Question

A local service station is open 7 days per week, 365 days per year. Sales of...

A local service station is open 7 days per week, 365 days per year. Sales of 10W40 grade premium oil average 25 cans per day. Inventory holding costs are $0.90 per can per year. Ordering costs are $7 per order. Lead time is two weeks. Backorders are not practical—the motorist drives away.
a.

Based on these data, calculate the economic order quantity and reorder point. Hint: Assume demand is deterministic. (Round your answers to the nearest whole number.)
  Economic order quantity cans
  Reorder point cans
b.

The boss is concerned about this model because demand really varies. The standard deviation of demand was determined from a data sample to be 7.55 cans per day. The manager wants a 90 percent service probability. Determine a new inventory plan based on this information and the data in a. Use Qopt from a. (Use Excel's NORMSINV() function to find the correct critical value for the given ?-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
  New reorder point   cans
Business   Operations-Management   
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Answer #1

Given are following data :

Annual demand of premium oil = D = 25 / day x 365 days = 9125 cans

Ordering cost = Co = $ 7 per order

Inventory holding cost = Ch = $0.90 per can per year

Economic order quantity ( EOQ )

= square root ( 2 x Co x D / Ch )

= square root ( 2 x 7 x 9125/ 0.90 )

= 376.75 ( 377 rounded to nearest whole number )

Demand per week = 25 cans / day x 7 days per week = 175 cans

Lead time = 2 weeks

Therefore , reorder point = Demand / week x Lead time = 175 / week x 2 weeks = 350 cans

ECONOMIC ORDER QUANTITY = 377 CANS

REORDER POINT = 350 CANS

Z value for 90 percent service level = NORMSINV ( 0.90 ) = 1.2815 ( 1.28 ROUNDED TO 2 DECIMAL PLACES )

Standard deviation of demand = 7.55 cans per day

Lead time ( i.e. 2 weeks ) = 14 days

Therefore , standard deviation of demand during lead time = 7.55 x Square root ( 14 ) = 7.55 x 3.741 = 28.2445

Therefore , safety stock = Z value x Standard deviation of demand during led time = 1.2815 x 28.2445 = 36.195 ( 36 rounded to nearest whole number )

Therefore , revised reorder point

= Average daily demand x Lead time ( days ) + safety stock

= 25 x 14 + 36

= 350 + 36

= 386

THE NEW INVENTORY PLAN WILL HAVE A REORDER POINT OF 386 CANS ( HAVING SAFETY STOCK OF 36 CANS)
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