Question

Sarah's Muffler Shop has one standard muffler that fits a large variety of cars. Sarah wishes to establish a reorder point system to manage inventory of this standard muffler.

Annual demand | 4,500 | mufflers | Ordering cost | $65 | per order |

Standard deviation of daily demand | 6 | mufflers per working day | Service probability | 90 | % |

Item cost | $35 | per muffler | Lead time | 3 | working days |

Annual holding cost | 20 | % of item value | Working days | 300 | per year |

Use the above information to determine the best order size and
the reorder point: Do not round intermediate
calculations. Round "z" value to 2 decimal places and
final answer to the nearest whole number.) |

Best order size | mufflers | |

Reorder point | mufflers |

Answer #1

**Solution:**

**(a) Best Order Size (Q):**

Q = SQRT [(2 x D x Co) / H]

where,

D = Annual demand

Co = Ordering cost

H = Holding cost

Putting the given values in the above formula,

Q = SQRT [(2 x 4500 x $65) / (0.20 x $35)]

Q = 289.09 or 289 *(Rounding off
to the nearest whole number)*

**Best Order Size = 289
mufflers**

**(b) Reorder point
(ROP):**

Using NORMSINV function in MS Excel, value of Z can be determined.

Z = NORMSINV (Service Probability)

Z = NORMSINV (0.90)

Z = 1.28

ROP = (d x L) + [Z x Sigma-d x Sqrt(L)]

where,

d = Daily demand = Annual demand / Number of working days

d = 4500 / 300 = 15 mufflers

L = Lead time

Sigma-d = Standard deviation of daily demand

Putting the given values in the above formula,

ROP = (15 x 3) + [1.28 x 6 x Sqrt(3)]

ROP = 45 + 13.30

ROP = 58.30 or 58 *(Rounding off to the nearest whole
number)*

**Reorder point = 58 mufflers**

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