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Chapter 6

Inventory Analysis

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Accurately Matching Demand with Supply is the Key Challenge: Inventories

• ... by 1990 Wal-Mart was already winning an important technological war that other discounters did not seem to know was on. “Wal-Mart has the most advanced inventory technology in the business and they have invested billions in it”. (NYT, Nov. 95).

• WSJ, Aug. 93: Dell Computer stock plunges. The company was sharply off in forecast of demand resulting in inventory writedowns.

• BW 1997:

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Costs of not Matching Supply and Demand

• Cost of overstocking – liquidation, obsolescence, holding

• Cost of under-stocking – lost sales and resulting lost margin

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Where is the Flow Time?

Buffer Operation

Waiting Processing

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Flow Times in White Collar ProcessesSource: J. Blackburn

Industry Process AverageFlow Time

TheoreticalFlow Time

Flow TimeEfficiency

Life Insurance New PolicyApplication

72 hrs. 7 min. 0.16%

ConsumerPackaging

NewGraphicDesign

18 days 2 hrs. 0.14%

CommercialBank

ConsumerLoan

24 hrs. 34 min. 2.36%

Hospital PatientBilling

10 days 3 hrs. 3.75%

AutomobileManufacture

FinancialClosing

11 days 5 hrs 5.60%

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6.1: Operational Flows

Throughput R

Inventory I

I = R T Flow time T = Inventory I / Throughput R

FLOW TIME T

I avg total inv = I input + I in-process + I output

I = Ii + Ip + Io

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6.2: Why do Buffers Build?Why hold Inventory?

• Economies of scale– Fixed costs associated with batches– Quantity discounts– Trade Promotions

• Uncertainty– Information Uncertainty– Supply/demand uncertainty

• Seasonal Variability• Strategic

– Flooding, availability

Cycle/Batch stock

Safety stock

Seasonal stock

Strategic stock

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6.3: Cost of Inventory• Physical holding cost

(out-of-pocket)• Financial holding cost

(opportunity cost)• Low responsiveness

– to demand/market changes

– to supply/quality changes

Holding cost

Inventory Unit Holding Cost =

H = (h + r) C

Physical holding cost Rate of return Cost/flow unit

Example 6.2

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6.4: Economies of Scale: Inventory Build-Up Diagram

R: Annual demand rate,Q: Number per

replenishment order

• Number of orders per year = R/Q.

• I cycle = Q/2

Q

Time t

Inventory Profile:# of jackets in inventory over time.

R = Demand rate

Inventory

T = Ti + Tp = (Q/2)/R + Ip/RExample 6.3

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Economies of Scale: Economic Order Quantity EOQ

R : Demand per year,

S : Setup or Order Cost ($/setup; $/order),

H : Marginal annual holding cost ($/per unit per year),

Q : Order quantity.

C : Cost per unit ($/unit),

r : Cost of capital (%/yr),

h : Physical unit holding cost

($/unit,yr),

H = (h + r) C.

2RSQ

H

Batch Size Q

Total annual costs

H Q/2: Annual holding cost

S R /Q:Annual setup cost

EOQ

Total Cost = S(R/Q) + H(Q/2) + CR

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Economies of Scale:

R = units C = $ / unit

r = %/yr S = $ / order

Example 6.4

Example 6.5

Total annual cost under current plan

EOQ

Total annual cost under current plan

Icycle = Q*/2

TC* Ti = I cycle / R

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Find most economical order quantity: Spreadsheet (Table 6.2, p. 146)

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6.6: Role of Leadtime L

• The two key decisions in inventory management

are:– How much to order?– When to order?

ROP = L * R = Lead Time * Throughput

Example 6.8

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6.8: Levers

Ith = R * Tth

• Reducing critical activity time• Eliminating NVA activities• Redesigning the process to replace

sequential with parallel processing

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Learning Objectives: Batching & Economies of Scale

• Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).

• Average inventory for a batch size of Q is Q/2.• The optimal batch size trades off setup cost and holding cost.• To reduce batch size, one has to reduce setup cost (time).• Square-root relationship between Q and (R, S):

– If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.

– To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.