What's the smartest thing to do when you over-produce your products and have an excess of inventory?

The question depends on what is it that you have produced and how much value you attach to excess production. Steel for instance can be recycled or even sold at a cost + minimal margin. That however is reactive operations management. 

CHANGE THE PRICE TAG. DON'T DISCLOSE TO PUBLIC. GIVE ATTRACTIVE DISCOUNT/CLEARANCE DISCOUNT.

Well in this case, The most effective way to reduce your excess inventory is to first eliminate the old batch of products in order to let the new batch come in. This can be done when the excess inventory can be sold at a much quicker rate if they are put on sale or given of at certain discounts. Another effective way is implementing the FIFO System. 

In case of regular orders you can always hold it back but you need to consider the carrying cost.At first triying to push products in market, offers and sales (based on the value you have in product) in order to keep the cash flow and reduce inventory. And most importantly, record and investigate the root cause starting with the market research department, sales department.  

Push products in market, offers and sales (based on the value you have in product) in order to keep the cash flow and reduce inventory. And most importantly, record and investigate the root cause starting with the market research department, sales department or check the forecast or demand.   

We shouldn't reach such point, QA/QC and internal procedures should control this point to the maximum accuracy and minimum difference.

Anyone who has manufacturing Industry experience is aware for certain products it is not 100% possible to product the exact quantity required by the customer and there will always be variation.  The smartest thing to do is to get a prior approval from the customer for  variation in supply (either more or less) so you don't face trouble in shipping the goods to your customer.   In case of regular orders you can always hold it back but you need to consider the carrying cost.

The bottom line is  any excess production beyond the tolerance limits  is a sign of inefficiency.

Every thing depends on demands but if we posses excess of inventory then we can 2 things 

1)Assign some other work to the manpower indulged in it or get them use where they are more required at that moment and plan to capitalise on that inventory for example by providing them for some specific new purpose for research , for cpri testing etc  but it should be in knowledge of all concerned  persons

2) if the above one is not possible as it is as per the rules and regulation and that varies from concern to concern so you can just ask /coordinate with your in-house inventory manager under the knowledge of  supreme head and ask him to assign a place in store to place it and deliever all the breakers to him and recieve a reciept from him and then its all will be issued by him as and where it will be required

First inform and discuss with your valuable customer because of it will be waste if not getting your customer.

The stock clearance & getting proper space in store.