Inventory

Inventory

Chapter 6

Inventory: is the set of the items that an organization holds for later use by the organization.

An Inventory System is a set of policies that monitors and controls inventory. It determines how much of each item should be kept, when low items should be replenished, and how many items should be ordered or made when replenishment is needed.

Inventory System

The Functions of Inventory• Provide a stock of goods to meet anticipated customer

demand and provide a “selection” of goods• Decouple suppliers from production and production

from distribution• Allow one to take advantage of quantity discounts• To provide a hedge against inflation• To protect against shortages due to delivery variation• To permit operations to continue smoothly with the

use of “work-in-process”

• Higher costs– Item cost (if purchased)– Ordering (or setup) cost

• Costs of forms, clerks’ wages etc.– Holding (or carrying) cost

• Building lease, insurance, taxes etc.

• Difficult to control– Uncertain demand– Uncertain lead time

Disadvantages of Inventory

Types of Inventory

• Raw materials• Purchased parts and supplies• Work-in-process • Component parts• Tools, machinery, and equipment• Finished goods

Raw materialComponent parts

and supplies

Purchasing part

Work-in process In-process (partially completed) products

Tools, machinery, and equipment

Finished goods

Types of Inventory

Independent Demand: are those items that we sell to customers. Ex. Ford Motor Company, their main independent demand will be the cars, trucks and van that they sell.A small part of the independent demand would the parts that they sell to customers.Finished productsBased on market demandRequires forecasting

Dependent Demand: are those items whose demand is determined by other items. When Ford Motors Company has demand for a car, that translates into demand for four tires, one engine, one transmission, and so on. The items used in the production of that car.

Parts that go into the finished productsDependent demand is a known function of independent demandNo forecasting is required

Two forms of Demands

Reasons To Hold Inventory• Meet unexpected,seasonal, cyclical, and

variations demand• Take advantage of price discounts• Hedge against price increases• Quantity discounts (To get a lower price)• To decouple work-centers• To allow flexible production schedule• As a safeguard against variations in delivery time

(lead time)

Visible Costs of Inventory. They are holding, shortage, reordering, and setup cost.Hidden Costs of InventoryCosts result from longer or uncertain lead-time, or by following bad inventory control system

Costs of Inventory

The Visible Cost of Inventory

1. Holding Cost: These are all the cost the organization incurs in the purchase and storing of the inventory. They include the cost of financing the purchase , storage costs, handling costs, taxes, obsolescence, pilferage, breakage, spoilage, reduced flexibility, and opportunity costs. They are also called Carriage cost. High holding cost favor low inventory levels and frequent replacements and vice versa.

2. Setup Cost: This is the cost of switching a production line from making one product to making a different product. Setup cost apply only to items the organization produces itself. High setup cost favors large production runs and the resulting larger inventory and vice versa.

3. Ordering Cost: This is the cost of placing an order for an item the organization purchases. It include placing the order, tracking the order, shipping costs, receiving and inspecting the order and handling the paperwork. High ordering costs favor fewer orders of larger size and resulting large inventory and vice versa.

4. Shortage Costs: This is the cost to the organization of not having an item when it is needed. These costs include loss of goodwill, loss of sale, loss of a customer, loss of profits and late penalties. Many of these costs are difficult or impossible to measure with any accuracy. High shortage cost favor large inventory and vice versa

The Visible Cost of Inventory

Cyclic Inventory ControlInventory control at Ware-Mart-ExampleThe purchasing department is offering 7 alternative cycles

and times (T):1. Order every week, 52 times per year, T=1 week2. Order every second week, 26 times per year, T=2

weeks3. Order every month, 12 times per year, T=1 month4. Order every second month, 6 times per year, T=2,

months5. Order quarterly, 4 times per year, T= 3 months6. Order semiannually, twice per year, T=6 months7. Order every year, once a year, T=1 year

