Question

**Optimal Inventory Policy**

The inventory manager has typically ordered a quantity of 800 each time an order is needed for one of their popular tires to take advantage of the discount provided by the supplier and save the company money. The following discount schedule has just been received reflecting recent changes in some of the discount percentages. The manager still maintains that an order quantity of 800 will save the company the most money because of the quantity discount.

Order Quantity |
Discount |
Acquisition Cost |

0-399 |
0% |
80 |

400-799 |
5% |
76 |

800 or more |
10% |
72 |

Last year, for an annual demand of 1600 tires and a lot size of 800 tires which resulted in an acquisition cost of $72, they had a total ordering cost of $82 and a total carrying cost of $17465. They forecast an annual demand of 1600 tires again for this year. Their unit carrying cost per dollar of inventory and their unit ordering cost per order for this year is assumed to be the same as last year.

What is the optimal inventory policy that minimizes total cost for a periodic review system?

Answer #1

Ans

D= 1600

Q= economic order quantity= 800

H= holding cost per unit per annum

P= purchase cost or acquisition cost

(Q/2)*H= 17465

H= 17465/400= 43.7

S= ordering cost per order

(D/Q)*S=82

S= 41

Total Cost (TC)= (Q/2)*H +(D/Q)*S + P*D

the various options as shown below are:

Q | 800 | 400 | 200 |

P | 72 | 76 | 80 |

D | 1600 | ||

H | =17465/400 | ||

S | 41 | ||

TC 800 | =(G3/2)*G7+(G6/G3)*G8+G4*G6 | ||

TC 400 | =(H3/2)*G7+(G6/H3)*G8+H4*G6 | ||

TC 200 | =(I3/2)*G7+(G6/I3)*G8+I4*G6 |

the values are:

Q | 800 | 400 | 200 |

P | 72 | 76 | 80 |

D | 1600 | ||

H | 43.6625 | ||

S | 41 | ||

TC 800 | 132747 | ||

TC 400 | 130496.5 | ||

TC 200 | 132694.3 |

Te answer is 400 units as TC is minimum

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