Inventory Management

Dr. Richard Jerz

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Learning Objectives

Describe• The functions of inventory and basic inventory models

Define• ABC analysis• Record accuracy• Cycle counting• Independent and dependent demand

• Holding, ordering, and setup costs

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Inventory

• One of the most expensive assets of many companies representing as much as 50% of total invested capital

• Operations managers must balance inventory investment and customer service

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Types of Inventory• Raw material

• Purchased but not processed• Work‐in‐process

• Undergone some change but not completed• A function of cycle time for a product

• Finished goods• Completed product awaiting shipment• Goods in transit to warehouses or customers

• Maintenance/repair/operating (MRO)• Necessary to keep machinery and processes productive

• Goods‐in‐transit to warehouses or customers© 2011 rjerz.com9

Functions of Inventory

• To meet anticipated demand• To smooth production requirements• To decouple or separate various parts of the production process

• To protect against stock‐outs• To hedge against inflation• To take advantage of quantity discounts• To permit operations

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Effective Inventory Management

• An accurate system to keep track of inventory• A reliable forecast of demand• Knowledge of lead times• Reasonable estimates of costs, including

• Holding costs• Ordering costs• Shortage costs

• A classification system to help focus on most important inventory

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ABC Classification System

• Divides inventory into three classes based on importance, using annual dollar volume• Class A – very important (high annual dollar volume

• Class B – moderately important (medium annual dollar volume)

• Class C – least important (low annual dollar volume)

• Used to establish policies that focus on the few critical parts and not the many trivial ones

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ABC Analysis

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A ItemsA ItemsA ItemsA Items

B ItemsB ItemsB ItemsB ItemsC ItemsC ItemsC ItemsC Items

Perc

ent o

f ann

ual d

olla

r usa

gePe

rcen

t of a

nnua

l dol

lar u

sage

80 80 –70 70 –60 60 –50 50 –40 40 –30 30 –20 20 –10 10 –

0 0 – | | | | | | | | | |

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percent of inventory itemsPercent of inventory items

Perc

ent o

f ann

ual d

olla

r usa

gePe

rcen

t of a

nnua

l dol

lar u

sage

80 80 –70 70 –60 60 –50 50 –40 40 –30 30 –20 20 –10 10 –

0 0 – | | | | | | | | | |

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percent of inventory itemsPercent of inventory items

ABC Analysis

• Other criteria than annual dollar volume may be used• Anticipated engineering changes• Delivery problems• Quality problems• High unit cost

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Record Accuracy

• Accurate records are a critical ingredient in production and inventory systems

• Necessary to make precise decisions about ordering, scheduling, and shipping

• Stockrooms should be secure

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Cycle Counting

• Items are counted and records updated on a periodic basis

• Often used with ABC analysis to determine cycle

• Has several advantages• Eliminates shutdowns and interruptions• Eliminates annual inventory adjustment• Trained personnel audit inventory accuracy• Allows causes of errors to be identified and corrected

• Maintains accurate inventory records

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Independent vs Dependent Demand 

• Independent demand ‐ the demand for item is independent of the demand for any other item in inventory

• Dependent demand ‐ the demand for item is dependent upon the demand for some other item in the inventory

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Inventory Control

• There is a cost associated with procuringmaterials

• There is a cost associated with holdingmaterials

• These costs are inversely proportional• What is the lowest cost solution?

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The Inventory Cycle

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Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receiveorder

Placeorder

Receiveorder

Lead time

Reorderpoint

Usage rate

Time

Examples of Ordering(Procurement/Setup) Costs

• Fixed• Staffing• Office & Equipment

• Variable• Shipping• Ordering• Setup cost• Lost materials• Receiving & inspection

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Examples of InventoryHolding (Carrying) Costs

• Fixed• Warehouse‐capital• Property taxes• Warehouse‐operating• Personnel

• Variable• Interest (cost of capital)• Insurance• Losses/breakage/theft• Inventory taxes• Rental costs

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Economic Order Quantity (EOQ)

• A mathematical approach to determining how much to order based upon minimizing costs.

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EOQ Solution

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2 2( )( )opt

DS Annual Demand Order or Setup CostQH Holding Cost

Cost Minimization Goal

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Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

Ann

ual C

ost

(optimal order quantity)

TC Q H DQ

S 2

Holding Costs

Total Cost

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Annualcarryingcost

Annualorderingcost

Total cost = +

Q2 H D

QSTC = +

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.

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2 2( )( )opt

DS Annual Demand Order or Setup CostQH Holding Cost

An EOQ Example

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Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 unitsunitsS S = $10= $10 per orderper orderH H = $.50= $.50 per unit per yearper unit per year

Q* =Q* = 22DSDSHHQ* =Q* = 22DSDSHH

22DSDSHH

22DSDSHH

Q* =Q* = 2(1,000)(10)2(1,000)(10)0.500.50Q* =Q* = 2(1,000)(10)2(1,000)(10)0.500.50 = 40,000 = 200= 40,000 = 200 unitsunits= 40,000 = 200= 40,000 = 200 unitsunits

Assumptions of EOQ Model

• 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

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When to Reorder

• 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.

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Safety Stock

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LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qua

ntity

Safety stock

Operations Strategy

• 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

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