copyright 2011 john wiley & sons, inc. chapter 9 inventory management 9-1

Copyright 2011 John Wiley & Sons, Inc.

Chapter 9

Inventory Management

9-1

Lecture Outline

9-2

• Basics of Inventory Management

• Inventory Systems

• Fixed-Order Quantity System

• Fixed-Time Period Systems

• Independent vs. Dependent Demand

• Managing Supply Chain Inventory

Copyright 2011 John Wiley & Sons, Inc.

What is Inventory?

9-3Copyright 2011 John Wiley & Sons, Inc.

Inventory is quantities of goods in stock

• Manufacturing Inventory– raw materials– component parts– work-in-process (WIP)– finished goods

• Service Inventory– involves all activities carried out in

advance of the customer’s arrival

Inventory Policy

Inventory policy addresses two questions concerning replenishment of inventory:

• When to order?

• How much to Order?


Reasons for Carrying Inventory

• Protect Against Lead Time Demand

• Maintain Independence of Operations

• Balance Supply and Demand

• Buffer Uncertainty

• Economic Purchase Orders


Types of Inventory

• Cycle Stock– inventory for immediate use– typically produced in batches (production cycle)

• Safety Stock– extra inventory carried for uncertainties in

supply and demand– also called buffer stock

• Anticipation Inventory– inventory carried in anticipation of events– smooth out the flow of products in supply chain– also called seasonal or hedge inventory


Types of Inventory Continued

• Pipeline Inventory– inventory in transit – exists because points of supply and

demand are not the same– also called transportation inventory

• Maintenance, Repair and Operating Items (MRO)

– inventories not directly related to product creation


Inventory Costs

• Holding Cost– costs that vary with the amount of inventory held– typically described as a % of inventory value– also called carrying cost

• Ordering Cost– costs involved in placing an order– sometimes called setup cost– inversely related to holding cost

• Shortage Cost– occur when we run out of stock


Inventory Systems

Inventory systems answer the questions: when to order and how much to order

There are two categories:

• Fixed-Order Quantity System– an order of fixed quantity, Q, is placed when

inventory drops to a reorder point, ROP

• Fixed-Time Period System– inventory is checked in fixed time periods, T,

and the quantity ordered varies


Fixed-Order Quantity System

– assumes a constant demand rate of d

– the inventory position, IP, is reduced by a rate of d

– order placed when the reorder point, ROP is reached

– when inventory is received, the IP is increased by the order quantity, Q


Fixed-Order Quantity System Continued

– there is a lead time, L, during which we have to wait for the order

– inventory is checked on a continual basis

– Q is computed as the economic order quantity, EOQ


Fixed-Time Period System

– inventory levels checked in fixed time periods, T

– a target inventory level, R, is restored when order received

– sometimes called Periodic Review System

– quantity ordered varies:

Q = R – IP

where: Q = order quantity

R = target inventory level

IP = inventory position


Fixed-Time Period System


Compare Inventory Systems



There are two main variables to calculate in the Fixed-Order Quantity System:

• Order Quantity (Q)– EOQ is the most Economic Order

Quantity

• Reorder Point (ROP)

Assume:– demand (d), lead time (L), holding cost (H),

stock-out cost (S), and unit price (C) are constant


Economic Order Quantity (EOQ)

The EOQ minimizes the total annual inventory cost

Total Cost = Purchase + Ordering + Holding

TC = DC + (D/Q)S + (Q/2)H

where: TC = Total cost D = Annual demand

C = Unit cost Q = Order quantity

S = Ordering cost H = Holding cost


cost cost cost

EOQ Continued

TC = DC + (D/Q)S + (Q/2)H

• Notice: DC = Annual purchase cost

D/Q = # orders placed per year

Annual ordering cost = # orders/yr x cost/order

Q/2 = average inventory level

Annual holding cost = avg. inventory x cost/unit


EOQ Continued


Solving for EOQ

The EOQ can be found by taking the derivative of TC with respect to Q and set = 0

• Total Cost Equation: TC = DC + (D/Q)S + (Q/2)H

• 1st Derivative:

• Solve for Q optimal:


02

H

Q

DS0

dQ

TC2

H

SD2EOQ

EOQ Example

Given: Demand = 1000 items per monthHolding Cost = 15% of product costOrdering Cost = $300 per orderProduct Cost = $60 per unit

• EOQ

• Orders per year

• Annual Holding Cost


8955.894)60)(15.0(

)300)(000,12(2

H

SD2

4.13895

000,12

Q

D

4028$92

895H

2

Q

Reorder Point (ROP)

The ROP provides enough inventory to ensure that demand is covered during the lead time (L)

ROP = Demand during Lead Time = dL

Given: Lead time = 1 weekd = 250 items/week

ROP = dL = (1) x (250) = 250 items

order is placed when inventory level = 250 items


Safety Stock

• Safety stock is inventory carried in addition to the demand during lead time

• It is common to carry safety stock when demand (d) or lead time (L) are not constant

ROP = demand during lead time + safety stock

ROP = dL + ZkσL

– value of Z for a particular service level (k)

– service level = probability of being in stock

– σL = standard deviation of demand over the lead time9-23Copyright 2011 John Wiley & Sons, Inc.

