Sample Paper 2

Individual Exercises

Exercise 1 – A large buyer buys in 25 kgs bags. The bakery uses an average of 4860 bags a year. Preparing an order and receiving a shipment of lour involves a cost of $10 per order. Annual carrying costs are $75 per bag. The lead time for supply of flour is 2 days.

1. Determine the economic order quantity

2. What is the average number of bags on hand

3. How many orders per year are placed by the bakery

4. Compute the total cost per year of ordering and carrying flour

5. What is the re-order point in number of bags of flour

6. If ordering costs were to increase by $1 per order, how much would the total annual cost be impacted

Solution 1 –

Given,

· D = 4860 bags per year

· S = $10 per order per year

· H = $75 per bag per year

· Lead Time = 2 days

Answer A –

Economic order quantity,

Q0 = sqrt (2*4860*10/75) = 36 bags per order

Answer B -

Average number of bags on hand = (Maximum inventory + Minimum Inventory or safety stock /2)

= Q0 / 2 = 36 / 2 = 18 bags

Answer C –

Number of order = D / Q0 = 4860 / 36 = 135 order per year

Answer D -

Total Cost = (Q0 / 2)* H + (D / Q0) * S = (36/2)*75 + (4860/36)*10 = 1350 + 1350 = $2700

Answer E –

Reorder Point (Using Lead Time)

1 year (365 days) = 135 orders

1 day = 135 / 365 orders = 0.37 order

2 days = 0.74 order = 0.74 * 36 bags = 26.64 bags = 27 bags

Answer F –

New EOQ = sqrt (2*4860*11 / 75) = 37.76 bags = 38 bags (approx)

TC = (38/2)*75 + (4860/38)*11 = 1425 + 1406.84 = $2831.84 = $2832

(The Inventory carrying cost is not equal to Ordering cost as the bags are not 37.76, but is taken as 38)

Exercise 2 – A producer-distributor uses 800 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35% of the purchase price per crate. Order processing costs are $28 per order. Currently, the manager orders once a month. How much would the firm save annually by switching over to the EOQ system?

Solution 2 –

Total Annual demand = 800*12 per year = 9600 per year

Purchase cost = $10 per crate per year

H = Annual carrying cost = (0.35)*Purchase Cost = $3.5 per crate per year

S = Order processing cost = $28 per order

As per EOQ model,

EOQ = sqrt (2*9600*28/3.5) = 392 crates

TC = (392/2)*3.5 (Holding cost) + (9600/392)*28 (Ordering cost) = $1372

Non-EOQ model,

Average inventory per month = (800+0)/2 = 400

Total Cost = 400*3.5 (Holding cost) + 12*28 (Ordering cost) = 1400 + 336 = $1736