Inventory ManagementInventory Management

Lecture OutlineLecture Outline Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System

Soal Latihan

What is Inventory?What is Inventory? Stock of items kept to meet future demand for internal customers external customers

Purpose of inventory management how many units to order when to order

Types of InventoryTypes of Inventory Raw materials Purchased parts and supplies Work-in-process (partially completed) products (WIP)

Items being transported Tools and equipment

Inventory and Quality Inventory and Quality ManagementManagement Customers usually perceive Customers usually perceive quality service as quality service as availability of goods they availability of goods they want when they want themwant when they want them

Inventory must be sufficient Inventory must be sufficient to provide high-quality to provide high-quality customer service in TQMcustomer service in TQM

Inventory CostsInventory Costs Carrying costCarrying cost

cost of holding an item in cost of holding an item in inventoryinventory

Ordering costOrdering cost cost of replenishing inventorycost of replenishing inventory

Shortage costShortage cost temporary or permanent loss of temporary or permanent loss of sales when demand cannot be metsales when demand cannot be met

Inventory Control SystemsInventory Control Systems

Continuous system Continuous system (fixed-order-quantity)(fixed-order-quantity)

constant amount constant amount ordered when inventory ordered when inventory declines to declines to predetermined levelpredetermined level

Periodic system Periodic system (fixed-time-period)(fixed-time-period)

order placed for order placed for variable amount after variable amount after fixed passage of timefixed passage of time

Economic Order Quantity Economic Order Quantity (EOQ) Models(EOQ) Models EOQEOQ

optimal order quantity that will optimal order quantity that will minimize total inventory costsminimize total inventory costs

Basic EOQ modelBasic EOQ model Production quantity modelProduction quantity model

Assumptions of Basic EOQ Assumptions of Basic EOQ ModelModel Demand is known with certainty Demand is known with certainty and is constant over timeand is constant over time

No shortages are allowedNo shortages are allowed Lead time for the receipt of Lead time for the receipt of orders is constantorders is constant

Order quantity is received all Order quantity is received all at onceat once

Inventory Order CycleInventory Order Cycle

Demand Demand raterate

TimeTimeLead Lead timetime

Lead Lead timetime

Order Order placedplaced

Order Order placedplaced

Order Order receiptreceipt

Order Order receiptreceipt

Inve

ntor

y Le

vel

Inve

ntor

y Le

vel

Reorder point, Reorder point, RR

Order quantity, Order quantity, QQ

00

EOQ Cost ModelEOQ Cost ModelCCoo - cost of placing order - cost of placing order DD - annual demand - annual demandCCcc - annual per-unit carrying cost - annual per-unit carrying cost QQ - order - order quantityquantity

Annual ordering cost =Annual ordering cost =CCooDDQQ

Annual carrying cost =Annual carrying cost =CCccQQ22

Total cost = +Total cost = +CCooDDQQ

CCccQQ22

EOQ Cost ModelEOQ Cost Model

TC = +CoDQ

CcQ2

= +CoDQ2

Cc

2TCQ

0 = +C0DQ2

Cc

2

Qopt =2CoD

Cc

Deriving Qopt Proving equality of costs at optimal point

=CoDQ

CcQ2

Q2 = 2CoDCc

Qopt =2CoD

Cc

EOQ Cost Model (cont.)EOQ Cost Model (cont.)

Order Quantity, Order Quantity, QQ

Annual Annual cost cost ($)($) Total CostTotal Cost

Carrying Cost =Carrying Cost =CCccQQ22

Slope = 0Slope = 0

Minimum Minimum total total costcost

Optimal orderOptimal order QQoptopt

Ordering Cost =Ordering Cost =CCooDDQQ

EOQ ExampleEOQ ExampleCCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards

QQoptopt = = 22CCooDDCCcc

QQoptopt = =2(150)(10,000)2(150)(10,000)

(0.75)(0.75)