Brent estimates :Yearly demand rate = 12000 pots

Quarterly demand = 3000 pots

Average inventory = 1500 pots

Every day demand = 100 pots

Price/ pots = $6.75

Corporate holding cost = 20% of the purchasing cost for holding cost

Unit Annual holding cost = 0.20 *6.75=$1.35

Forecast for the annual holding cost = 1500 * 1.35 = 2025

Ordering cost is between $25 and $30

Average Ordering cost = $28

Annual Ordering cost = 4*28 = $112

Annual Combined Cost = Annual Ordering Cost + Annual Holding cost = $2025+$112 = $2137

Ware-Mart

ModelWeekly Orders

Bi-Weekly Orders

Monthly Orders

Bi-Monthly Orders

Quarterly Orders

Semi-Annual Orders

Annual Orders

Annual demand D 12,000 12,000 12,000 12,000 12,000 12,000 12,000Cost per unit C $6.75 $6.75 $6.75 $6.75 $6.75 $6.75 $6.75Interest rate to hold i 20% 20% 20% 20% 20% 20% 20%Ordering cost O $28.00 $28.00 $28.00 $28.00 $28.00 $28.00 $28.00Quantity each order D/N 230 461 1,000 2,000 3,000 6,000 12,000Number of orders N 52 26 12 6 4 2 1Unit holding cost H=C*i $1.35 $1.35 $1.35 $1.35 $1.35 $1.35 $1.35Annual holding cost QH/2 $155 $311 $675 $1,350 $2,025 $4,050 $8,100Annual ordering cost NO $1,456 $728 $336 $168 $112 $56 $28Combined cost QH/2+NO $1,611 $1,039 $1,011 $1,518 $2,137 $4,106 $8,128Annual purchase cost DC $81,000 $81,000 $81,000 $81,000 $81,000 $81,000 $81,000Total cost $82,611 $82,039 $82,011 $82,518 $83,137 $85,106 $89,128

Smallest

Order Plans For Pots

$78,000$80,000$82,000$84,000$86,000$88,000$90,000

52 26 12 6 4 2 1

Orders Per Year

• Purpose of the inventory system is to decide how much to order and when

• Objectives of inventory system• Keep enough inventory to meet customer

demand• Control inventory costs

According to that there are different models for the inventory

Model

VariablesTime sequence of orderingQuantity sequence of ordering

Performance measureProfitCostService level

ParametersOrdering costHolding costsStock out costsDemand (Certainty,Uncertainties)

Inventory Control Models

Influence Chart for selecting Inventory Controls Models

Continues review modelAlso known as a Fixed order quantity models– Economic order quantity EOQ– Production order quantity– Quantity discount

Inventory Control Models

Probabilistic

Periodic review model Also known as a Fixed order period models– Single-period models– Multi-period models

Triggered policy Quantity triggered model

Time triggered model

Deterministic

Inventory Controls Models

Probabilistic Model: Where performance measures use expected values in realistic cases which involves uncertainty.

Deterministic Models: are sufficient by ignoring uncertainty , provided the decision maker takes both qualitative and quantitative factors into account.

Continuous Review Models: Assumes that inventory levels are monitored continuously and that orders are placed depending on the level of inventory.

Periodic Review Models: assume that the monitoring is performed only at a stated times, such as monthly or quarterly.

Fixed Order Quantity Models: assume that a constant quantity is order each time an order is placed.

Fixed Order Period Models: assume that a ordering cycle is fixed, such as 1 week or 1 month

Multi period Models: assumes that the orders will be placed repeatedly.

Single Period Models: deals with situations in which only single orders is placed.

Quantity-Triggered Models: specify ordering when the inventory level sinks to a stated quantity.Time-Triggered Models: specify ordering at specific time periods, such as weekly, monthly or quarterly.

