Assume the following data for an item,
| XY1: |
Unit price = Mu 200, |
|
Ordering cost = Mu
1000, |
|
Annual Demand= 5000
units and |
|
Inventory carrying
rate = 20 %. |
|
a) If the minimum order size is 250 units,
what should be the EOQ?
b) What is the added cost if the firm orders 400 units or 600
units at a time rather than the EOQ?
c) Suppose delivery takes 2 weeks. Assuming certainty in delivery
and usage, at what inventory level should the firm reorder?
d) Assume a 200-unit safety stock is carried. What effect would
this have on total inventory costs?
e) Suppose the firm could receive a discount of 1% on orders
of 1,000 or more. Should the firm take the discount?
| a) EOQ |
= Sqrt (2AD/H) |
|
= Sqrt(2 x 5000 x 1000/(0.2
x200)) |
|
= Sqrt(10,000 x 1000/40) |
|
= Sqrt(10,000 x 25)
= 100 x 5 = 500 units |
|
Total variable cost when EOQ is ordered:
| TVC |
= Inv Holding + ordering
cost |
|
= (0.2)(Mu 200)(500/2)
+ Mu 1,000(5,000/500) |
|
= Mu 40(250) + Mu 1,000(10) |
|
= Mu 10,000 + Mu 10,000
= Mu 20,000. |
|
| b) At Q= 400
units: |
| TVC |
= 0.2(Mu 200)(400/2)
+ 1,000(5,000/400) |
|
= Mu 8,000 + Mu 12,500 |
|
= Mu 20,500 |
| Added cost = Mu 20,500
- Mu 20,000 = Mu 500 |
|
| At Q= 600 units: |
| TVC |
= 0.2(Mu 200)(600/2)
+ Mu 1,000(5,000/600) |
|
= Mu 12,000 +Mu 8,333
|
|
= Mu 20,333 |
| Added cost = Mu 20,333
- Mu 20,000 = Mu 333 |
|
| c) Assuming
52 weeks per year, |
| Weekly usage rate |
= 5,000/52 = 96 units |
| If order lead-time |
= 2 weeks |
| firm
must reorder when Inventory level = 2(96) = 192
units |
| Without safety stocks,
the firm's total inventory costs = Mu 20,000 |
|
| d) Cost of carrying
additional 200 units, |
| H(Safety stock) |
= 0.2(Mu 200)(200)
= Mu 8,000 |
| Total inventory
costs |
= Mu 20,000
+ Mu 8,000 = Mu 28,000 |
| Alternatively, |
| Average inventory |
= (500/2) + 200 =450
units |
| TVC |
= 0.2(Mu 200)(450) +
Mu 1,000(5,000/500) |
|
= Mu 18,000 + Mu 10,000
=Mu 28,000. |
|
| e) Discount
affects operating inventory only, |
| Discount price |
= Mu 200(0.99) = Mu
198 |
| TVC |
= 0.2(Mu
198)(1,000/2) + Mu 1,000(5,000/1,000) |
|
= Mu 19,800
+ Mu 5,000 = Mu 24,800 |
| Savings |
= 0.01(Mu
200)(5,000) |
|
= Mu 10,000 |
| Added costs |
= Mu 24,800
- Mu 20,000 |
|
= Mu 4,800 |
| Net savings
|
= Mu 10,000
- Mu 4,800 |
|
= Mu 5,200 |
|
Firm should take the discount.
|
|
