Question

During the next four months, a customer requires, respectively, 600, 800, 1,200, and 900 units of a commodity, and no backlogging is allowed (that is, the customer's requirements must be met on time). Production costs are $80, $100, $105, and $90 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory. Determine how to minimize the net cost incurred in meeting the demands for the next four months.

Answer 1

Answer:

Minimal Net cost: $ 335,000

Explanation:

In order to minimize net costs, the first step is to obtain the unitary cost including all the concepts: production + storage

The period with lower production cost is Month 1 ( $ 80 ) , and after adding storage cost ( $ 20 ) it sums $ 100.  

The second Month is the next convenient one in terms of production costs ( $ 100 ).  

However, is not convenient to produce the whole demand in this periods because the extra stock remaining will increase storage expenses, specially considering that storage cost is accumulative ( $ 20 per unit per each end of month).

Remaining inventory after Month 4: not efficient, as $ 60 does not cover production cost.

Therefore, the best option is:

Month 1 : to produce from 600 up to 1,400 units  

Month 2 : to produce from 0 up to 800 units, according to Month 1 production ( formula=  1,400 less Month 1 production)

Month 3 : 1,200 units

Month 3 : 900 units.

Net cost:  $ 335,000  

*Optionally, it is correct producing 600 u in Month 1, and 800 u in Month 2: the result is the same ( Month: 1 $ 80 + $ 20  = Month 2: $ 100 )