Problem 2. (r,Q) Model. Mobil Films buy a petroleum based raw material that it u
ID: 332469 • Letter: P
Question
Problem 2. (r,Q) Model. Mobil Films buy a petroleum based raw material that it uses in its production process for films. The production process demand for this raw material can be approximated by a Normal random variable with mean 20000lbs and standard deviation 4000lbs per day. The supplier of the raw material is far away, and it takes 10 days for the supplier to deliver an order. Each time an order is issued to the supplier Mobil Films incur $355 fixed transportation cost and an additional $45 for handling the paperwork. Annual holding cost for each pound of raw material is 15% and each pound of raw material costs $1.20. Assume that the plant works for 330 days a year. Mobil Films use (r,Q) model to manage inventory and order according to EOQ. a) What is the order quantity for raw materials in lbs? b) If Mobil Films would like to be in stock 99% of all reorder periods, what would be the inventory level that Mobil Films should issue an order?Explanation / Answer
Following details are provided :
Annual demand = D = 20,000 lbs/ day x 330 days = 6600000 lbs
Ordering cost = Co = Fixed transportation cost + Paperwork handling cost = $355 + $45 = $400
Annual unit holding cost = Ch = 15% of $1.2 = $0.18
= Square root ( 2 x Co x D/ Ch )
= Square root ( 2 x $400 x 6600000/ 0.18 )
= 171269.76
ORDER QUANTITY = 171269.76 lb
Standard deviation of daily demand = 4000 lbs
Lead time = 10 days
Therefore , standard deviation of demand during lead time = 4000 x square root ( 10 ) = 4000 x 3.162 = 12648 lbs
Therefore ,
Safety stock = Z value x Standard deviation of demand during lead time = 2.3263 x 12648 lbs =29423 lbs ( rounded to nearest whole number )
Inventory level at which mobile firm should issue an order
= 20,000 x 10 + 29423 lbs
= 200,000 + 29423 lbs
= 229423 lbs
INVENTORY LEVEL AT WHICH MOBILE FIRM SHOULD ISSUE AN ORDER = 229423 lbs
Safety stock = 29423 lbs
Safety stock = 29423 lbs
Therefore , average inventory throughout the year = 100,000 + 29423 lbs = 129423 lbs
Since annual unit inventory holding cost . Ch = $0.18
Therefore , annual cost per year in managing this inventory = $0.18 x 129423 lbs =$23296.14
ANNUAL COST PER YEAR IN MANAGING THIS RAW MATERIAL INVENTORY = 423296.14
ORDER QUANTITY = 171269.76 lb
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