1

Inventory ControlInventory Control

Chapter 12

2

Chapter 12Inventory Control

Inventory System Defined

Inventory Costs

Independent vs. Dependent Demand

Basic Fixed-Order Quantity Models

Basic Fixed-Time Period Model- we will omit.

Economic Production Quantity Model- we will omit.

Single Time Period Model- we will omit.

Quantity Discounts-also known as price break models.

3

Inventory SystemDefined

Inventory 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.

4

Purposes of Inventory1. 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.

5

Inventory CostsHolding (or carrying) costs.

Costs for storage, handling, insurance, etc.

Setup (or production change) costs.Costs for arranging specific equipment setups, etc.

Ordering costs.Costs of someone placing an order, etc.

Shortage costs.Costs of canceling an order, etc.

6

Independent vs. Dependent Demand

Independent Demand (Demand not related to other items or the final end-product)

Dependent Demand

(Derived demand items for

component parts,

subassemblies, raw materials,

etc.)

7

Independent Demand

8

9

Classifying Inventory ModelsFixed-Order Quantity Models Event triggered (Example: running out of

stock)

The sale of an item reduces the inventory position to the re order point.

Fixed-Time Period Models Time triggered (Example: Monthly sales call by sales representative)

10

Fixed-Order Quantity Models:Model Assumptions (Part 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.

11

Fixed-Order Quantity Models:Model Assumptions (Part 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.)

12

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

13

Cost Minimization Goal

Ordering Costs

HoldingCosts

QOPT

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

14

Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D + DC = TC

Total Annual Cost =Annual

PurchaseCost

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

15

Deriving the EOQ

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = QOPT

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

16

EOQ Example Problem Data

Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ and reorder point?

17

EOQ Example Solution

Q = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 units

d = 1,000 units / year

365 days / year = 2.74 units / day

Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units

18

Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Figure 12.12

Safety stock reduces risk ofstockout during lead time

19

Reorder Point

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

Figure 12.13

The ROP based on a normalDistribution of lead time demand

20

Special Purpose Model: Price-Break Model Formula

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

iC

2DS = QOPT

Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula:

i = annual percentage of unit cost attributed to carrying inventoryC = cost per unit

21

Price-Break Example Problem Data (Part 1)

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

22

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, start with the lowest price per unit.

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.

23

Price-Break Example Solution (Part 3)

iC 2

Q + S

Q

D + DC = TC

TC(1826)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12,043.82

TC(2500) = $10,041

TC(4000) = $9,949.20

Next, Compare total cost for the feasible root Q and price break Q values.

24

Price-Break Example

Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Total annual costs

Because the total annual cost function is a “u” shaped function.

25

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.