Question

The MRP gross requirements for Item A are shown here for the next 10 weeks. Lead time for A is three weeks and setup cost is $10. There is a carrying cost of $0.010 per unit per week. Beginning inventory is 92 units. WEEK 1 2 3 4 5 6 7 8 9 10 Gross requirements 35 40 17 25 75 85 20 60 200 87 Use the least total cost and the least unit cost lot-sizing methods to determine the quantity to order with the first order released with each method and which periods' requirements will be covered by that order. Quantity Ordered Periods Covered Least total cost Least unit cost

Answer 1

ANSWER:

First determine net requirement for each week:

	WEEK
	1	2	3	4	5	6	7	8	9	10
Gross requirements	35	40	17	25	75	85	20	60	200	87
On-hand inventory = 92	92-35= 57	57-40 = 17	17-17 = 0
Net req.	0	0	0	25	75	85	20	60	200	87

Aggregate requirements of the subsequent periods and order them in first period such that cost change from first period to next is least.  

Weeks	Quantity Ordered	Carrying Cost	Ordering Cost	Total Cost	Total Cost change	Unit cost = Total cost/order qty
4	25	0	10	10		10/25 = 0.4
4 to 5	25 + 75 = 100	75 x 0.010 = 0.75	10	10.75	0.75	10.75/100 = 0.1075
4 to 6	100 + 85 = 185	(75+(2x85))x 0.01 = 2.45	10	12.45	1.7	12.45/185 = 0.0673
4 to 7	185 + 20 = 205	(75 + 2x85 + 3x20) x 0.01 = 3.05 or 2.45 + (3x20)x0.01 = 3.05	10	13.05	0.6	0.0637
4 to 8	205 + 60 = 265	3.05 + (4x60)x 0.01 = 5.45	10	15.45	2.4	0.0583
4 to 9	265 + 200 = 465	5.45 + (5x200x0.01) = 15.45	10	25.45	10	0.0547
4 to 10	465 + 87 = 552	15.45 + (6 x 87x 0.01) = 20.67	10	30.67	5.22	0.055

According to least total cost lot sizing method: place first order in week 4 for periods 4, 5, 6, and 7 as the total cost change in week seven is least of all change.

Order quantity in week 4 = 205 units

Total cost of ordering and holding cost = $13.05

According to least unit cost lot sizing method: place first order in week 4 for periods 4 to 9 as the unit cost of order quantity till week 9 is least cost.

Order quantity in week 4 = 465 units

Total cost of ordering and holding cost = $25.45