QQoptopt = 2,000 yards = 2,000 yards

TCTCminmin = + = +CCooDDQQ

CCccQQ22

TCTCminmin = + = +(150)(10,000)(150)(10,000)2,0002,000

(0.75)(2,000)(0.75)(2,000)22

TCTCminmin = $750 + $750 = $1,500 = $750 + $750 = $1,500

Orders per year =Orders per year = DD//QQoptopt

== 10,000/2,00010,000/2,000== 5 orders/year5 orders/year

Order cycle time =Order cycle time = 311 days/(311 days/(DD//QQoptopt))== 311/5311/5== 62.2 store days62.2 store days

Production QuantityProduction QuantityModelModel An inventory system in which an order An inventory system in which an order is received gradually, as inventory is is received gradually, as inventory is simultaneously being depletedsimultaneously being depleted

AKA non-instantaneous receipt modelAKA non-instantaneous receipt model assumption that Q is received all at once assumption that Q is received all at once is relaxedis relaxed

p - daily rate at which an order is p - daily rate at which an order is received over time, a.k.a. production received over time, a.k.a. production raterate

d - daily rate at which inventory is d - daily rate at which inventory is demandeddemanded

Production Quantity Model Production Quantity Model (cont.)(cont.)

QQ(1-(1-d/pd/p))

InventoryInventorylevellevel

(1-(1-d/pd/p))QQ22

TimeTime00

OrderOrderreceipt receipt periodperiod

BeginBeginorderorderreceireceiptpt

EndEndorderorder

receiptreceipt

MaximumMaximuminventorinventory levely level

AverageAverageinventorinventory levely level

Production Quantity Model Production Quantity Model (cont.)(cont.)

pp = production rate = production rate dd = demand = demand raterate

Maximum inventory level =Maximum inventory level = QQ - - dd

== QQ 1 - 1 -

QQpp

ddpp

Average inventory level = Average inventory level = 1 - 1 -QQ22

ddpp

TCTC = + 1 - = + 1 -ddpp

CCooDDQQ

CCccQQ22

QQoptopt = =22CCooDD

CCcc 1 - 1 - ddpp

Production Quantity Production Quantity Model: ExampleModel: Example

CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yardsdd = 10,000/311 = 32.2 yards per day = 10,000/311 = 32.2 yards per day pp = 150 yards = 150 yards per dayper day

QQoptopt = = = 2,256.8 yards = = = 2,256.8 yards22CCooDD

CCcc 1 - 1 - ddpp

2(150)(10,000)2(150)(10,000)

0.75 1 - 0.75 1 - 32.232.2150150

TCTC = + 1 - = $1,329 = + 1 - = $1,329ddpp

CCooDDQQ

CCccQQ22

Production run = = = 15.05 days per orderProduction run = = = 15.05 days per orderQQpp

2,256.82,256.8150150

Production Quantity Production Quantity Model: Example (cont.)Model: Example (cont.)

Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 yards

dp

32.2150

Quantity DiscountsQuantity Discounts

Price per unit decreases as Price per unit decreases as order quantity increasesorder quantity increases

TCTC = + + = + + PDPDCCooDDQQ

CCccQQ22

wherewhere

PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand

Quantity Discount Model Quantity Discount Model (cont.)(cont.)

QQoptopt

Carrying cost Carrying cost

Ordering cost Ordering cost

Inve

ntory

cost (

$)In

ventor

y co

st (

$)

QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200

TC TC ((dd2 2 = $6 ) = $6 )

TCTC ( (dd1 1 = $8 )= $8 )

TC TC = ($10 )= ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)

Quantity Discount: Quantity Discount: ExampleExample

QUANTITYQUANTITY PRICEPRICE1 - 491 - 49 $1,400$1,40050 - 8950 - 89 1,1001,10090+90+ 900900

CCoo = = $2,500 $2,500 CCcc = = $190 per computer $190 per computer DD = = 200200

QQoptopt = = = 72.5 PCs = = = 72.5 PCs22CCooDDCCcc

2(2500)(200)2(2500)(200)190190

TCTC = + + = + + PD PD = $233,784 = $233,784 CCooDDQQoptopt

CCccQQoptopt

22

For For QQ = 72.5 = 72.5

TCTC = + + = + + PD PD = $194,105= $194,105CCooDDQQ

CCccQQ22

For For QQ = 90 = 90

Reorder PointReorder Point

Level of inventory at which a new order Level of inventory at which a new order is placed is placed