Safety Stock Example

Given: Desired service level = 95%

Demand = 1000 items per month

Lead time = 1 week

σL2 = 64

Determine the Reorder Point

ROP = dL + ZkσL

ROP =


16.26364645.1)week1)(250(

Economic Production Quantity (EPQ)

• Recall that EOQ assumes the entire order, Q, arrives at once at the end of the lead time

• When produced items are delivered to the operation during completion of the order, it is called economic production quantity (EPQ)

– sometimes called the production rate model– maximum inventory position (and therefore

average inventory) are less than with EOQ– Q and ROP calculated differently


EPQ


Calculating EPQ

Annual Total Cost:

where: Imax = maximum inventory

p = daily production rate

d = average daily demand rate


H2

IS

Q

DDCTC max

p

QdQImax

Calculating EPQ Continued

Substitute Imax into Annual Total Cost:

Use calculus to solve for EPQ:


HQp2

dpS

Q

DDCTC

pd

1H

SD2EPQ

EPQ Example

A manufacturer uses 50,000 wheels per year. The manufacturer produces its own wheels at a rate of 600 per day. Carrying cost per wheel is $1/year and setup cost for a production run is $45. The plant operates 250 days per year.

What is EPQ and Imax?


EPQ Example Continued


598,2

600200

11

)45)(000,50(2

pd

1H

SD2EPQ

732,1600

25982002598

p

QdQImax

Fixed-Time Period Systems

An order is placed after a set time interval, T, to bring inventory up to the target inventory level

Q = R - IP

where: Q = order quantity

R = target inventory level

IP = inventory position at time T

T can be set for a particular Q:


d

QT

Computing Target Inventory

Target inventory should cover:– demand during lead time, L

– demand during review period, T

– safety stock

R = demand during L + demand during T + safety stock

where t = interval over which standard deviation is given


t

TLZdTdLR tk

Fixed-Time Period Example

Given: T = 14 daysd = 30 units per dayL = 7 daysσday = 10 units

no more than 2 stockouts/year

calculate k =


t

TLZdTdLR tk

9231.026

226

6921

147)10(426.1)14)(30()7)(30(R

Independent vs. Dependent Demand

Inventory policy is based on the type of demand

• Independent Demand– demand for a finished product

• Dependent Demand– demand for components parts or subassemblies

– order quantities computed with Material Requirements Planning (MRP)

– relationship between independent and dependent demand is shown in a bill of materials (BOM)


Bill of Materials


Managing Supply Chain Inventory

In addition to the quantitative models, there are a number of practical implications to consider:

• ABC Inventory Classification

• Practical Considerations of EOQ

• Measuring Inventory Performance

• Vendor Managed Inventory


ABC Inventory Classification

ABC system classifies inventory based on its degree of importance

Steps:

1. Determine annual usage or sales for each item

2. Determine % of total usage or sales for each item

3. Rank items from highest to lowest %

4. Classify items into groups:

A: highest value, B: moderate value, C: least valuable


ABC Inventory Classification


Practical Considerations of EOQ

• Lumpy Demand– can use Periodic Order Quantity (POQ) when

demand is not uniform

• EOQ Adjustments– total cost changes little on either side of the EOQ managers can adjust to accommodate needs

• Capacity Constraints– storage capacity and costs should be considered

when ordering large quantities


Measuring Inventory Performance

Common metrics for inventory:

• Units – # units available

• Dollars– dollars tied up in inventory

• Weeks of Supply– (avg. on-hand inventory) / (avg. weekly usage)

• Inventory Turns– (cost of good sold) / (avg. inventory value)


Average Inventory Example

Given a fixed-order quantity model with:Annual Demand (D) = 1,000 units

Order Quantity (Q) = 250 units

Safety Stock (SS) = 50 units

• Average Inventory = Q/2 + SS

= 250/2 + 50 = 175 units

• Inventory Turn = D/(Q/2 + SS)

= 1,000/175 = 5.71 turns per year9-41Copyright 2011 John Wiley & Sons, Inc.

Vendor Managed Inventory (VMI)

VMI arrangements have the vendor responsible for managing the inventory located at a customer’s facility

The vendor:– stocks inventory

– places replenishment orders

– arranges the display

– typically owns inventory until purchased

– is required to work closely with customer


Review

1. Reasons to carry inventory include protecting against lead time demand, maintaining independence, buffering against uncertainty.

2. Inventory types include: cycle stock, safety stock, anticipation, pipeline, and MRO.

3. 3 inventory costs: holding, ordering, & shortage.

4. a. Inventory systems answer: when to order and how much to order.


Review Continued

4. b. Two most common systems are: fixed-order quantity and fixed-time period.

5. Fixed-order quantity systems have a reorder point (ROP). The basic system utilizes the economic order quantity (EOQ), and when production feeds demand, it utilizes the economic production quantity (EPQ).

6. In fixed-time period systems the time between orders, T, is constant, and the order quantity varies. Orders bring the IP to a target level, R.


Review Continued

7. Independent demand is for a finished product and dependent demand is for components.

8. ABC classification defines the degree of importance for inventory.

9. The most common ways to measure inventory are in units, dollars, weeks of supply, and inventory returns.

10.Vendor managed inventory (VMI) is where the vendor is responsible for the inventory located at a customer’s facility.


Copyright 2011 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.

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copyright 2011 john wiley & sons, inc. chapter 9 inventory management 9-1

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