I am going to conduct an analysis in order to "weight" different possibilities of actions in a given market. I have an overall level of effort that can be distributed accross the different actions over an entire day. Lets assume that the total effort is 1 and it can be splitted in different action_efforts (summing to 1) i.e. effort level for each possible action. There are 5 actions all with different horizions and an actions must be taken for each half-hour of the day. Action 1 will terminate 1 half-hour later, Action 2 will terminate 2 half-hours later, and so on up to action 5 terminating 5 halfhours after the action is taken.
The overall objective is to maximize realized profit. At the start of each half-hour a forecast on the revenue of the actions are made. If a given action is chosen, the realized profit will be equal to action_effort*realized_revenue. The realized revenue is stochastic and is based on the forecast: the first time a price in the market exceeds the forecast, the revenue is locked being this value. If the forecast is never exceeded, the realized_revenue is 0. Hence there is no guarantee of profit, no matter what the forecast is. If an action with longer horizon is chosen, it also limits the possibilities in the next half-hour as the effort is locked for all of the half hours.
I have timeseries data for each half hour of the day for 3 years. The data contains 1) perfect foresight data i.e. best realized_revenue for each action for each halfhour (if the forecast equaled this value, then the optimal revenue would be yieleded) 2) The forecast of revenue for each action for each halfhour 3) The realized revenue for each action for each halfhour, which is based on the forecast.
The overall aim of the analysis is to see whether it is profitable to take actions with longer horizons because they may have larger revenues, but lock some effort, or if short-term actions are best. Hence I want to determine a "weighting"/split of the different actions to use following a forecast. However, I have trouble finding out how to do that. I think that I want some weighting that is either constant for every half-hour or at least constant for a given half hour of the day i.e. half-hour 15:30-16:00 on each day used the same weighting/split but it may be different from the split in 16:00-16:30.
Taking the perfect foresight data I guess I can make some maximization problem and determine the optimal split, but in reality I only have the forecasts to work with and that is nowhere near optimal - the ordinality of the different actions is not captured either. I imagine the split of effort level for each action to be given by something like: (expected_revenue/ sum of expected revenue) * adjustment_weight because it takes into account the expected_revenue of the given action compared to the other, but also a genereal adjustment_weight based on historical data that takes the precision of the forecats into account (i.e. realized_revenue vs. expected_revenue of the forecast). But I dont know how to determine this adjustment_weight.
So my question is how you would conduct such analysis based on the data and determine this adjustment_weight in order for me to know how to split the effort based on my forecast in the future? A fairly simple statistical analysis would be fine - it does not need to be extremely complex, but right now I just need some inspiration.