You can add custom delivery time rules depending on the attributues:
Product
Collection
Vendor
Product type
Tag
This is great for any custom made products you have that take longer to ship than your standard products. It's also great for any products you might have that ship from fulfillments centers that are far from your customer (e.g. You're testing out a new product that ships from a warehouse in China and might not be delivered for a few weeks).
Shopify expects all orders to shipped within 30 days except under special circumstances, so keep that in mind when creating your delivery times.
Adding a custom delivery time rule
Press the "Rules" section. You can also press the "Customize" button for the Delivery Times app block on the Overview page.
Press "Create rule"
From here you can set the delivery time and which products (or collections, vendor, etc) for the rule.
When you're done press "Save rule" and your rule will be live.
Note
It can sometimes take a few minutes for new rules to apply. Please be patient and refresh your product page to see the new rule in effect.
Careful
If multiple rules apply to the same product we cannot guarantee which rule will be displayed to the customer. After creating a custom rule you should always verify the behavior on your online store.