1-1

1

Inventory Control

Chapter 17

1-2

2

Inventory System

Inventory is the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process

An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

1-3

3

Purposes of Inventory

1. To maintain independence of operations

2. To meet variation in product demand

3. To allow flexibility in production scheduling

4. To provide a safeguard for variation in raw material delivery time

5. To take advantage of economic purchase-order size

1-4

4

Inventory Costs

• Holding (or carrying) costs

– Costs for storage, handling, insurance,

etc

• Ordering costs

– Costs of someone placing an order, etc

• Shortage costs

– Costs of canceling an order, etc

1-5

5

Fixed-Order Quantity Model (assumption 1)

• Demand for the product is constant and uniform throughout the period

• Lead time (time from ordering to receipt) is constant

• Price per unit of product is constant

1-6

6

Fixed-Order Quantity Model (assumption 2)

• Inventory holding cost is based on average inventory

• Ordering or setup costs are constant

• All demands for the product will be satisfied (No back orders are allowed)

1-7

7

Basic Fixed-Order Quantity Model and Reorder Point Behavior

R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

1. You receive an order quantity Q.

2. Your start using them up over time. 3. When you reach down to

a level of inventory of R, you place your next Q sized order.

4. The cycle then repeats.

1-8

8

Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D + DC = TC H

2

Q + S

Q

D + DC = TC

Total Annual =Cost

AnnualPurchase

Cost

AnnualOrdering

Cost

AnnualHolding

Cost+ +

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

1-9

9

Cost Minimization Goal

Ordering Costs

HoldingCosts

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

QOPT

1-10

10

Deriving the EOQ

solving for the optimized (cost minimized) value of Qopt

solving for the optimized (cost minimized) value of Qopt

Q = 2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPTQ =

2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPT

Reorder point, R = d L_

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

We also need a reorder point to tell us when to place an order

We also need a reorder point to tell us when to place an order

1-11

11

14

EOQ Example

All-Jeans sells 300 pairs of jeans per month. Holding cost is estimated to be $2 per pair of jeans per year. The production cost per pair of jeans is $20. The ordering cost is $120.

1. What is All-Jeans’ inventory control policy?

2. If the order lead time is 10 days, when should they place order to avoid shortage?

1-12

12

15

Solution

1-13

13

16

In-Class Exercise

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = $15

Determine the economic order quantity and the reorder point.

1-14

14

17

Solution

1-15

15

Price Break (Quantity Discount) Model

• The more you buy, the more you save …

• The unit purchase cost reduces as the quantity increases.

• Given the incentive, how much should you buy?

1-16

16

How to find the best order quantity?

• Calculate the EOQ at each price range

• If all are feasible, pick the one with minimum cost. Stop.

• If some are not feasible (most of the time)– start with the lowest cost– find the minimum feasible quantity and

calculate total cost. The quantity that gives the lowest cost is the answer.

1-17

17

Quantity Discount-Example

A particular raw material is available to a company at three different prices, depending on the size of the order:

Less than 100 kg $20 per kg100 kg to 999 kg $19 per kgmore than 1,000 kg $18 per kg

The cost to place an order is $40. Annual demand is 3,000 kg. Holding cost is 25% of the material cost.

What is the best quantity to buy each time?

1-18

18

Solution

1-19

19

Price-Break Example Problem Data (Part 1)

A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?

A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?

Order Quantity(units) Price/unit($)0 to 2,499 $1.202,500 to 3,999 1.004,000 or more .98

1-20

20

Price-Break Example Solution (Part 2)

units 1,826 = 0.02(1.20)

4)2(10,000)( =

iC

2DS = QOPT

Annual Demand (D)= 10,000 unitsCost to place an order (S)= $4

First, plug data into formula for each price-break value of “C”

units 2,000 = 0.02(1.00)

4)2(10,000)( =

iC

2DS = QOPT

units 2,020 = 0.02(0.98)

4)2(10,000)( =

iC

2DS = QOPT

Carrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, the Qopt value is feasible

Interval from 2500-3999, the Qopt value is not feasible

Interval from 4000 & more, the Qopt value is not feasible

Next, determine if the computed Qopt values are feasible or not

1-21

21

ABC Classification System

• Items kept in inventory are not of equal importance in terms of:

– dollars invested

– profit potential

– sales or usage volume

– stock-out penalties

0

30

60

30

60

AB

C

% of $ Value

% of Use

So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items

1-22

22

Inventory Accuracy and Cycle Counting

• Inventory accuracy refers to how well the inventory records agree with physical count

• Cycle Counting is a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year