- Definition
- Purposes of inventory
- Inventory costs
- Inventory models

Inventory -- stored resource (raw material, work-in-process, finished goods) that is used to satisfy present or future demand

Inventory management -- determine how much to order? When to order?

**ABC Analysis** -- classify inventory into 3 groups according to
its annual dollar volume/usage

Annual dollar volume = annual demand x cost

An example:

A | Top 80% of total dollar volume |

B | Next 15% |

C | Next 5% |

Item# | Annual Demand | Cost | Demand x Cost | % of total cost | Class |

234 | 50 | 200 | 10000 | 10% | B |

170 | 10 | 200 | 2000 | 2% | C |

222 | 100 | 800 | 80000 | 80% | A |

410 | 50 | 100 | 5000 | 5% | B |

160 | 15 | 200 | 3000 | 3% | C |

Total | 100000 |

**Exercise**

Pg.541 Problem 13, 27

1. Smooth-out variations in operation performances

2. Avoid stock out or shortage

3. Safeguard against price changes and inflation

4. Take advantage of quantity discounts

1. Holding or carrying costs: storage, insurance, investment,
pilferage, etc.

Annual holding cost = average inventory level x holding cost per unit per year

= order quantity/2 x holding cost per unit per year

2. Setup or ordering costs: cost involved in placing an order
or setting up the equipment to make the product

Annual ordering cost = no. of orders placed in a year x cost per order

= annual demand/order quantity x cost per order

__EOQ (Economic Order Quantity) Model__

**Assumptions**

1. Order arrives instantly

2. No stockout

3. Constant rate of demand

**What is the order quantity such that the total cost is minimized?**

1. Total cost = holding cost + ordering cost

= (order quantity/2) x holding cost per unit per year + (annual demand/order quantity) x cost per order

2. Optimal order quantity (Q*) is found when annual holding
cost = ordering cost

3. Number of orders = Annual Demand/Q*

4. Time between orders = No. of working days per year / number of orders

5. Reorder point = daily demand x lead time + safety stock

**Example:**

Given:

Annual Demand = 60,000Then, it can be computed:

Ordering cost = $25 per order

Holding cost = $3 per item per year

No. of working days per year = 240

Q* = 1000

Total cost = $3000

Number of orders = 60000/1000 = 60

Time between orders = 240/60 = 4 days

Daily demand = 60000/240 = 250

If lead time = 3 days (lead time < time between orders)

Reorder point = (60000/240)x3=750

Reorder when inventory on hand = 750

If lead time = 5 days (lead time > time between orders)

Reorder point = 250x5 = 1250

Reorder when inventory on hand = 1250-Q*=1250-1000=250

In class exercise

Pg.540, Problems 10

Annual demand = 2000

Ordering cost = $10

Holding cost = $5

EOQ = sqrt(2*2000*10/5) = 89

Annual ordering cost = 2000/89*$10 = $223.6

Annual holding cost = 89/2*$5 = $223.6

**Exercise**

Pg. 539, Problem 1, 7a

1. Total cost = holding + ordering + purchasing

2. Holding cost is a % of the purchasing cost

__Case 1__

Annual Demand =100 per year

Ordering cost = 45 per order

Holding cost = 20% of cost of item

Order quantity |
Cost per item |

50 or less | $18 |

51 to 59 | $16 |

60 or more | $12 |

à Should order 62 units

__Case 2__

Same as case 1 except:

Order quantity |
Cost per item |
EOQ |
Remark |

50 or less | $18 | 50 | |

51 to 99 | $16 | 54 | |

100 or more | $12 | 62 | Infeasible |

Need to compare:

Total cost (Q=54) and Total cost (Q=100)

Total cost (Q=54) = (100/54)x45 + (54/2)x(0.2x16) + 16x100 =1780.53

Total cost (Q=100) = (100/100)x45 + (100/2)x(0.2x12) + 12x100 = 1425

à Order 100 units

__Case 3__

Same as case 1 except:

Order quantity |
Cost per item |
EOQ |
Remark |

55 or less | $18 | 50 | Feasible |

56 to 99 | $16 | 54 | Infeasible |

100 or more | $12 | 62 | Infeasible |

Need to compare:

Total cost (Q=50), Total cost (Q=56) and Total cost (Q=100)

Total cost (Q=50) = (100/50)x45 + (50/2)x(0.2x18) + 18x100 = 1980

Total cost (Q=56) = (100/56)x45 + (56/2)x(0.2x16) + 16x100 =1781.16

Total cost (Q=100) = 1425

à Order 100 units

Pg.540, problem 7b

**Exercise**

Pg. 540, problems 12, 26