Question

1)

Annual sales (=demand), D = 4000 sets

Order cost, S = $ 25

Holding cost, H = $ 5

Current order quantity, Q = D/2 = 4000/2 = 2000 sets

Optimal order quantity, EOQ = sqrt(2DS/H)

= sqrt(2*4000*25/5)

= 200 sets

Annual holding cost of current policy = H*Q/2

= 5*2000/2

= $ 5000

Annual holding cost of optimal policy = H*EOQ/2

= 5*200/2

= $ 500

Difference in holding costs = 5000 - 500

= $ 4,500

2) A distribution center operates for a major electronics company that fulfills orders that customers make from the website. (15 pts.)

Estimated annual demand: 16,936 laptops (50 weeks per year)

Cost: $840 per laptop

Lead Time: 5 weeks

Standard deviation of weekly demand: laptops

Standard deviation of lead time: 0.9 weeks

Holding cost per unit per year: 60% of item cost

Ordering cost: $37 per order

Desired service level: 98% (z=2.05)

***Calculate the reorder point and the safety stock? Note that you need to convert the annual demand to weekly demand based on 50 wks/yr.

Answer 1

A= annual demand = 16,936 units per year

Weeks per year = 50 weeks

d = mean weekly demand = 16936/50 = 338.72 units per week

σd = standard deviation of weekly demand = “Y” laptop per week (the value is not provided in question, but I am assuming it as Y units of laptop)

L = mean lead time = 5 weeks

σL = standard deviation of lead time = 0.9 weeks

Service level = 98%

For the service level of 98%, the z-score is 2.05

The reorder level for variation in demand and lead time is given as follows:

Reorder Level = Demand during lead time + Safety stock

Reorder Level = dL + SS

The Safety stock is given as follows:

SS = z√(Lσd2 + dσL2)

SS = 2.05 x √[(5)(y)2 + (338.72)(0.9)2]

SS = 2.05 x √[(5)(y)2 +274.3632]

Safety Stock = 2.05 x √[(5)(y)2 +274.3632] units

Reorder Level = dL + SS = (338.72)(5) + 2.05 x √[(5)(y)2 +274.3632]

Reorder Level = 1693.6 + 2.05 x √[(5)(y)2 +274.3632]

(substitute the actual value of σd = y in above formula)