Question

Betty bakes and sells bagels all year round. Betty plans and manages inventories of paper take-out bags with her logo printed on them. Daily demand for take-out bags is normally distributed with a mean of 90 bags and a standard deviation of 30 bags. Betty’s printer charges her $10 per order for print setup independent of order size. Bags are printed at 5 cents ($0.05) each bag. It takes 4 days for an order to be printed and delivered. Betty has a storage room big enough to hold all reasonable quantities of bags. The holding cost is estimated to be 25% per year. Assume 360 days per year. (Use the H= i × C formula to compute the annual holding cost).

a.) What is Betty’s total annual inventory-related cost (cost of placing orders and carrying inventory)?  

b.) What is the total cost per bag?

c.) What is Betty’s monthly inventory turns?

d.) If Betty’s printer charges her $12 per order irrespective of order size, what is the total annual inventory-related costs per bag?

e.) Assume that the print cost can be reduced to 3 cents per bag if Betty prints 9000 bags or more at a time. If Betty is interested in minimizing her total cost (i.e., purchase and inventory-related costs), should she begin printing 9000 or more bags at a time?

Answer 1

a) Daily Demand = d = 90 bags

Std. Deviation = = 30 bags

Lead Time = L = 4 days

No. of days per year = 360 days

Annual Demand = D = d * No. of days per year = 90 * 360 = 32400 bags

Order cost = S = $10

Cost of bag = C = $0.05

Holding cost = H = 25% = 25% * 0.05 = $0.0125

Optimal Order Quantity = EOQ = = = 7,200 bags

Total Inventory cost = Annual Ordering Cost + Annual Holding Cost = = = 45 + 45 = $90

The total annual inventory-related costs per bag = $90

b) The total cost per bag = The total annual inventory-related costs per bag + Purchase Cost = 90 + D * C = 90 + 32400 * 0.05 = $1,710 / 32400 = $0.0528

c) Average Inventory = EOQ / 2 = 7200 / 2 = 3,600

Average inventory value = 3600 * 0.05 = 180

Annual Inventory turn = Annual Cost of goods sold / Average inventory = 1710 / 180 = 9.5

Monthly inventory turn = Annual Inventory turn / 12 = 9.5 / 12 = 0.79 turns

d) Annual Demand = D = d * No. of days per year = 90 * 360 = 32400 bags

Order cost = S = $12

Cost of bag = C = $0.05

Holding cost = H = 25% = 25% * 0.05 = $0.0125

Optimal Order Quantity = EOQ = = = 7,887.2 bags

Total Inventory cost = Annual Ordering Cost + Annual Holding Cost = = = 49.30 + 49.30 = $98.6

The total annual inventory-related costs per bag = $98.6

e) Discount price = Pd = $0.03

Holding cost = Hd = 25% * 0.03 = $0.0075

Q = 9000

Total Cost = Annual Ordering Cost + Annual Holding Cost + Purchase Cost = = = 36 + 33.75 + 972 = $1,041.75

Since Total Cost for Q = 9000 is less than EOQ, She should begin printing 9000 bags at a time.

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