1. Inventory Management - Shared

Inventory Management

Lecture Outline

• Elements of Inventory Management• Inventory Control Systems• Economic Order Quantity Models• Quantity Discounts• Reorder Point• Order Quantity for a Periodic Inventory System

What Is Inventory?

• Stock of items kept to meet future demand• Purpose of inventory management

• how many units to order• when to order

Importance of Inventory

• Balance the advantages and disadvantages of small and large inventories

• Pressures for small inventories– Inventory holding cost– Cost of capital– Storage and handling costs– Taxes, insurance, and shrinkage

Importance of Inventory

• Pressures for large inventories– Customer service– Ordering cost– Setup cost– Labor and equipment utilization– Transportation cost– Payments to suppliers

Reasons for Holding Inventory

• To meet anticipated customer demand• To protect against stock outs• To take advantage of economic order cycles• To maintain independence of operations• To allow for smooth and flexible production

operations• To guard against price increases

In Short,

Buffer against uncertainty in…..

Supply (Raw material inventories)

Production process ( Work in process inventories)&Demand (Finished good inventories)

Supply Chain Management

• Bullwhip effect• demand information is distorted as it moves away

from the end-use customer• higher safety stock inventories to are stored to

compensate• Seasonal or cyclical demand• Inventory provides independence from vendors• Take advantage of price discounts• Inventory provides independence between

stages and avoids work stoppages

Inventory ManagementTo have the correct inventory at the right place at the right time to minimize system costs while satisfying customer service requirements•Raw material/WIP/Finished goods

Inventory PolicyThe strategy, approach, or set of techniques used to determine how to manage inventory

Quality Management in the Supply Chain

• Customers usually perceive quality service as availability of goods they want when they want them

• Inventory must be sufficient to provide high-quality customer service in QM

Type of Inventory

Process stage

Demand Type Others

Raw Materials WIP Finished Goods

Independent Dependent

Spares Consumable

Purpose

CycleSafetySeasonalPipeline

Independent Demand(demand for item is independent of demand for any other item)

Dependent Demand(demand for item is dependent upon the demand for some other item)

Independent vs. Dependent Demand

Independent vs. Dependent Demand..

Item Materials WithIndependent Demand

Materials WithDependent Demand

DemandSource Company Customers Parent Items

MaterialType Finished Goods WIP & Raw Materials

Method ofEstimatingDemand

Forecast & BookedCustomer Orders

Calculated

PlanningMethod EOQ & ROP MRP

Inventory Type : Purpose • Seasonal stocks

– These are accumulated to absorb seasonal fluctuations in supply or demand.

• Cycle stocks– Due to fixed transportation and handling charges or set up

requirements, it is economical to order or produce large quantities at a time.

• Safety stocks– These are built as a hedge against uncertainties in supply or

demand.

• Pipeline stocks– Inventories in-transit.

Inventory Costs

• Carrying cost• cost of holding an item in inventory

• Ordering cost• cost of replenishing inventory

• Shortage cost• temporary or permanent loss of sales when

demand cannot be met

What are these costs made of? How to estimate these?

Terms used in Inventory• Material cost = C (per unit of product)

• Fixed ordering cost = S (a fixed cost of receiving one order)

• Holding cost = H (% of C) – carrying one unit in inventory for a specified period of time i.e. Rs. H/Unit/Year

• Quantity in a lot or batch size = Q – Quantity is either produced or purchased at a time

• Demand per unit time = D – Demand in one 1 year, d = average demand per week, So, D = d *52 / years

Inventory Cost Holding Costs

(H)

• Obsolescence• Insurance• Extra staffing• Interest• Pilferage• Damage• Warehousing• etc.

Ordering Costs (S)

• Supplies• Forms• Order processing• Clerical support• etc.

• Clean-up costs• Re-tooling costs• Adjustment costs• etc.

Setup Costs (S)

Holding cost (H)

• Cost of Capital

• Obsolescence cost

• Handling cost Vary with quantity of product received , ZERO otherwise

• Occupancy cost Vary with quantity of product stored, ZERO otherwise

• Miscellaneous costs

Theft, security, damage, tax, insurance

Inventory Cost

Ordering cost (S)

• Buyer time Time of buyer for placing extra order, ZERO otherwise Internet and communication has reduced this cost significantly

• Receiving costs Administrative work such as purchase order matching with updating

inventory records Quantity dependent should not be included here

• Transportation costs Fixed cost should be included here

Inventory Cost

Shortage Costs

When occurs, company faces two possibilities…..

