C13
We need to supply electricity to a remote region that is not part of our network. A small gas generator will be ideal for this environment, but we are excited to try accompanying it with a new 80 MWh battery. This battery will allow us to have days where we do not need to turn on the generator, a positive outcome for the area.
The forecast daily electricity demands (MWh) for June are as follows:
34, 37, 37, 37, 37, 27, 36, 35, 39, 40, 26, 28, 33, 26, 33, 40, 47, 40, 36, 32, 37, 35, 30, 35, 37, 24, 32, 24, 35, 37
Each night we put in our order for the gas to power the generator for the following day. Effectively, our orders are placed in integer numbers of MWh, x, with a total cost of buying the gas and running the generator for a day of 0, when x = 0).
We need to meet the forecast demand each day, either directly from the generator or from the battery. Any surplus electricity will be stored in the battery. Once the battery is at capacity, subsequent gas is wasted.
Suppose our battery is initially empty and can be left empty at the end of the month. How much electricity should we plan to generate for each day in June?
Please provide us with the optimal total cost.
Communication 14
It turns out that our initial forecasts for June were rather limited. Each day there is in fact a 40% chance that demand will be higher than normal, as follows: 52, 60, 58, 62, 56, 44, 56, 57, 71, 68, 48, 51, 60, 49, 53, 67, 75, 72, 67, 59, 61, 66, 46, 54, 66, 42, 60, 37, 63, 57 The remaining 60% of the time the demand will be as previously forecast. Unfortunately, we do not know whether demand will be high or normal when we order the gas the night before. Please provide us with the optimal expected total cost.
Communication 15
In line with the demand-reduction strategy you helped us with in Communication 12, for this new region in June we have been allocated 5 days for which we can reduce the chance of high demand from 40% to only 10% (with a 90% chance of normal demand instead). We can make this request the night before, around the same time that we order our gas. The days do not have to be consecutive. Given this opportunity, please provide us with the optimal expected total cost.
Communication 16
Communication 16
Our forecasters have advised us that high and normal demands tend to come in runs, so if demand is high one day, then there is actually a 50% chance it will be high again the next day, while if it is normal one day then there is only a 20% chance it will be high the next day. Requesting the next day for demand reduction will still reduce this to 10%, regardless of whether it was high or normal the previous day. Based on this updated forecasting, please provide us with the optimal expected total cost. You can assume May 31st has normal demand. We look forward to reading your final report.