Your company is about to introduce this year's model of a product, which you expect to offer for sale for the next twelve months. You have no inventory of the product at present. You have capacity to hold up to 50 units of the product in inventory, and you can produce up to 45 units per month. Each month you produce the product, you incur a $10,000 setup cost, which does not apply to months in which you have zero production. At the beginning of each month, you decide your production level for that month, and you cannot alter your decision. Your direct cost of producing the product is $2,000 per unit, and you sell it for $3,000 per unit.
You do not know the exact demand for the product over the coming year. However, from an analysis of past orders, you have the following estimates of the expected (average) level of demand:
You have a large customer base, and each of your customers tends to order products of this type infrequently. To make way for next year's model, all units in stock at the end of month 12 will immediately be sold to "overstock.com" for $1800 per unit. You do not incur direct holding costs for keeping inventory, but your firm's internal cost of funds is 0.5% per month, compounded monthly.
Customer demand for a given month may be satisfied from that month's starting inventory and that month's production. Any sales above this amount are lost, with customers buying your competitors' products instead. Your policy is not to produce any amount of stock that risks overflowing your inventory capacity. Your management is unwilling to incur any risk, no matter how small, of overflowing the capacity of the inventory storage facility.