• Continuous inventory systems– also known as fixed-order-quantity system– whenever inventory decreases to predetermined

level known as a reorder point, new order is placed– order is for fixed amount (EOQ) that minimizes total

inventory costs

• Periodic inventory systems– also known as fixed-time-period system– inventory on hand is counted at specific time

intervals – after inventory level determined, order is placed

which will bring inventory back to desired level– new order quantity determined each time

Deterministic ModelFixed Order Quantity ModelsEconomic order quantity EOQ

The Economic Order Quantity Model (EOQ)

• EOQ model is a deterministic model with a fixed ordering cycle and fixed quantity ordered.

• The model determines the EOQ that minimizes the combined total cost of ordering and holding inventory over a fixed time interval, often one year.

• Excels what-if capabilities make the EOQ a potentially useful tool by allowing the decision maker to learn about inventory cost structure while performing the analysis.

• The what-if scenario result can be useful inputs to decision making.

Economic Order Quantity (EOQ) Models

• EOQ – the optimal order quantity that will minimize total inventory carry costs

• Basic EOQ model– determines optimal order size that

minimizes the sum of carrying costs and ordering costs

Developing the EOQ Model

Annual DemandUnit Holding CostUnit Ordering Cost

EOQ FormulaOptimum order quantity Q*Minimum annual combined (holding and ordering) cost

•Known and constant demand

•Known and constant lead time

•Instantaneous receipt of material

•No quantity discounts

•Only order (setup) cost and holding cost

•No stock outs

EOQ Assumptions

Parameter Performance measure

Decision Variable

Quantity sequence of ordering

D Annual Demand

C Cost per unit

I interest to hold the Inventory.

H Expressed as a percentage of costs (C*I)

O Ordering costs

Q The Quantity to be ordered

T Length of the Time

N Number of annual order

EOQ Model notations

Unit holding Cost (H)= c * iEOQ or Qopt or Q*=squareroot((2*D*O)/H)

No. of orders (N)=D/EOQAnnual Holding Cost (AHC)=H * EOQ/2Annual ordering Cost (AOC)= O *NCombine Cost (CC)= AHC+ AOCPurchase Cost (PC)= D*CTotal Cost= CC + PCDuration between Orders or Time between orders (T) = No of Working Days/N

HO*D*2 =Q*

EOQ Models

– Optimal order quantity (Qopt) = square root [(2OD) / H ]

• Occurs where total cost is at a minimum• This happens where Holding cost curve

intersects with Ordering cost curve• Is an approximate value• Round to nearest whole number• EOQ model is robust (resilient to errors)

Order Quantity (Order Quantity (Qopt))

Annual CostAnnual Cost

Holding Cost Curve

Holding Cost Curve

Total (Combined) Cost Curve

Total (Combined) Cost Curve

Order (Setup) Cost CurveOrder (Setup) Cost Curve

Optimal Optimal Order Quantity Order Quantity ((Qopt))

EOQ ModelHow Much to Order?

0

500

1000

1500

2000

2500

3000

3500

4000

100 400 700 1000 1300 1600 1900 2200 2500 2800 3100

[(H)(Q)] / 2

[(O)(D)] / Q

[(O)(D)] / Q + [(H)(Q)] / 2

Purchasing cost C $6.75 H 1.35Holding cost (I) 20%Ordering cost O $28.00Demand D 12000

Order Quentity

Number of order per year Holding Cost Order Cost combined cost

100 120 67.5 $3,360.00 $3,427.50400 30 270 $840.00 $1,110.00700 17 472.5 $480.00 $952.50

1000 12 675 $336.00 $1,011.001300 9 877.5 $258.46 $1,135.961600 8 1080 $210.00 $1,290.001900 6 1282.5 $176.84 $1,459.342200 5 1485 $152.73 $1,637.732500 5 1687.5 $134.40 $1,821.902800 4 1890 $120.00 $2,010.003100 4 2092.5 $108.39 $2,200.89

EOQ

The graphical figure shows the combined cost as a function of the order quantity Q.

The annual holding costs are a linear, straight-line function of Q.

The ordering costs are represented by an inverse, diminishing curve.