• It can meet the shortage with some type of rush, special handling or priority shipment

• It cannot meet the shortage at all

So…. It depends on How company handles the problem

?

• Permanent– Lost profits due to unsatisfied demand– Lost profits of future sales

• Temporary (CB)– Backordered, so not necessarily lost– Special clerical & paperwork costs– Extraordinary transportation cost to customer

Shortage Costs

Inventory policy considerations:

• Customer demand: known/random• Replenishment lead time: known/random• Product variety (# of SKUs)• Length of planning horizon• Costs: Order costs Vs Inventory costs• Service level requirements

Inventory management policies/ control systems:

• Periodic review policy• No tracking of inventory position on a regular basis. • Inventory position is reviewed after a fixed period,• Based on a pre-specified order up to level the firm decides the

order size. • Continuous review policy

• As soon as the inventory position goes down a certain pre-specified level the order is placed.

Since most firms have real time inventory information systems in place, the continuous review policy would be the focus.

ABC Analysis

• Stock-keeping units (SKU) • Identify the classes so management can

control inventory levels• A Pareto chart

ABC Classification

• Class A• 5 – 15 % of units• 70 – 80 % of value

• Class B• 30 % of units• 15 % of value

• Class C• 50 – 60 % of units• 5 – 10 % of value

ABC Classification

1 $ 60 90 (60 * 90) 54002 350 403 30 1304 80 605 30 1006 20 1807 10 1708 320 509 510 60

10 20 120

PART UNIT COST ANNUAL USAGE TOTAL VALUE

ABC Classification

9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

TOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE

A

B

C

$85,400

ABC Classification

% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0

ABC Problem

Booker’s Book Bindery divides SKUs into three classes, according to their dollar usage.Calculate the usage values of the following SKUs and determine which is most likely to be classified as class A.

SKU Number Description Quantity Used per Year

Unit Value ($)

1 Boxes 500 3.002 Cardboard

(square feet)18,000 0.02

3 Cover stock 10,000 0.754 Glue (gallons) 75 40.005 Inside covers 20,000 0.056 Reinforcing tape

(meters)3,000 0.15

7 Signatures 150,000 0.45

Seating arrangement (E)

11

1

1

1

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1 1 1 11

1 11

1

1

1

111

2

2

2

2

2

2

22

2

2

Seating arrangement (F)

1 1

1

1

1

1

1

1

1

1 1

1

1

1

1 1 1

111 1

11 1

1 1

1

1

1

1

1

1

1

1

1

Top margin:

Name: Roll No.: Group#: (1 or 2)-------------------------------------------------------------------

Economic Order Quantity (EOQ) Models

• EOQ• optimal order quantity that will minimize

total inventory costs• Basic EOQ model• Production quantity model

Assumptions of Basic EOQ Model

• Demand is known with certainty and is constant over time

• No shortages are allowed• Lead time for the receipt of orders is constant• Order quantity is received all at once

Inventory Order Cycle

Demand rate

TimeLead time

Lead time

Order placed

Order placed

Order receipt

Order receipt

Inve

ntor

y Le

vel

Reorder point, R

Order quantity, Q

0

Average inventory

Q2

EOQ Cost Model

S - cost of placing order D - annual demandH - annual per-unit carrying cost Q - order quantity

Annual ordering cost =SDQ

Annual carrying cost =HQ2

Total cost = +SDQ

HQ2

EOQ Cost Model

TC = +SDQ

HQ2

= – +SDQ2

H2

TCQ

0 = – +SDQ2

H2

Qopt =2SD

H

Deriving Qopt Proving equality of costs at optimal point

=SDQ

HQ2

Q2 =2SD

H

Qopt =2SD

H

EOQ Cost Model

Order Quantity, Q

Annual cost ($) Total Cost

Carrying Cost =HQ2

Slope = 0

Minimum total cost

Optimal order Qopt

Ordering Cost =SDQ

EOQ Example

H = $0.75 per gallon S = $150 D = 10,000 gallons

Qopt =2SD

H

Qopt =2(150)(10,000)

(0.75)

Qopt = 2,000 gallons

TCmin = +SDQ

HQ2

TCmin = +(150)(10,000)

