Time Series Forecast Question - Weekly Sparse Data with Variable Starting Point

#1
Hi Folks,

I am working on building a time series forecast model for a problem which involves dataset of manufacturers and their product offerings in a large retail outlet.

The problem is as follows:
1 - Lets say you have thousands of manufacturers. (M1 to Mn)
2 - There is a retail outlet who would take goods from these manufacturers to sell.
3 - The manufacturers supply product offerings to the store on weekly basis. (same product or new product with same price or different price, but for simplicity lets say they supply new distinct products) (from week W1 to Wn)
4 - Each manufacturer would have started working with the retail outlet on different dates.(which can be anything in past)
5 - From the time they started working with the retail outlet, the history suggests that some manufacturers have been constantly supplying products weekly and some have been sparse.

-->Dataset Below (N/A means they hadn't started doing business with the retail outlet e.g manufacturer M1 joined the retailer on Week3 in our time window with their first offering count to be 10)

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| W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | . | . | . | Wn |
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M1 - | N/A | N/A | 10 | 0 | 5 | 0 | 10 | 15 | 12 | . | . | 23 |
M2 - | 10 | 5 | 12 | 8 | 4 | 9 | 0 | 0 | 0 | . | . | 4 |
M3 - | 9 | N/A | 0 | 0 | 45 | 45 | 45 | 38 | 12 | . | . | 11 |
. - | N/A | N/A | N/A | N/A | 12 | 0 | 10 | 15 | 12 | . | . | 28 |
. - | N/A | N/A | N/A | 0 | 5 | 0 | 8 | 15 | 12 | . | . | 12 |
. - | 5 | N/A | 60 | 0 | 5 | 0 | 40 | 67 | 23 | . | . | 46 |
. - | N/A | N/A | 12 | 9 | 12 | 15 | 10 | 15 | 43 | . | . | 9 |
Mn - | 0 | N/A | 90 | 78 | 65 | 0 | 10 | 15 | 12 | . | . | 65 |


Now assuming that for all the manufacturers, I want to forecast, from the point Wn their next 8 weeks of supply they would do from this historical data ( i.e. from Wn for next 8 weeks i..e Wn+1 to Wn+8). What is the best forecast model that would fit this problem.

I am exploring the Exponential Smoothing and ARIMA models, but I am not an expert in this field. Any thoughts and opinion would be really helpful.