rachmat a. anggara pmbs, bopr 5301, session 5 o peration m anagement inventory management

Rachmat A. AnggaraPMBS, BOPR 5301, Session 5

Operation Management

INVENTORY MANAGEMENT

INVENTORY??

INVENTORY is…

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

Type 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

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

processes productive Finished goods

Completed product awaiting shipment

Material Flow Cycle..

Input Wait for Wait to Move Wait in queue Setup Run Outputinspection be moved time for operator time time

Cycle time

95% 5%

INVENTORY Management..

How inventory items can be classified How accurate inventory records can

be maintained How inventory cost can be minimized

while keep customer order fulfilled

INVENTORY Management..

• Record Accuracy.– Manual.– Automate.

• Cycle Counting.– Reconciliation of inventory.– ABC analysis system.

• Control of Service Inventories.– Good personnel selection, training, and discipline– Tight control on incoming shipments– Effective control on all goods leaving facility

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#11526A72%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#10572C.2%504.421,200#01307C5%.4%8508.5010050%#01036C.5%1,200.602,000#14075C3.7%$ 8,502$ 14.17600#12572

17.5 %

33.9 %

48.5 %

ABC-Analysis

Pareto rule..A Items

B ItemsC Items

Pe

rce

nt o

f an

nua

l do

llar

usa

ge

80 –

70 –

60 –

50 –

40 –

30 –

20 –

10 –

0 – | | | | | | | | | |

10 20 30 40 50 60 70 80 90 100

Percent of inventory items

Control of Inventory

Can be a critical component of profitability Losses may come from shrinkage or

pilferage Applicable techniques include

1. Good personnel selection, training, and discipline2. Tight control on incoming shipments3. Effective control on all goods leaving facility

Inventory ModelsINPUT MODEL

(Independent)OUTPUT

Demand Type:-Independent-Dependent

Economic Order Quantity Order size

Inventory Cost:-holding

-order/setup-product

Production Order Quantity Reorder point

Forecasted Demand Quantity Discount

Order time

Probabilistic Model Total Inventory Cost

1. Economic Order Quantity

Order quantity = Q

(maximum inventory

level)

Inve

nto

ry le

vel

Time

Usage rate Average inventory on

handQ2

Minimum inventory

Inventory Usage overtime

1. Economic Order QuantityObjective Minimise Cost

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

1. Economic Order Quantity

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 demand

Number of units in each orderSetup or order cost per order

=

= (S)DQ

Calculate Setup Cost

1. Economic Order Quantity

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

Calculate Holding Cost

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

Order quantity

2= (Holding cost per unit per year)

= (H)Q2

1. Economic Order Quantity

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

DQ

S = HQ2

Solving for Q* 2DS = Q2HQ2 = 2DS/H

Q* = 2DS/H

Annual setup cost = SDQ

Annual holding cost = HQ2

1. Economic Order Quantity(Example)

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

Q* =2DS

H

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

0.50= 40,000 = 200 units

1. Economic Order Quantity(Example)

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

1. Economic Order Quantity(Example)

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 annual cost = Setup cost + Holding cost

TC = S + HDQ

Q2

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

2002

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

1. Economic Order Quantity(Reorder Point)

EOQ answers the “how much” question The reorder point (ROP) tells when to

order

ROP =Lead time for a

new order in daysDemand per day

= d x L

d = D

Number of working days in a year

1. Economic Order Quantity(Reorder Point)

Demand = 8,000 DVDs per year250 working day yearLead time for orders is 3 working days

ROP = d x L

d = D

Number of working days in a year

= 8,000/250 = 32 units

= 32 units per day x 3 days = 96 units

2. Production Order Quantity

Used when inventory builds up over a period of time after an order is placed

Used when units are produced and sold simultaneously

2. Production Order QuantityIn

vent

ory

leve

l

Time

Demand part of cycle with no production

Part of inventory cycle during which production (and usage) is taking place

t

Maximum inventory

2. Production Order QuantityQ = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage

ratet = Length of the production run in days

= (Average inventory level) xAnnual inventory holding cost

Holding cost per unit per year

= (Maximum inventory level)/2Annual inventory level

= –Maximum inventory level

Total produced during the production run

Total used during the production run

= pt – dt

2. Production Order QuantityQ = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days

Setup cost = (D/Q)SHolding cost = 1/2 HQ[1 - (d/p)]

