Page 270 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 13: Inventory Control

Solution: Notes
Table showing different order sizes and the associated annual costs

A. Order size (O.S) Tonnes 200 250 800 2,000 4,000
(Q)
B. Number of orders (U/Q 20 16 5 2 1
where U = 4,000)
C. Purchase Prize (OS x (200 × 6) (250 × 59) (800 × ` 5.8) (2,000 × 5.7) (4,000 × 5.6)
PP/tonne) (`) 1,200 1,475 4,640 11,400 22,400
D. Purchase Prize 600 738 2,320 5,700 11,200
(value of O.S/2) (C/2)
Ordering cost (Number of (`) (`) (`) (`) (`)
orders × O.C per order) (B) × 120 96 30 12 6
O.C is ` 6
Carrying cost (20% of average 120 148 464 1140 2.240
inventory) [20/100 × (D)]
Total cost 240 244 494 1,152 2,246
Annual cost of Material (U × 24,000 23,600 23,200 22,800 22,400
PP per tonne)
Total annual cost 24,240 23,844 23,694 23,952 24,646

The total annual cost is minimum at 800 tonnes, therefore, the best quantity to be ordered is 800
tonnes.

Example: Find the optimum ordering quantity for a product for which the price breaks
are as follows:
Quantity Unit cost (`)
0 < 80 20/- unit
80 < 100 18/- unit
100 < 200 16/- unit
200 < above 16/- unit

The monthly demand for the product is 400 units. The storage cost is 20% of the unit cost of the
product and the cost of ordering is ` 25 per month.

Solution:
Calculation of Economic Order Quantity

1. Order size 80 100 200 400
2. No. of order placed 5 4 2 1
3. Value of materials (Q 800 900 1,600 3,200
x P.P/U)
4. Value of inventory 800 900 1,600 3,200
value of material / 2
5. Ordering cost (No. of 125 100 50 25
order x C.P.O) (25)
6. Carrying cost (800 x 0.2) 160 (900 x 0.2) 180 (1,600 x 0.2) 320 (3,200 x 2) 640
Total cost 285 280 370 665
Annual cost of Material 8,000 7,200 6,400 6,400
Total annual cost 8,285 7,480 6,770 7,065

LOVELY PROFESSIONAL UNIVERSITY 265