11 inventory management (abc & eoq)

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Inventory (ABC & EOQ)

MGNT 3430

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Overview

Inventory Functions and Types

ABC Analysis & Cycle Counting

Fixed Period System

EOQ Inventory Model

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Inventory: Functions & Types

Expensive assetFunctions

Buffer between demand and supplyDecouple production processesHedge against inflationTake advantage of quantity discounts

TypesRaw material: unprocessed by the firmWork-in-process (WIP): partially transformed 4

Overview



Fixed Period System

EOQ Inventory Model

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Inventory ClassificationABC Analysis

Pareto principleClassify items as A, B or C

Annual dollar volume

Taking Inventory Audit of what is in stock/storage

Reconcile purchases and usageOn hand=Purchases - Usage

Cycle countingTaking partial inventory dailyFrequency of counting

A items most frequentC items least frequent 6

ABC Analysis

B5.4%12,50012.501,000#10500

B23%6.4%15,00142.8635030%#10867

B11.3%26,35017.001,550#12760

A33.2%77,000154.00500#11526

A72%38.8%$ 90,000$ 90.001,00020%#10286

Class

Percent of Annual

Dollar Volume

Annual Dollar

Volume=Unit Costx

Annual Volume (units)

Percent of

Number of Items Stocked

Item Stock

Number

C.1%150.60250#10572

C.2%504.421,200#01307

C5%.4%8508.5010050%#01036

C.5%1,200.602,000#14075

C3.7%$ 8,502$ 14.17600#12572

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5,000 items in inventory:500 A items, 1,750 B items, 2,750 C itemsPolicy is to count:

A items every month (20 working days)

B items every quarter (60 days)

C items every six months (120 days)

77/day

2,750/120 = 23/dayEvery 6 months2,750C

1,750/60 = 29/dayEach quarter1,750B

500/20 = 25/dayEach month500A

Number of Items Counted per Day

Cycle Counting PolicyQuantity

Item Class

Cycle Counting

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Overview



Fixed Period System

EOQ Inventory Model

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Fixed-period system

Inventory counted at end of periodOrdering policy is “order up to” type

Set target or par levels for each item

Example: The GAP

Order amount (Q) =

Target – (On-hand inventory) - Earlier orders not yet received + Back orders

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Costs of Inventory

Holding CostsHousing/storageMaterial handling & laborInvestmentShrinkage & obsolescence

Ordering / Setup CostsSupplies, processing time, clerical supportMachine preparation

Unit CostsPurchase cost per item

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Overview



Fixed Period System

EOQ Inventory Model

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1. Demand is known, constant, and independent2. Lead time is known and constant3. Receipt of inventory is instantaneous and

complete4. Quantity discounts are not possible5. Only variable costs are setup and holding6. Stockouts completely avoidable

Important assumptionsBasic EOQ Model

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Inventory Usage Over Time

Figure 12.3

Order quantity = Q (maximum inventory

level)

Inve

ntor

y le

vel

Time

Usage rate Average inventory on hand

Q2

Minimum inventory

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Objective is to minimize total costs

Table 11.5

Ann

ual c

ost

Order quantity

Curve for total cost of holding

and setup

Holding cost curve

Setup (or order) cost curve

Minimum total cost

Optimal order

quantity

Minimizing Total Costs

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Q = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the Inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year

Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)

Annual demandNumber of units in each order

Setup or order cost per order=

= (S)DQ

Annual setup cost = SDQEOQ Model

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Annual holding cost = (Average inventory level) x (Holding cost per unit per year)

Order quantity2

= (Holding cost per unit per year)

= (H)Q2

Annual setup cost = SDQ

Annual holding cost = HQ2

EOQ Model

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Optimal order quantity is found when annual setup cost equals annual holding cost

Annual setup cost = SDQ

Annual holding cost = HQ2

DQ S = HQ

2Solving for Q*

2DS = Q2HQ2 = 2DS/H

Q* = 2DS/H

EOQ Model

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Determine optimal number of needles to orderD = 1,000 unitsS = $10 per orderH = $.50 per unit per year

Q* = 2DSH

Q* = 2(1,000)(10)0.50

= 40,000 = 200 units

EOQ Example: optimal order quantity

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Determine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per orderH = $.50 per unit per year

= N = =Expected number of

orders

DemandOrder quantity

DQ*

N = = 5 orders per year 1,000200

EOQ Example: # of orders/ year

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Determine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year

= T =Expected

time between orders

Number of working days per year

N

T = = 50 days between orders2505

EOQ Example: Order cycle length

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Determine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days

Total (relevant) annual cost = Setup cost + Holding cost

TC = S + HDQ

Q2

TC = ($10) + ($.50)1,000200

2002

TC = (5)($10) + (100)($.50) = $50 + $50 = $100

EOQ example: Total Cost

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Determine optimal number of needles to orderD = 1,500 unitsS = $10 per orderH = $.50 per unit per year

Q* = 2DSH

Q* = 2(1,500)(10)0.50

= 60,000 = 244.9 units

EOQ Example:New optimal order quantity

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Actual EOQ for new demand is 244.9 unitsD = 1,000 units Q* = 244.9 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days

TC = S + HDQ

Q2

TC = ($10) + ($.50)1,500244.9

244.92

1,500 units

TC = $61.24 + $61.24 = $122.48

Only 2% less than the total cost of $125

when the order quantity

was 200

EOQ Robustness: New TC

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Management underestimated demand by 50%D = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days

TC = ($10) + ($.50) = $75 + $50 = $1251,500200

2002

1,500 units

Total annual cost increases by only 25%

EOQ Robustness: 1st Q* but D=1500

TC = S + HDQ

Q2

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• The EOQ model is robust• It works even if all parameters

and assumptions are not met• The total cost curve is relatively

flat in the area of the EOQ

Robustness of EOQ

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Homework

Discussion Questions1, 3, 4

Problems12.1, 12.4, 12.5, 12.8

11 inventory management (abc & eoq)

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