(D/Q)S = 1/2 HQ[1 - (d/p)]

Q2 = 2DSH[1 - (d/p)]

Q* = 2DSH[1 - (d/p)]

2. Production Order Quantity(example)

D = 1,000 units p = 8 units per dayS = $10 d = 4 units per dayH = $0.50 per unit per year

Q* = 2DSH[1 - (d/p)]

= 282.8 or 283 hubcaps

Q* = = 80,0002(1,000)(10)

0.50[1 - (4/8)]

3. Quantity Discount Model

Reduced prices are often available when larger quantities are purchased

Trade-off is between reduced product cost and increased holding cost

Total cost = Setup cost + Holding cost + Product cost

TC = S + + PDDQ

QH2

3. Quantity Discount Model

Discount Number Discount Quantity Discount (%)

Discount Price (P)

1 0 to 999 no discount $5.00

2 1,000 to 1,999 4 $4.80

3 2,000 and over 5 $4.75

A typical quantity discount schedule

3. Quantity Discount Model

1. For each discount, calculate Q*, I= holding cost, P= percentage

2. If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount

3. Compute the total cost for each Q* or adjusted value from Step 2

4. Select the Q* that gives the lowest total cost

Steps in analyzing a quantity discount

Q* =2DSIP

3. Quantity Discount Model(example)

Calculate Q* for every discountExample 9

Q1* = = 700 cars order2(5,000)(49)

(.2)(5.00)

Q2* = = 714 cars order2(5,000)(49)

(.2)(4.80)

Q3* = = 718 cars order2(5,000)(49)

(.2)(4.75)

3. Quantity Discount Model(example)

Adjusting Q* for every discount

Q1* = = 700 cars order2(5,000)(49)

(.2)(5.00)

Q2* = = 714 cars order2(5,000)(49)

(.2)(4.80)

Q3* = = 718 cars order2(5,000)(49)

(.2)(4.75)

1,000 — adjusted

2,000 — adjusted

3. Quantity Discount Model(example)

Discount Number

Unit Price

Order Quantity

Annual Product

Cost

Annual Ordering

Cost

Annual Holding

Cost Total

1 $5.00 700 $25,000 $350 $350 $25,700

2 $4.80 1,000 $24,000 $245 $480 $24,725

3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50

Choose the price and quantity that gives the lowest total cost

Buy 1,000 units at $4.80 per unit

4. Probabilistic Model

Used when demand is not constant or certain

Use safety stock to achieve a desired service level and avoid stockouts

ROP = d x L + ss

Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit

x the number of orders per year

4. Probabilistic Model

Number of Units Probability

30 .2

40 .2

ROP 50 .3

60 .2

70 .1

1.0

ROP = 50 units Stockout cost = $40 per frameOrders per year = 6 Carrying cost = $5 per frame per year

4. Probabilistic Model

ROP = 50 units Stockout cost = $40 per frameOrders per year = 6 Carrying cost = $5 per frame per year

Safety Stock

Additional Holding Cost Stockout Cost

Total Cost

20 (20)($5) = $100 $0 $100

10 (10)($5) = $50 (10)(.1)($40)(6) = $240 $290

0 $0 (10)(.2)($40)(6) + (20)(.1)($40)(6) =$960 $960

A safety stock of 20 frames gives the lowest total cost

ROP = 50 + 20 = 70 frames

4. Probabilistic Model

Another method for calculating safety stock..

ROP = demand during lead time + Zsdlt

where Z = number of standard deviationssdlt = standard deviation of demand during lead time

Safety stock

4. Probabilistic ModelExample…

Average demand = m = 350 kitsStandard deviation of demand during lead time = sdlt = 10 kits5% stockout policy (service level = 95%)

Using Appendix I, for an area under the curve of 95%, the Z = 1.65

Safety stock = Zsdlt = 1.65(10) = 16.5 kits

Reorder point = expected demand during lead time + safety stock= 350 kits + 16.5 kits of safety stock= 366.5 or 367 kits

Resume of Inventory ModelMODEL CONDITION FORMULA

Economic Order Quantity

Demand is known, constant, and independent

Lead time is known and constant

Production Order Quantity

units are produced and sold

simultaneously

Quantity Discount

There is quantity discount

Probabilistic Model

demand is not constant or certain

Q* =2DS

H

Q* = 2DSH[1 - (d/p)]

Q* = 2DSIP

ROP = d x L + ss