Production Entries after items are sold (Bill of Materials)

We manufacture a lot of custom goods and we typically do not know how much raw material is going to be used for any given product code in a week, so we do after-the-fact production entries using Bill of Materials. The issue with this, is that the cost of components can vary significantly week over week, and we get an inaccurate Cost of Goods Sold at the end of the month because of it (valuation of Bills is currently set to Average). 

We essentially let the quantities of the bills go negative and then make production entries for the negative quantity on the weekends. 

Our idea was to change the valuation of the Bills to LIFO and then back-date production entries accordingly, but it seems that if the orders are already invoiced, it will not update the Cost of Good sold after-the-fact. 

Does anyone have any ideas or solutions for this problem? Is BOM just completely unsuitable for manufacturers of custom items? 

Our order fullfillment department does not do production entries, this is something we have an employee do on the weekend. Is invoicing all the orders on Monday (even if they shipped in the prior week) really the only way to get around this? That certainly isn't acceptable. 

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    Another idea was having the production entries debit the cost of good sold G/L account instead of inventory and then set the bill valuation to standard cost (which would then be set to zero). I am not sure how to change the G/L account that the production entry debits into, however. 

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    Another idea was having the production entries debit the cost of good sold G/L account instead of inventory and then set the bill valuation to standard cost (which would then be set to zero). I am not sure how to change the G/L account that the production entry debits into, however. 

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