Question

The president of Hill​ Enterprises, Terri​ Hill, projects the​ firm's aggregate demand requirements over the next 8 months as​ follows:  

January	1,400	May	2,100
February	1,700	June	2,300
March	1,800	July	1,900
April	1,800	August	1,500

Her operations manager is considering a new​ plan, which begins in January with

200

units on hand and ends with zero inventory. Stockout cost of lost sales is

​$125

per unit. Inventory holding cost is

​$25

per unit per month. Ignore any​ idle-time costs. The plan is called plan B.

Plan​ B: Produce at a constant rate of

1,400

units per​ month, which will meet minimum demands. Then use​ subcontracting, with additional units at a premium price of

​$80

per unit. Subcontracting capacity is limited to

900

units per month. Evaluate this plan by computing the costs for January through August.

In order to arrive at the​ costs, first compute the ending inventory and subcontracting units for each month by filling in the table below ​(enter your responses as whole​ numbers).

                                                                                                                           

Period	Month	Demand	Production	Ending Inventory	Subcontract Units
0	December			200
1	January	1,400	1,400	nothing	nothing
2	February	1,700	1,400	nothing	nothing
3	March	1,800	1,400	nothing	nothing
4	April	1,800	1,400	nothing	nothing
5	May	2,100	1,400	nothing	nothing
6	June	2,300	1,400	nothing	nothing
7	July	1,900	1,400	nothing	nothing
8	August	1,500	1,400	nothing	nothing

Answer 1

This is a hybrid (Level + subcontracting) Plan

Level/Production = 1400 units per month

Starting inventory for this period is ending inventory of last period.

Calculations for January

Subcontracting units =  Demand - (Production + Starting Inventory)

Subcontracting units = 1400 - 200 -1400

Subcontracting units = -200 (-ve value Indicated Ending inventory)

Ending inventory = 200

Calculations for February

Subcontracting units = Demand - (Production + Starting Inventory)

Subcontracting units = 1700-200-1400

Subcontracting units = 100

Ending inventory = 0

Calculations for March

Subcontracting units = 1800 - 1400 - 0

Subcontracting units = 400

Ending inventory = 0

Calculation for April

Subcontracting units = 1800 - 1400 - 0

Subcontracting units = 400

Ending inventory = 0

Calculation for May

Subcontracting units = 2100 - 1400 - 0

Subcontracting units = 700

Ending inventory = 0

Calculation for June

Subcontracting units = 2300 - 1400 - 0

Subcontracting units = 900

Ending inventory = 0

Calculation for July

Subcontracting units = 1900 - 1400 - 0

Subcontracting units = 500

Ending inventory = 0

Calculation for August

Subcontracting units = 1500 - 1400 - 0

Subcontracting units = 100

Ending inventory = 0

Total subcontracting cost = Subcontracting cost per unit * Number of units subcontracted

Total subcontracting cost = 80*(100 + 400 + 400 + 700 +900 + 500 + 100)

Total subcontracting cost = 80*3100 = 248,000

Total inventory carrying cost = inventory carrying cost per unit * Number of units carried

Total inventory carrying cost =25*200 = 5000

Total cost = Total inventory carrying cost + Total subcontracting cost + Total stockout cost

As no stockouts were observed, Stockout cost = 0

Total cost = 248,000 + 5000 = $ 253,000