2,000(0.75)(2,000)

2

TCmin = $750 + $750 = $1,500

Orders per year = D/Qopt

= 10,000/2,000= 5 orders/year

Order cycle time = 311 days/(D/Qopt)

= 311/5= 62.2 store days

Production Quantity Model

• Order is received gradually, as inventory is simultaneously being depleted• AKA non-instantaneous receipt model• assumption that Q is received all at once is relaxed

• p - daily rate at which an order is received over time, a.k.a. production rate

• d - daily rate at which inventory is demanded


Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

Beginorder

receipt

Endorder

receipt

Maximuminventory level

Averageinventory level


p = production rate d = demand rate

Maximum inventory level = Q - d

= Q 1 -

Qp

dp

Average inventory level = 1 - Q2

dp

TC = + 1 -dp

SDQ

HQ2

Qopt =2SD

H 1 - dp


S = $0.75 per gallon H = $150 D = 10,000 gallonsd = 10,000/311 = 32.2 gallons per day p = 150 gallons per day

Qopt = = = 2,256.8 gallons2SD

H 1 - dp

2(150)(10,000)

0.75 1 - 32.2150

TC = + 1 - = $1,329dp

SDQ

HQ2

Production run = = = 15.05 days per orderQp

2,256.8150


Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 gallons

dp

32.2150

Quantity Discounts

Price per unit decreases as order quantity increases

TC = + + PDHDQ

SQ2

whereP = per unit price of the itemD = annual demand

Quantity Discount Model

Qopt=72.5

Carrying cost

Ordering cost

Inve

ntor

y co

st ($

)

Q1 = 49 Q2= 90

TC ($900)

TC ($1100)

TC = ($1400) ORDER SIZE PRICE1 - 49 $140050 – 89 $110090+ $900

Quantity Discount

QUANTITY PRICE

1 - 49 $1,40050 - 89 1,100

90+ 900

S = $2,500 H = $190 per TV D = 200 TVs per year

Qopt = = = 72.5 TVs2SDH

2(2500)(200)190

TC = + + PD = $233,784 SDQopt

HQopt

2

For Q = 72.5

TC = + + PD = $194,105SDQ

HQ2

For Q = 90

Reorder Point

• Inventory level at which a new order is placed

R = dLwhere

d = demand rate per periodL = lead time

Reorder Point

Demand = 10,000 gallons/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 gallons/dayLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 gallons

Safety Stock

• Safety stock• buffer added to on hand inventory during lead time

• Stockout • an inventory shortage

• Service level • probability that the inventory available during lead

time will meet demand• P(Demand during lead time <= Reorder Point)

Variable Demand With Reorder Point

Reorderpoint, R

Q

LTTime

LT

Inve

ntor

y le

vel

0

Reorder Point With Safety Stock

Reorderpoint, R

Q

LTTime

LT

Inve

ntor

y le

vel

0Safety Stock

Reorder Point With Variable Demand

R = dL + zd L

where

d = average daily demandL = lead time

d = the standard deviation of daily demand z = number of standard deviations

corresponding to the service levelprobability

zd L = safety stock

Reorder Point For a Service Level

Probability of meeting demand during lead time = service level

Probability of a stockout

R

Safety stock

dLDemand

zd L

Reorder Point For Variable Demand

The paint store wants a reorder point with a 95% service level and a 5% stockout probability

d = 30 gallons per dayL = 10 days

d = 5 gallons per day

For a 95% service level, z = 1.65

R = dL + z d L

= 30(10) + (1.65)(5)( 10)

= 326.1 gallons

Safety stock = z d L

= (1.65)(5)( 10)

= 26.1 gallons

Order Quantity for a Periodic Inventory System

Q = d(tb + L) + zd tb + L - I

where

d = average demand ratetb = the fixed time between ordersL = lead time

d = standard deviation of demand

zd tb + L = safety stockI = inventory level

Fixed periodicity between two orders, T = tb + L

Derivation of optimal ordering frequency (N)

To determine optimum N (or T):

We know that minimum cost occurs at,

Periodic Inventory System

Fixed-Period Model With Variable Demand

d = 6 packages per dayd = 1.2 packagestb = 60 daysL = 5 daysI = 8 packagesz = 1.65 (for a 95% service level)

Q = d(tb + L) + zd tb + L - I

= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 packages

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