Question

In: Operations Management

Sports Stuff, Inc. (SSI) is a manufacturing firm that produces sporting goods. They have started operating...

Sports Stuff, Inc. (SSI) is a manufacturing firm that produces sporting goods. They have started operating a factory in the U.S. and have opened a company owned store adjacent to the factory. The production manager at the factory is trying to ascertain the optimal number of footballs to produce with each production run. After careful analysis, she believes that the following data are correct:

  • Annual demand is 21,875 footballs per year
  • The store is open 350 days per year
  • The daily production capacity of the factory is 200 units
  • Setup cost incurred to start football production is $25
  • Annual storage cost per football is $17.50
  • Lead time is two days
  • Safety stock is 10 footballs

Answer the following questions for SSI.

a) What is the optimal lot size for football production? (round to 2 decimals)   footballs


b) What is the minimum inventory level of footballs?   footballs


c) What is the maximum inventory level of footballs? (round to 2 decimals)   footballs


d) What is the average inventory level of footballs? (round to 2 decimals)   footballs


e) What is the reorder point in units?   footballs


f) What is the annual setup cost for football production? (round to 2 decimals)  $


g) What is the annual holding cost for the football inventory? (round to 2 decimals)  $

Solutions

Expert Solution

Answer: Given: Annual Demand = D = 21,875 nos.

No. of working days N = 350 days

Daily demand = D / N = 21875 / 350 = 62.5 nos.

Daily production = p = 200 units

Set-up cost = S = $25

Annual storage cost = H = $17.50

Lead time = LT = 2 days

Safety stock = SS = 10 nos.

Economic Production Order quantity = = = 301.51

Minimum inventory = 0 nos.

Maximum inventory = = = 207.29 nos.

Average inventory = (Max. Inventory + Min Inventory) / 2 = (207.29 + 0) / 2 = 103.64 nos.

Re-order point = d * LT + SS = 62.5 * 2 + 10 = 135 nos.

Annual set-up cost = =   = $1813.79

Annual Holding cost = Average Inventory * H = 103.64 * 17.50 = $1813.79

Hence, we get answers as:

a) What is the optimal lot size for football production? 301.51 footballs

b) What is the minimum inventory level of footballs? 0 footballs

c) What is the maximum inventory level of footballs? 207.29 footballs

d) What is the average inventory level of footballs? 103.64 footballs

e) What is the reorder point in units?  135 footballs

f) What is the annual setup cost for football production? $1813.79

g) What is the annual holding cost for the football inventory? $1813.79

keosha answered 2 hours ago
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