The combined cost is U-shaped, starting high, decreasing to minimum and then increasing again.

The minimum cost is at the bottom of the U, (intersection of the Holding and Ordering cost) where the slope is zero.

Purchasing cost C $6.75 H 1.35Holding cost (I) 20%Ordering cost O $28.00Demand D 12000

Optimal Q 705.53368Holding cost 476.23524Ordering cost 476.23524Combined cost 952.47047

Number of order per year 17.0084Time between orders 0.058794 0.71 21.17

Optimal EOQ

0

500

1000

1500

2000

2500

3000

3500

4000

100 400 700 1000 1300 1600 1900 2200 2500 2800 3100

Base Case: Order 26 Times a Year

Base Case: Use EOQ Formula

Pots PotsDemand 12,000 Demand 12,000Cost per unit $6.75 Cost per unit $6.75Interest rate to hold 20% Interest rate to hold 20%Ordering cost 28 Ordering cost 28Quantity each order 462 Unit holding cost 1.35Number of orders 26 Quantity each order 706Unit holding cost $1.35 Number of orders $17Annual holding cost $312 Annual holding cost $476Annual ordering cost $728 Annual ordering cost $476Combined cost $1,040 Combined cost $952Annual purchase cost $81,000 Annual purchase cost $81,000Total cost $82,040 Total cost $81,952

6.7Economic Production Lot

(EPL) Size

Fundamental Assumptions of Traditional Manufacturing

• It is expensive to process orders for purchased items, and quantity discounts are available– as a result, orders for parts are placed infrequently, in

large quantities• Setups are lengthy and expensive

– as a result, large batches of each product are made

Production Lot Size

According to traditional thinking, • Setup costs decrease as production lot or batch size

increases• Inventory levels and holding cost increases as batch

size increases• The lot size that minimizes the net cost is called the

Economic Production Lot (EPL)

Kinds of Lots• Production or process lot• Purchase or order quantity• Transfer batch• Delivery quantity

Economic Production Lot Size

• The Economic Production Lot (EPL) size model is a variation of the basic EOQ model.

• A replenishment order is not received in one lump sum as it is in the basic EOQ model.

• Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate).

• This model's variable costs are annual holding cost and annual set-up cost (equivalent to ordering cost).

• For the optimal lot size, annual holding and set-up costs are equal.

Economic Production Lot SizeAssumptions

– Demand occurs at a constant rate of D items per year.

– Production rate is P items per year (and P > D ).– Set-up cost O per run.– Holding cost H per item in inventory per year.– Purchase cost per unit C is constant (no quantity

discount).– Set-up time (lead time) is constant.– Planned shortages are not permitted.

Production, Demand and Inventory

0102030405060

1 2 3 4 5 6 7 8 9 10Time period

Qua

ntity

ProductionDemandInventory

EconomicProductionLot

FluctuatingInventory

EPL or EPQ

Inv

Time

Slope=P-D

Unless you stop production,since you cannot sell the partsat the same or faster rate that you are making them, your inventory will grow. Note: P and D should be in same units

EPL

T1 T2Start Prod.

Inv

Time

Slope=P-D Slope=-D

H

Stop Prod.

Start Prod.

Economic Production lot Size Model

O Ordering Cost

P Production rate

t time need to produce the lot

Q = P x t

t = Q/P

Maximum inventory = ( P x t) – ( D x t ) = ( P – D ) x t

= ( P – D) x Q/P =(1 – D/P) x Q

Average inventory = (1 – D/P) x Q/2

F = 1 – D/P is critical in lot size calculations.

To Establish the model, we use the same EOQ formulas, but when calculating the holding cost,

we replace Q by Q x (1 – D/P) = QF

Annual holding cost = [ Q x ( 1 – D/P)] x C x (i/2) = Q x F x (Ci/2)

Annual setup cost = D/Q x O

To minimize the total combined cost, we use the same EOQ formulas, but Q is Q x (1- D/P) for the holding cost.

