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Inventory BA 339Mellie Pullman

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Inventory Definitions

Inventory vs. Inventory systemDependent vs. Independent

environmentsTypes

Safety StockAnticipation InventoryHedge inventory (unusual events)Transportation or Pipeline Inventory

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Purposes of Inventory

1. Independence of operations.

2. Variation

Product demand

Material Delivery Time

3. Scheduling flexibility

4. Volume Discounts

5. Material price fluctuations

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Inventory Costs

Holding (or carrying) costs

Setup (or production change) costs

Ordering costs.

Shortage costs.

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Inventory Systems

Rules to manage inventory, specifically: timing (when to order) sizing (how much to order)

Continuous Review or Fixed-Order Quantity Models (Q) Event triggered (Example: running out of

stock) Periodic Review or Fixed-Time Period Models (P)

Time triggered (Example: Monthly sales call by sales representative)

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Comparison of Periodic and Continuous Review Systems

Periodic Review Fixed order intervals Variable order sizes Convenient to

administer Inventory position only

required at review

Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review

frequencies Possible quantity discounts Lower, less-expensive

safety stocks

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Inventory costs C = Unit cost or production cost: the

additional cost for each unit purchased or produced.

H = Holding costs: cost of keeping items in inventory(cost of lost capital, taxes and insurance for storage, breakage, etc., handling and storing)

S = Setup or ordering costs: a fixed cost incurred every time you place an order or a batch is produced.

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Total costs of carrying inventory

Assumptions demand is constant and uniform throughout the

period for your products (5 cases per day) Price per unit is constant for the period ($16/case) Inventory holding cost is based on an average cost.

Total Inventory Policy Cost annually= annual purchase cost + annual order cost + annual holding cost

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Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Cost Minimization Goal

Ordering Costs

HoldingCosts

QOPT

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

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Total cost of Inventory Policy

= annual purchase cost (annual demand * Cost/item)+ annual order cost (annual # orders * Cost to order)+ annual holding cost (average units held*cost to carry one unit)

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HQ

SQ

DCDTC

2*

D = yearly demand of unitsC = cost of each unitQ = quantity orderedS = cost to place orderH = average yearly holding cost for each unit = storage+interest*CD/Q = number of orders per yearQ/2 = average inventory held during a given period assuming with start with Q and drop to zero before next order arrives (cycle inventory).

Total Inventory Cost Equation

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Deriving the EOQ :Economic Order Quantity

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

Cost Holding Annual

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

H

2DS = EOQQ

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EOQ Model--Basic Fixed-Order Quantity Model (Q)

R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

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The Reorder Point

Reorder point = (average period demand)*Lead Time periods= d * L

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Another EOQ Example

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

Determine the economic order quantity & reorder point.

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Minor Deviations Here

What causes minor deviations from the ideal order size?

Assumptions behind the regular EOQ Model?

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Variations in lead time

If we have variations in lead time, how should we change the reorder point so we rarely run out?

Reorder Point = Average demand during lead time(d*L) + safety stock (Z* L)

where: d = average daily (or weekly) demandL = Lead time (matching days or weeks)L = standard deviation of demand during lead time. D = standard deviation of demand (days or weeks).

LDL

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Service Level or % of time inventory will meet demand during lead time

Z Value Resulting Service Level

1.28 90%

1.65 95%

2.33 99%

3.08 99.9%

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Example

Annual Demand = 1000 units 250 work days in the year

d=1000/250 = 4 units/day Q= 200 units

L=9 days L = 3 units

z=2 (97.7% likelihood that we won’t run out during lead time)

Reorder point= d*L +z*L = (4*9) + (2*3) = 42 units

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P Method (periodic review)

You have a predetermined time (P) between orders (sales rep comes by every 10 days) or the average time between orders from EOQ = Q/D

How much should you order to bring inventory level up to some predetermined level, R where:

R = restocking level Current Inventory position = IP Order Quantity= R-IP

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Restocking Level Needs to meet most demand situations R= Restocking level

= Average demand during lead time & review period+ safety stock= P+L + z* P+Lwhere:P+L = average demand during lead time and review period z = # of standard dev from mean above the average demand (higher z is lower probability of running out). RP+L = standard deviation of demand during lead time + review period

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ABC Inventory Management

Based on “Pareto” concept (80/20 rule) and total usage in dollars of each item.

Classification of items as A, B, or C based on usage.

Purpose is to set priorities on effort used to manage different SKUs, i.e. to allocate scarce management resources.

SKU: Stock Keeping Unit

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ABC Inventory Management

‘A’ items: 20% of SKUs, 80% of dollars‘B’ items: 30 % of SKUs, 15% of dollars‘C’ items: 50 % of SKUs, 5% of dollarsThree classes is arbitrary; could be any

number.Percents are approximate.Danger: dollar use may not reflect

importance of any given SKU!

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Item

Annual Usage in

Units Unit Cost Dollar Usage

Percentage of Total

Dollar Usage

1

5,000 $ 1.50 $ 7,500 2.9%

2

1,500 8.00 12,000 4.7%

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10,000 10.50 105,000 41.2%

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6,000 2.00 12,000 4.7%

5

7,500 0.50 3,750 1.5%

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6,000 13.60 81,600 32.0%

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5,000 0.75 3,750 1.5%

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4,500 1.25 5,625 2.2%

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7,000 2.50 17,500 6.9%

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3,000 2.00 6,000 2.4%

Total     $ 254,725 100.0%

Example of SKU list for 10 items

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ABC Chart for SKU List

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

3 6 9 2 4 1 10 8 5 7

Item No.

Pe

rce

nt

Usa

ge

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

Cu

mu

lati

ve %

Usa

ge

Percentage of Total Dollar Usage Cumulative Percentage

A B C

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ABC Application

Jewelry StoreFine Dining RestaurantOutdoor RetailerLarge Department Store