Question

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. |

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 Do not round intermediate calculations. Round "z"
value to 2 decimal places and final answer to the nearest whole
number.) |

New reorder point |
cans |

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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