RR = = dLdLwherewhere

dd = demand rate per period = demand rate per periodLL = lead time = lead time

Reorder Point: ExampleReorder Point: Example

Demand = 10,000 yards/yearDemand = 10,000 yards/yearStore open 311 days/yearStore open 311 days/yearDaily demand = 10,000 / 311 = Daily demand = 10,000 / 311 = 32.154 yards/day32.154 yards/dayLead time = L = 10 daysLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 R = dL = (32.154)(10) = 321.54 yardsyards

Safety Stocks Safety Stocks Safety stockSafety stock

buffer added to on hand buffer added to on hand inventory during lead timeinventory during lead time

Stockout Stockout an inventory shortagean inventory shortage

Service level Service level probability that the inventory probability that the inventory available during lead time will available during lead time will meet demandmeet demand

Variable Demand with a Variable Demand with a Reorder PointReorder Point

ReorderReorderpoint, point, RR

QQ

LTLTTimeTime

LTLT

Inventory level

Inventory level

00

Variable Demand with a Variable Demand with a Reorder Point and Safety Reorder Point and Safety StockStock

ReorderReorderpoint, point, RR

QQ

LTLTTimeTime

LTLT

Inventory level

Inventory level

00Safety Stock

Reorder Point With Reorder Point With Variable DemandVariable Demand

RR = = dLdL + + zzdd L Lwherewhere

dd == average daily demandaverage daily demandLL == lead timelead time

dd == the standard deviation of daily the standard deviation of daily demand demand

zz == number of standard deviationsnumber of standard deviationscorresponding to the service corresponding to the service

levellevelprobabilityprobability

zzdd L L == safety stocksafety stock

Reorder Point for a Reorder Point for a Service LevelService Level

Probability of Probability of meeting demand during meeting demand during lead time = service levellead time = service level

Probability of Probability of a stockouta stockout

RR

Safety stock

ddLLDemandDemand

zd L

Reorder Point for Reorder Point for Variable DemandVariable Demand

The carpet store wants a reorder point The carpet store wants a reorder point with a 95% service level and a 5% with a 95% service level and a 5% stockout probabilitystockout probabilitydd = 30 yards per day= 30 yards per day

LL = 10 days= 10 daysdd = 5 yards per day= 5 yards per day

For a 95% service level, For a 95% service level, zz = 1.65 = 1.65

RR = = dLdL + + zz dd L L

= 30(10) + (1.65)(5)( 10)= 30(10) + (1.65)(5)( 10)= 326.1 yards= 326.1 yards

Safety stockSafety stock = = zz dd L L

= (1.65)(5)( 10)= (1.65)(5)( 10)= 26.1 yards= 26.1 yards

Soal LatihanSoal Latihan

12-12-3636

Inventory Management:Inventory Management: Permintaan mingguan dari sebuah produk dari Perusahaan A adalah

mengikuti sebaran normal dengan rata-rata 250 unit dengan standar deviasi 14 unit. Produk ini dibeli dengan harga $17.50 per unit. “Lead-time” untuk pasokan produk ini adalah 4 minggu. Setiap kali pemesanan dikenakan biaya sebesar $50, dan biaya penyimpanan (carrying cost) per tahunnya adalah 20% dari harga per unit produk. Perusahaan yang anda kelola ini beroperasi selama 5 hari per minggu dan 50 minggu per tahun.

Pertanyaan: Berapa nilai EOQ-nya? Berapa jumlah “safety-stock” untuk produk ini dengan tingkat

perlindungan 99% (nilai Z=2.33)? Jika “lead-time” berubah menjadi 2 minggu, berapa persen terjadi

peningkatan atau penurunan “safety stock”? (Tingkat perlindungan tetap 99%)

Gambarkan fungsi EOQ terhadap waktu pada kasus ini (point a- c) Jika standar deviasi berubah menjadi 7 unit (dan “lead-time” tetap 4

minggu), berapa persen terjadi peningkatan atau penurunan “safety-stock”? Gambarkan fungs EOQ terhadap waktu! (Catatan : Tingkat perlindungan tetap 99%)

12-12-3737