The value of Q that minimizes the combined cost available when:

Q(1-D/P)H/2 + DO/Q = QFH/2 + DO/QSo the optimal value of the order quantity Q is

The annual cost of holding and ordering (which are equal) is

SO the minimum annual combined cost is

D/P)-H(12DO =Q*

22

)1( DxOxHxFPDDxOxH

xDxOxHxFPDxDxOxHx 2)1(2

Economic Production Lot Size Model

• Production Build-up = (P-D)• Production Duration = Q/P• Maximum Inventory = (P-D)Q/P or (1-D/P)Q• Average Inventory = (1-D/P)Q/2• Time between production starts = Q/D• Number of Production runs per year = D/Q• Total Annual Cost =

Y(Q) = ADQ

h D P Q

Dc( / )1

2

Setups Holding Purchase

Economic Production Lot Size

D/P)-H(12DO =Q*

What-If Analysis for Microphones

Model

Economic

Production

Demand D 12,000 12000Cost per unit C $6.75 6.75Percent to hold i 20% 0.2Ordering cost O 28 28Production rate P 48,000 48000Lot size Q* =sqrt((2DO)/((Ci)*(1-D/P))) 815 =sqrt((2*C4*C7)/((C5*C6)*(1-C4/C8)))Number of orders N=D/Q 15 =C4/C9Unit holding cost H=C*i $1.35 =C6*C5Annual holding cost AHC=(QH/2)*(1-D/P) $412 =(C9*C11/2)*(1-C4/C8)Annual ordering cost NO $412 =C10*C7Combined cost QH/2*(1-D/P)+NO $825 =C12+C13Annual purchase cost DC $81,000 =C5*C4Total cost $81,825 =C15+C14

Zap Electronics

CASE1: Brent order 26 times a year, so each additional dollar cost CASE1: Brent order 26 times a year, so each additional dollar cost of ordering should increase annual cost by $26.of ordering should increase annual cost by $26.

CASE 2: If the ordering cost goes up by $1, the combined cost CASE 2: If the ordering cost goes up by $1, the combined cost goes by 17 x $1= $17.goes by 17 x $1= $17.

Ordering cost Combined annual cost Ordering cost Combined

annual cost$1,040 $952

20 831.54 26.00 20 816.40 17.0121 857.54 21 833.4122 883.54 22 850.4223 909.54 23 867.4324 935.54 24 884.4425 961.54 25 901.4526 987.54 26 918.4527 1013.54 27 935.4628 1039.54 28 952.4729 1065.54 29 969.4830 1091.54 30 986.4931 1117.54 31 1003.5032 1143.54 32 1020.5033 1169.54 33 1037.5134 1195.54 34 1054.5235 1221.54 35 1071.53

CASE 1: What-if the ordering cost goes up 10%? The ordering cost is $28, so a 10% increase leads to an increase of $2.80. = 26x2.80=72.80

CC=$1039 + $72.80=$1112.80 means increase of 7%.

A 10% increase in ordering cost leads to 7% increase in combined cost.

What about CASE2 ?

% increase in ordering cost

Combined annual cost

% increase in ordering cost


$1,039 $95210% 1111.98 72.80 7.01% 10% 998.96 44.42 4.66%20% 1184.78 20% 1043.3830% 1257.58 30% 1085.9840% 1330.38 40% 1126.9850% 1403.18 50% 1166.5360% 1475.98 60% 1204.7970% 1548.78 70% 1241.8780% 1621.58 80% 1277.8790% 1694.38 90% 1312.89

100% 1767.18 100% 1347.00

CASE 1 : What if the interest rate charged as holding cost i changes ? Only the holding cost changes, and the formula to use is CC= QCi/2 +DO/Q= 1557.6 x i + 728

If the percentages goes to 30%-50% increase, then

CC= 1557.6 x .3 + 728= 467.3 +728= 1195

This is $155 higher than the base-case cost of $1039. To summarize, 50% increase in the percentage results in a 155/1039=14.9% increase in CC.

