Question

Chartsworth is a shoe producing company and sells an excellent quality shoe. After production, the shoes are distributed to 20 warehouses around the country. Each warehouse services approximately 100 stores in its region. Chartsworth uses an EOQ model to determine the number of pairs of shoes to order for each warehouse from the factory. Annual demand for Warehouse OR2 is approximately 120 000 pairs of shoes. The ordering cost is R250 per order. The annual carrying cost of a pair of shoes is R2.40 per pair.

Required:

2.1 Use the EOQ model to determine the optimal number of pairs of shoes per order.

2.2 Assume each month consists of approximately 4 weeks. If it takes 1 week to receive an order, at what point should Warehouse OR2 reorder shoes?

2.3 Although Warehouse OR2’s average weekly demand is 2 500 pairs of shoes (120 000 / 12 months / 4 weeks), demand each week may vary with the following probability distribution:

Total demand for 1 week (pairs)
2 000
2 250
2 500
2 750
3 000

Probability (sums to 1.00)
0.04
0.20
0.52
0.20
0.04

a. If a store wants shoes and Warehouse OR2 has none in stock, Warehouse OR2 can “rush” them to the store at an additional cost of R2.00 per pair. How much safety stock should Warehouse OR2 hold?

b. How will this affect the reorder point and reorder quantity?

Answer 1

Solution :  

Economic Order Quantity (EOQ) as the name suggests, is the quantity that should result in an economical cost that the company should incur for ordering and holding an inventory.

Re-order point is that point or level of inventory when the company should place an order to re-stock the inventory.

Safety Stock is the minimum level of stock that the company should maintain to avoid stock-outs.

PART 2.1. EoQ: EOQ= 2x T Annual demand & Ordering cost per order - Carrying cost per unit Annual demand = 120,000 pairs ordering cost = $250 per order Carrying cast = $2.40 per unit EOQ = (2x 120,000 x $250 $ 2140 = $25,000,000 oes . 5000 pair of shoes PART 2.2 : REORDER POINT Re-order Point - Demand & Lead time . (weeks) (per week) Annual demand= 120,000 pair of shoes No. of weeks in a year = 12 x 4 = 48 weeks Demand for week = 1201000 2500 pairs 48

Part 2.a: Sarens stolt SAFETY STOCK PART 2.3 A: Demand in Probability Stockout orders per Stact out units 12) Espected Stock out ugst cost $2 ber Year Resulting in Stock out 0 or 5 13) داداد) 2750 250 020 (4) = (2)x15) 500 24 (120,000/6000 000 4 2400 7600 3000 500 24 (120000 5001 500 A 0.09 - 1000 (12005000) $ 3360 Continuing the aboue taule when sakety stock of 250 A 500 units are mountated Safety Stock = 250 mnits Demand stock out Stockat probability order cost Expected Stock out cost resultin in stock ber year units out 2000 250 x 0.04 - 500 24 480 (30007 -2790 To.o4x7 L500 X 24 stock out cost $ 480 It carruging regst - Relevant to be 1250 X2,40) Total costs $ 1080 When extra safety stock of 500 units are maintained & There will be no stock outs. Carrying Cost = 500 units = $1200 (Relevant ) X $2.40

Sabety Alternative When safety stock Relevant cast - Stock (stock out) 2500 250 - $ 3360 s loso $ 1200 2750 3000 500 " Safety stock = 250 units. PART 2.3 B: RevisED REORER POINT Reorder Point 2500 + 250 = 2750 pairs 2500 units remains unchanged due to no change in ordering a carrying lost

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