unit08 - inventory_management

Dr. Rameez Khalid, PMP, CQSSBB Faculty, Department of Management

Institute of Business Administration, Karachi

Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Independent demand is uncertain. Dependent demand is certain.

Inventory: a stock or store of goods

Inventory

2

Types of Inventories

Raw materials & purchased parts Partially completed goods called

work in progress (WIP) Finished-goods inventories

(manufacturing firms) or merchandise (retail stores)

Unit-8: Inventory Management [email protected] 3

Types of Inventories

Replacement parts, tools, & supplies

Goods-in-transit to warehouses or customers


Functions of Inventory

To meet anticipated demand To smooth production requirements To decouple operations To protect against stock-outs To take advantage of order cycles To help hedge against price increases To permit operations To take advantage of quantity discounts


Objective of Inventory Control

To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service

Costs of ordering and carrying inventory

Inventory turnover is the ratio of: average cost of goods sold to average inventory investment.


A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of

Holding costs Ordering costs Shortage costs

A classification system

Effective Inventory Management


Inventory Counting Systems

Periodic System (T or P System) Physical count of items made at periodic intervals

Perpetual Inventory System (Q System) System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

Unit-8: Inventory Management

Inventory Counting Systems (Contd)

Two-Bin System - Two containers of inventory; reorder when the first is empty

Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

0

214800 232087768


Lead time: time interval between ordering and receiving the order

Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year

Ordering costs: costs of ordering and receiving inventory

Shortage costs: costs when demand exceeds supply

Key Inventory Terms


Holding Costs

Obsolescence Insurance Extra staffing Interest Pilferage Damage Warehousing Etc.


Ordering/Setup Costs

Supplies/Freight Incoming QC Order processing Clerical support Etc.


Clean-up costs Re-tooling costs Adjustment costs Etc.

ABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

A - very important B - mod. important C - least important

0 20 40 60 80

100

0 50 100 % of Inventory Items

% A

nnua

l $ U

sage

A

B C

Class % $ Vol % Items A 80 15 B 15 30 C 5 55

Unit-8: Inventory Management

Inventory

Process stage

Demand Type

Number & Value Other

Raw Material WIP Finished Goods Independent

Dependent

A Items B Items C Items

Maintenance Dependent Operating

Inventory Classifications


Cycle Counting

A physical count of items in inventory

Cycle counting management

How much accuracy is needed?

When should cycle counting be performed?

Who should do it?


Fixed order-quantity models Economic order quantity (EOQ) Economic production quantity (EPQ)

or Production order quantity (POQ) Quantity discount

Probabilistic models Fixed order-period models

Help answer the inventory planning questions!

Inventory Models

Economic order quantity (EOQ) model The order size that minimizes total annual cost

Economic production model

Quantity discount model

Economic Order Quantity Models


Only one product is involved

Annual demand requirements known

Demand is even throughout the year

Lead time does not vary

Each order is received in a single delivery

There are no quantity discounts

Assumptions of EOQ Model


The Inventory Cycle

Profile of Inventory Level Over Time

Quantity on hand

Q

Receive order

Place order

Receive order

Place order

Receive order

Lead time

Reorder point

Usage rate

Time

Total Cost

Annual carrying cost

Annual ordering cost

Total cost = +

TC = Q 2 H D Q

S +


Cost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

Annu

al C

ost

(optimal order quantity)

TC Q H DQ

S 2

Holding Costs

22

Deriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Q = 2DSH

= 2(Annual Demand )(Order or Setup Cost )Annual Holding CostOPT


Minimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q

2 H D Q

S =


EOQ A local distributor for a national tire company

expects to sell approx. 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year.

a. EOQ? b. How many Orders? c. Length of an order cycle? d. Total Annual Cost?

