Consider a firm that purchases polystyrene as a raw material for use in a styrof
ID: 471022 • Letter: C
Question
Consider a firm that purchases polystyrene as a raw material for use in a styrofoam plant. The plant runs 250 days a year. Polystyrene costs $1,500 per ton and the plant uses 125,000 tons per year. Delivery charges consist of a "per ton" charge, which is included in the material costs, plus a fixed charge of $225 for each delivery, which covers paperwork, receiving expenses, and so forth. The firm uses a 15 percent carrying cost rate for inventory.
A. Use the EOQ model to compute the batch size that minimizes the sum of the holding plus ordering costs.
B. How many days of supply does the above batch size represent?
C. Suppose the firm decides for convenience to have polystyrene delivered every other day. What will the batch size be and how much will this cause the total (holding plus ordering) cost to increase?
Explanation / Answer
ANNUAL DEMAND = 125000 TONS
ORDERING COST PER ORDER = 225
CARRYING COST PER UNIT = 1500*15% = 225
A] EOQ = SQUARE ROOT OF [2*ANNUAL DEMAND*ORDERING COST PER ORDER/CARRYING COST PER UNIT ]
=SQUARE ROOT OF [2*125000*225/225]
= 500 UNITS
B]How many days of supply does the above batch size represent?
NO OF ORDERS DURING THE YEAR = 125000/500
=250 ORDERS
DAYS OF SUPPLY THE ABOVE BATCH SIZE REPRESENT = NO OF ORDERS/NO OF WORKING DAYS IN A YEAR
= 250/250
= 1 DAY
C]C. Suppose the firm decides for convenience to have polystyrene delivered every other day. What will the batch size be and how much will this cause the total (holding plus ordering) cost to increase?
IF THE POLYSTYENE IS DELIVERED EVERY OTHER DAY THEN THE FIRM IS ORDERING AT EOQ. SO BATCH SIZE = EOQ = 500 UNITS
CARRYING COST= AVG INVENTORY*CARRYING COST P.U.
= EOQ/2*225
=500/2 * 225
=250*225
=56250
THIS WILL HAVE NO EFFECT . THAT IS NO INCREASE OR DECREASE IN THE CARRYING COST.
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