What about CASE 2 ?

% Increase in Interest rate to hold


Ordering cost % Increase in Interest rate to hold

$1,039 $95210% 883.59 155.59 14.97% 10% 714.35 238.12 25.00%20% 1039.18 155.59 20% 952.4730% 1194.76 155.59 30% 1190.5940% 1350.35 40% 1428.7150% 1505.94 50% 1666.8260% 1661.53 60% 1904.9470% 1817.11 70% 2143.0680% 1972.70 80% 2381.1890% 2128.29 90% 2619.29

100% 2283.88 100% 2857.41

% Increase in quantity each order


% Increase in quantity each order

Combined annual cost$1,039 $952

10% 1070.29 31.12 2.99% 10% 956.80 4.33 0.45%20% 1101.41 62.23 5.99% 20% 968.34 15.87 1.67%30% 1132.53 93.35 8.98% 30% 985.44 32.97 3.46%40% 1163.65 124.47 11.98% 40% 1006.90 54.43 5.71%50% 1194.76 155.59 14.97% 50% 1031.84 79.37 8.33%60% 1225.88 186.71 17.97% 60% 1059.62 107.15 11.25%70% 1257.00 217.82 20.96% 70% 1089.74 137.27 14.41%80% 1288.12 248.94 23.96% 80% 1121.80 169.33 17.78%90% 1319.23 280.06 26.95% 90% 1155.50 203.03 21.32%

100% 1350.35 311.18 29.94% 100% 1190.59 238.12 25.00%

CASE 2 :The minimum cost obtained by using the EOQ is $952.50, so increasing the order quantity by 10% leads to a total cost increase of only $4.30, which is only 0.45% of the base cost.

Changing the order quantity by a small amount has very little effect on the combined cost. And this allow more flexibility in using the EOQ as a guide to decision making.

What about CASE1?

3) The formula are simpler if we use factors instead of percent changes. What if the unit cost C or the interest rate is I changes by a factor of F, F=1.1 corresponding to 10% increase?The annual ordering cost does not changes, but the annual holding cost is multiplied by the factor F, so the formula for the combined cost is CC=AH x F + AO= 311.50 x F +728

4) What if the ordering cost O changes by a factor of K? The annual holding cost remains the same but the annual ordering cost changes by the factor K. The formula to use is CC=AH+AO x K= 311.50 + 728 x K

What- IF Scenarios

Digram 26 Order per Year

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Cahnge Factor

Cost

EOQ1039

Holding

Ordering

Holding Combined cost

Ordering Combined Cost

Pots Pots $1,071 $1,112Demand 12,000 12,000 0.5 883.8 0.5 675.54

Cost per unit $6.75 $6.75 0.6 914.9 0.6 748.34

Interest rate to hold 20% 20% 0.7 946.1 0.7 821.14

Ordering cost 28 28 0.8 977.2 0.8 893.94

Quantity each order 461.54 461.54 0.9 1008.4 0.9 966.74

Number of orders 26 26 1 1039.5 1 1039.54

Unit holding cost $1.35 $1.35 1.1 1070.7 1.1 1112.34

Annual holding cost $312 $312 1.2 1101.8 1.2 1185.14

Annual ordering cost $728 $728 1.3 1133.0 1.3 1257.94

Combined cost $1,071 $1,112 1.4 1164.2 1.4 1330.74

Annual purchase cost $81,000 $81,000 1.5 1195.3 1.5 1403.54

Total cost $82,071 $82,112 1.6 1226.5 1.6 1476.34

1.7 1257.6 1.7 1549.14

F 1.1 1.8 1288.8 1.8 1621.94

k 1.1 1.9 1319.9 1.9 1694.74

2 1351.1 2 1767.54

EOQ Model With Price Breaks

Discount Quantities

An Inventory ordering situation in which there are small price breaks when ordering in quantity. These is called Quantity Discounts.

