Question

Sam's Shoes has problems with its best-selling shoe—the FastShoe. Sam, the owner, tells you that he always seems to have too many or too few of the FastShoe. He has hired you to help determine how much and when to order. At the same time, the company is considering quotes from 2 different suppliers, and you will help compare suppliers. You estimated the following information from the detailed records that Sam kept on the shoe. You calculated the standard deviation of daily demand to be able to estimate the variation of demand during lead time—useful for calculating the amount of extra shoes to have on hand to minimize stockouts that plagued Sam. Sam wanted to have the FastShoe available no less than 95% of the time.

Requirements (annual forecast)	900	units
Average daily demand	2.47	units (365 days)
Standard deviation of daily demand	0.06
Order processing cost	435	per order
Annual inventory holding cost factor	35%	per year

Description	Supplier 1	Supplier 2
Per unit price of shoe	60	76
Average lead time in days	3.00	1.00
Standard deviation of lead time days	0.56	0.84

ote, do the interim calculations first and then use this supporting data in the total cost calculations. For instance, use number of orders (rounded) to calculate order cost. Round all answers to the nearest whole number.

Interim calculations	Supplier 1	Supplier 2
EOQ	193
Number of orders	5
Number of units for safety stock	2
Reorder point with safety stock	9
Total Cost Calculations	Supplier 1	Supplier 2
Total purchasing cost	$ 54,000	$
Ordering cost	2,175
1st year cost of safety stock	120
Holding cost of safety stock	42
Holding cost of cycle stock	2,027
TOTAL COST	$ 58,364	$ 73,171

Answer 1

Supplier 1 Calculation

Annual Demand = 900 units

Ordering cost =Set up cost =S = $ 435

Holding Cost at $ 60 per unit for supplier 1 = H = 35% of 60 = $21

Hence, EOQ = Sqrt(2*D*S/H) = Sqrt(2*900*435 / 21) = 193 Units

Number of Annual Orders = Annual Demand / EOQ = 4.66 ~ 5 orders

Safety Stock = (Maximum Daily Usage - Average Daily Usage) × Lead Time

Average Daily Usage = 2.47 Units

Standard Deviation of Daily Demand = 0.06 units

For more than 95 % confidence level the value of Z = 1.96

Also, Q(Max) = Average Demand + Z * Sigma = 2.47 + 1.96 * 0.06 = 2.58

Therefore, Maximum Quantity Demanded = 2.587

Average Lead time for the supplier = 3 days

Standard Deviation of lead time = 0.56 days

Maximum Lead Time for the given level of confidence = 3 + 1.96 * 0.56 ~ 4 days

Hence Safety Stock = 2.58 * 4 – 2.47 * 3 = 10 - 7. 5 ~ 2 units

Reorder Level = Safety Stock + Average Daily Usage * Lead time = 2 + 2.47 * 3 ~ 9

Total Purchase cost = 900 * 60 = 54000

Ordering cost = 5*435 = $ 2175

1^st year cost of safety stock = 2* unit price = 2 *60 =120

Holding cost of safety stock = 2 *21 = $42

Holding Cost of cycle stock = (EOQ/2)* Holding cost = (193/2)* 21 = $ =2026.5

Holding cost of cycle stock = $ 2027

Supplier 2 Calculation

Annual Demand = 900 units

Ordering cost =Set up cost =S = $ 435

Holding Cost at $ 76 per unit for supplier 1 = H = 35% of 76 = $ 26.6

Hence, EOQ = Sqrt(2*D*S/H) = Sqrt(2*900*435 / 26.6) = 172 Units

Number of Annual Orders = Annual Demand / EOQ = 5.23 ~ 6 orders

Safety Stock = (Maximum Daily Usage - Average Daily Usage) × Lead Time

Average Daily Usage = 2.47 Units

Standard Deviation of Daily Demand = 0.06 units

For more than 95 % confidence level the value of Z = 1.96

Also, Q(Max) = Average Demand + Z * Sigma = 2.47 + 1.96 * 0.06 = 2.58

Therefore, Maximum Quantity Demanded = 2.58

Average Lead time for the supplier = 1 days

Standard Deviation of lead time = 0.84 days

Maximum Lead Time for the given level of confidence = 1 + 1.96 * 0.84 ~ 3 days

Hence Safety Stock = 2.58 * 3 - 2.47 * 1 = 5 units

Reorder Level = Safety Stock+ Average Daily Usage * Lead time = 5 + 2.47 * 1 = 8 units

Total Purchase cost = 900 * 76 = 68400

Ordering cost = 6 *435 = $ 2610

1^st year cost of safety stock = 5* unit price = 5 *76 = $380

Holding cost of safety stock = 5 * 26.6 = $ 133

Holding Cost of cycle stock = (EOQ/2)* Holding cost = (172/2)* 26.6 = $ =2287.6

Holding cost of cycle stock = $ 2288