Question

Smart Home manufactures environmentally efficient ceiling lights to replace those in existing homes. It just received a contract for the next 6 months, requiring 100, 250, 190, 140, 220, and 110 units for each month. Production costs for ceiling lights vary with time due to the specialized materials. Smart Home estimates production will cost $250, $450, $350, $400, $520, and $500 per unit in months 1 through 6, respectively. To take advantage of cost variations, AGW may produce more lights than the contract requires in some months and hold up to 375 of the overproduced in inventory for later months. But holding inventory costs $30 per light per month. Assume there is no beginning inventory. Required: Formulate a time-phased LP to compute an optimal manufacturing and inventory plan for the next 6 months to minimize total cost.

Answer 1

Calculation of Inventory Plan & Minimum Purchase & Holding Cost:

S.no.	Month	1	2	3	4	5	6
A	Opening Stock (units)	0	420	330	420	330	110
B	Sales (units)	100	250	190	140	220	110
C	Purchase Cost per unit	$          250	$        450	$          350	$        400	$     520	$     500
D	Purchase (units)	850	160	280	50	0	0
E=A-B+D	Closing stock (units)	750	330	420	330	110	0
F=(A+E)/2	Average stock (units)	375	375	375	375	220	55
G=F*$30	Holding Cost	$    11,250	$ 11,250	$    11,250	$ 11,250	$ 6,600	$ 1,650
H=C*D	Purchase Cost	$ 212,500	$ 72,000	$    98,000	$ 20,000	-	-
I=G+H	Total Cost	$ 223,750	$ 83,250	$ 109,250	$ 31,250	$ 6,600	$ 1,650

Note 1) We should start with month 6 & assuming there is no closing stock at the end of month 6, hence opening stock should be equal to the unit to be sale i.e. 110.

Note 2) For month 5, 4, 3 & 2 opening stock has been calculated by using following formula:

(closing stock + unit sold) or (Avg unit *2 - closing stock) which ever is lower

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