Results$$ tab. Make sure to indicate in Row $2$ of the sheet what unit your model solved for, i$.$e$.$ Unit $1,2,3$ or $4.$

$3.$ Model III: you must solve for the single best $($optimal$)$ unit to be used under water profile Data $1.$ The objective must be to maximise accumulated air cooling over time $($equivalent to the highest average$).$ Times when sufficient water is available the unit may provide air cooling and for the times when sufficient water is not available, the unit must be switched off and provide zero air cooling. When the unit is switched off, it must remain switched off for at least three time$-$steps $($i$.$e$.18$ hours: time period unit switches off and at least the two following time periods.$).$ Furthermore, the unit may only be restarted if the water flow from the last time period before it is restarted, is also above the minimum operational value. This is to ensure that a unit is not restarted directly after a time period where there was not enough water flow to potentially have supported air cooling. For each

time step the air$-$cooling rates of the optimally selected unit must be written to the Excel file under the provided column in the $$Results$$ tab. Make sure to indicate in Row $2$ of the sheet what unit your model solved for, i$.$e$.$ Unit $1,2,3$ or $4.$

$4.$ Model IV: you must formulate to solve for the two best optimal units to be used in combination. It might be that another mine has more cooling water available, and that a single Unit is sub$-$optimal to utilise. Note that this may be two of the same units.

The objective must be to maximise accumulated air cooling between the two units over time $($equivalent to the highest average$).$ Your formulation must determine how the water flow rate should be split between the two units at any time; and is therefore not known in advance. Times when sufficient water is available one or both units may provide air cooling and for the times when sufficient water is not available, one or both units must be switched off. It is therefore possible that one unit is switched off and the other one still in operation. When the unit is switched off, it must remain switched off for at least three time$-$steps $($i$.$e$.18$ hours: time period unit switches