Quantity discount occur in numerous situations where suppliers provide an incentive for large order quantities by offering a lower purchase cost when items are ordered in larger lots of quantities.

In this section we show how the EOQ model can be used when quantity discount are available.


Discount QuantitiesThe parameters of the model are as:

Yearly Demand ( D ) = 10000 units

Unit ordering cost (O ) =$30

Inventory holding percentage (I ) = 20%

Unit cost is given as follows:

If Q < 600, then C= $7.50If Q < 600, then C= $7.50

If 600 >= Q<=1000 then C=$7.48If 600 >= Q<=1000 then C=$7.48

If 1000 <= Q then C=7.46If 1000 <= Q then C=7.46

The purchasing cost is include in this model because it is not constant its varying with the discount related to the amount of quantity.


Discount QuantitiesTo get the total annual cost, we need to add three annual costs:

Annual holding cost : AH = Q x C x I/2

Annual ordering cost : AO = D x O/Q

Annual purchasing cost : C x D

If Q < 600, then C= $7.50If Q < 600, then C= $7.50

Total = 1000 * 7.5 * 0.2/2 + 10,000 * 30/1000 + 7.5 * 10,000 = 76,050Total = 1000 * 7.5 * 0.2/2 + 10,000 * 30/1000 + 7.5 * 10,000 = 76,050

If 600 >= Q<=1000 then C=$7.48If 600 >= Q<=1000 then C=$7.48

Total = 1000 * 7.48 * 0.2/2 + 10,000 * 30/1000 + 7.48 * 10,000 = 75,848Total = 1000 * 7.48 * 0.2/2 + 10,000 * 30/1000 + 7.48 * 10,000 = 75,848

If 1000.<= Q then C=7.46If 1000.<= Q then C=7.46

Total = 1000 * 7.46 * 0.2/2 + 10,000 * 30/1000 + 7.46 * 10,000 = 75,646Total = 1000 * 7.46 * 0.2/2 + 10,000 * 30/1000 + 7.46 * 10,000 = 75,646

D 10,000 O 30I 20.00%

CIF Q < 600 7.5IF 600 <= Q <= 1000 7.48IF 1000 <= Q 7.46

Quentity C Annual holding

cost

Annual ordering

cost

Annual purchasing

cost

Total cost

400 7.5 300 750 75,000 76,050450 7.5 337.5 666.7 75,000 76,004500 7.5 375 600.0 75,000 75,975550 7.5 412.5 545.5 75,000 75,958600 7.48 448.8 500.0 74,800 75,749650 7.48 486.2 461.5 74,800 75,748700 7.48 523.6 428.6 74,800 75,752750 7.48 561 400.0 74,800 75,761800 7.48 598.4 375.0 74,800 75,773850 7.48 635.8 352.9 74,800 75,789900 7.48 673.2 333.3 74,800 75,807950 7.48 710.6 315.8 74,800 75,826

1000 7.46 746 300.0 74,600 75,6461050 7.46 783.3 285.7 74,600 75,6691100 7.46 820.6 272.7 74,600 75,6931150 7.46 857.9 260.9 74,600 75,7191200 7.46 895.2 250.0 74,600 75,7451250 7.46 932.5 240.0 74,600 75,7731300 7.46 969.8 230.8 74,600 75,8011350 7.46 1007.1 222.2 74,600 75,829

75,400

75,50075,60075,700

75,800

75,90076,000

76,100

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1250

1300

1350

.

EOQ with C = 7.5

Q = SQRT( 2*10,000*30/(7.5*.2)) = 632.45

EOQ with C = 7.48

Q = SQRT( 2*10,000*30/(7.48*.2)) = 633.31

EOQ with C = 7.46

Q = SQRT( 2*10,000*30/(7.46*.2)) = 634.14

When purchase depends on quantity, the total global or overall minimum is either at a point where the slope is zero, as identified by the EOQ formula, or where is a price break.

Minimum at C = 7.48

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