25

Production done in batches or lots Capacity to produce a part exceeds the parts

usage or demand rate Assumptions of EPQ are similar to EOQ except

orders are received incrementally during production

Economic Production Quantity (EPQ)


EOQ EPQ Model When To Order

Reorder Point (ROP)

Time

Inventory Level

Lead Time

Optimal Order Quantity (Q*)


EPQ Model Inventory Levels Inventory Level

Time Supply Begins

Supply Ends

Production portion of cycle

Demand portion of cycle with no supply


EPQ Model Inventory Levels

Time

Inventory Level

Production Portion of Cycle

Imax Max. Inventory Q(1- u/p)

Q*

Supply Begins

Supply Ends

Inventory level with no demand

Demand portion of cycle with no supply


Economic Run Size

Q DSH

pp u

02


D = Demand per year S = Setup cost H = Holding cost u = Demand per day p = Production per day

EPQ Model Equations

Optimal Order Quantity

Setup Cost

Holding Cost

= = -

= *

= *

=

Q H* u

p

Q

D Q

S

p *

1

(

0.5 * H * Q - u p

1

) - u p 1

( )

2*D*S

( ) Maximum inventory level

Imax

32

EPQ A toy manufacturer uses 48,000 rubber wheels

per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year.

a. EPQ or POQ or Optimal Run Size? b. Minimum Total Annual Cost? c. Cycle Time? d. Run Time?

33

Answers how much to order & when to order Allows quantity discounts

Reduced price when item is purchased in larger quantities

Other EOQ assumptions apply Trade-off is between lower price & increased

holding cost Buyers Goal:

Select the order quantity that will minimize the total cost.

Quantity Discount Model


Total Costs with Purchasing Cost

Annual carrying cost

Purchasing cost TC = +

Q 2 H

D Q

S TC = +

+ Annual ordering cost

PD +


Total Costs with PD C

ost

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing cost doesnt change EOQ

37

Case1: Constant Holding Costs

OC

EOQ Quantity

Tota

l Cos

t

TCa

TCc

TCb Decreasing Price

HC a,b,c

38

Quantity Discount When D = 816 cases per year, S =$12, and

H=$4 per case per year, determine for the following discounts:

a. Optimal Order Quantity? b. Total Cost?

Range Price 1 to 49 $20 50 to 79 18 80 to 99 17 100 or more 16

39

Quantity Discount


Case2: Holding Cost as Percentage of Purchase Price

Quantity Discount When D = 4000 switches per year, S =$30,

and H=0.40P per unit per year, determine for the following discounts:

a. Optimal Order Quantity? b. Total Cost?

Range Price 1 to 499 $0.90 500 to 999 0.85 1000 or more 0.80


Case2: Holding Cost as Percentage of Purchase Price


When to Reorder with EOQ Ordering

Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered

Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

Service Level - Probability that demand will not exceed supply during lead time.


Determinants of the Reorder Point

The rate of demand The lead time Demand and/or lead time variability Stock-out risk (safety stock)


ROP and Safety Stock

Safety stock

reduces risk of

Stock-out during lead

time

ROP = d x LT

= Expected Demand during Lead time + Safety Stock



ROP = expected demand during LT + Safety Stock

Unit10-Inventory Mgt [email protected] 48

ROP and Safety Stock Service Level = 100% - Stock-out Risk


Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory

levels Risk of stockout Fill rate the percentage of demand filled by the

stock on hand

Fixed-Order-Interval Model


Time

Inventory Level Target maximum

Period Period Period

Fixed Period Model When to Order?

54

Benefits: Items from same supplier may yield savings in:

Ordering Packing Shipping costs

May be practical when inventories cannot be closely monitored

Disadvantages: Requires a larger safety stock Increases carrying cost Costs of periodic reviews

Fixed-Interval Model

55

Too much inventory Tends to hide problems Easier to live with problems than to eliminate

them Costly to maintain

Wise strategy Reduce lot sizes Reduce safety stock

Operations Strategy


REFERENCES

Operations Management William J. Stevenson

Operations Management Barry Render & Jay Heizer

[email protected] 58

Solution: Slide#25 = a. 300 tires; b. 32; c. 9 working days; d. $4800 Slide#33 = a. 2400 wheels; b. $1800; c. 12 days; d. 3 days Slide#39 = a. 100 cases; b. TC100=$13354 Slide#42 = a. 1000 switches; b. TC1000=$3480

unit08 - inventory_management

Documents

inventory management

inventory costs

inventory inventory

inventory items

track of inventory

inventory shortage costs

functions of inventory

store of goods inventory