Which algorithm can I use for breaking down monthly forecast into daily forecasts / buckets? I'm a trainee at a medical device distribution center. My internship project is to break down monthly forecast into daily forecasts / buckets. in the current situation the monthly forecast is broken down by dividing it by the number of workdays in that month. The result is that the forecast is not accurate because the daily amount of orders fluctuates.
I have 3 years of historic daily data that consists of the amount of products ordered. In the first period of my internship I couldn't find a algorithm that suits for my problem. So I created my own. In this algorithm I look at the historic data and calculate the day of the week factors. See an example in the image. I've also done this for day in the month and week of the year.

My question is: there an algorithm that is similar to my approach? or is there a different algorithm I can use for breaking down the monthly forecast into daily forecasts?
 A: You are doing hierarchical forecasting, specifically using the top-down method. That is, you first forecast the aggregate, then break it down. An alternative would be the bottom-up method, where we first forecast daily orders, then aggregate them up.
In top-down forecasting, there are of course different ways of disaggregating. What you are doing is disaggregation by historical proportions. A very common alternative would be disaggregation by forecasted proportions: forecast the aggegrate, as you have been doing, but also forecast the daily orders. Then use the forecasted daily orders within a month to calculate disaggregation proportions, which you then apply to the aggregate forecast.
Disaggregation by historical proportions is of course a special case of disaggregation by forecasted proportions - where we just use the naive mean forecast for the daily orders.
So, all you have been doing makes sense. Yet another alternative would be optimum reconciliation hierarchical forecasting, where you forecast both the aggregate and the disaggregate levels. These forecasts will not be consistent. But we can post-process them, and typically the reconciliated forecasts are better at all levels than the original forecasts.
Chapter 10 in Forecasting: Principles and Practice (2nd ed.) by Athanasopoulos & Hyndman gives a very good introduction to all kinds of hierarchical forecasting.
Finally, a word of caution. You write that "the forecast is not accurate". You may find that no matter what you do, you will not manage to get very accurate forecasts, at least not as accurate as you (or your clients) want. This is very common.
