Question 1: Inventory Management (a) Several managers of a service company are r
ID: 3053211 • Letter: Q
Question
Question 1: Inventory Management
(a) Several managers of a service company are reviewing some rather disturbing news at their monthly financial review meeting. The Vice president of finance states that the cost of financing the company’s supplies inventories has increased 40% and the acquisition cost of the company’s components has increased 20%. Increased labour rates and fringe benefits have caused ordering costs to rise by 25%, and annual demand for components has declined 5%. Mr James Phiri, the vice President of operations, sits quietly at the end of the conference table waiting for the inevitable question. Finally it comes from the company’s president: “James, how much, percentage-wise, will your order quantities change and how much will your total annual stocking costs change for the components?”. Can you answer for James?
(b) Patapata stores at COMESA market-Lusaka, carries a basic shoe for men that sells at an approximate constant rate of 500 pairs of shoes every three months. Patatpata’s current buying policy is to order 500 pairs of shoes each time an order is placed. It costs Patapata K120,000 to place an order. The annual holding cost rate is 20%. With the order quantity of 500, Patapata obtains the shoes at the lowest possible unit cost of K112,000 per pair. Other quantity discounts offered by the manufacturer are as follows:
(i) What order quantity for the shoes would you recommend?
(ii) What are the annual savings of your inventory policy over the policy currently being used by Patapata?
ORDER QUANTITY PRICE PER PAIR 1 - 99 K 144, 000 100 - 199 K 128, 000 200 - 299 K 120, 000 300 or more K 112, 000Explanation / Answer
Solution
Back-up Theory
EOQ (Economic Order Quantity): Q = sqrt{(2DS)/(Ch)}, where
D = annual demand in units
S = ordering cost per order
C = cost (price) per unit
h = holding host (% per annum).
Now, to solve the given problem,
Given D = 2000, S = 120000, h = 0.2 and C varies with the order quantity.
Q for the different values of given discount prices are given below:
Order Quantity
Discount Price
Q
Remarks
1 - 99
K 144, 000
129
Q does not qualify for discount
100 - 199
K 128, 000
137
Q qualifies for discount
200 - 299
K 120, 000
141
Q does not qualify for discount
300 or more
K 112, 000
146
Q does not qualify for discount
Since only Q = 137 fits in with the discount system,
the recommended order quantity is 137. ANSWER for Part (i)
Part (ii)
The annual TVC (Total Variable Cost) for current policy of ordering 500 units per order:
Ordering cost = (2000/500) x 120000 = 480000
Holding cost = (500/2) x 112000 x 0.2 = 5600000
TVC = 1140000
TVC under EOQ = sqrt(2DSCh)
= sqrt(2 x 2000 x 120000 x 128000 x 0.2)
= sqrt(12288 x 1010)
= 11085125
Thus, saving is: K 9945125 ANSWER
Order Quantity
Discount Price
Q
Remarks
1 - 99
K 144, 000
129
Q does not qualify for discount
100 - 199
K 128, 000
137
Q qualifies for discount
200 - 299
K 120, 000
141
Q does not qualify for discount
300 or more
K 112, 000
146
Q does not qualify for discount
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