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Inventory Management

OPERATIONS MANAGEMENT

BYDR. ASIF MAHMOOD

Institute of Business & Management

University of Engineering and Technology,

Lahore

drasif@uet.edu.pk

Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Inventory: a stock or store of goods

InventoryInventory

Independent demand – finished goods, items that are ready to be sold Demand is uncertain.

E.g. a computer

Dependent demand – components of finished products Demand is certain. E.g. parts that make up the computer

Types of InventoriesTypes of Inventories Raw materials & purchased parts Partially completed goods called

work in progress

Finished-goods inventories (manufacturing firms) or

Merchandise (retail stores)

Replacement parts, tools, & supplies

Goods-in-transit to warehouses or customers

Functions of InventoryFunctions of Inventory Meet anticipated demand Smooth production requirements Decouple operations Protect against stock-outs Take advantage of order cycles Help hedge against price increases Permit operations Take advantage of quantity discountsLevel of customer service vs costs of ordering and

carrying inventory

Inventory Counting SystemsInventory Counting Systems Periodic System

Physical count of items made at periodic intervals

Perpetual Inventory SystemSystem that keeps track of removals from inventory continuously, thus monitoring current levels of each item

Two-Bin System Two containers of inventory;

reorder when the first is empty

Universal Product Code Bar code printed on a label that has

information about the item to which it

is attached 0

214800 232087768

Lead time: time interval between ordering and receiving the order

Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year

Ordering costs: costs of ordering and receiving inventory

Shortage costs: costs when demand exceeds supply

Key Inventory TermsKey Inventory Terms

Classification SystemsClassification SystemsABC ApproachABC Approach

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - mod. important

CC - least important Annual $ value of items

AA

BB

CC

High

Low

Low HighPercentage of Items

Economic order quantity (EOQ) model The order size that minimizes total annual

cost

Economic Order Quantity ModelsEconomic Order Quantity Models

The Inventory CycleThe Inventory Cycle

Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2

H DQ

S+

Total CostTotal Cost

U-Shaped

Linear and positive Non-linear and inverse

Cost Minimization GoalCost Minimization Goal

Carrying and ordering Carrying and ordering costs are equalcosts are equal

Deriving the EOQDeriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Length of order cycle = Q0/D

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

Example 1Example 1 A local distributor for a national tire company

expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying costs are $16 per tire, and ordering costs are $75. The distributor operates 288 days a year.

a.What is the EOQ? (300 tires)

b.How many times per year does the store reorder? (32)

c.What is the length of an order cycle? (nine working days)

Example 2Example 2

Piddling Manufacturing assembles television sets. It purchases 3,600 black and white pictures tubes a year at $65 each. Ordering costs are $31, and annual carrying costs 20% of the purchase price. Compute the optimal quantity and the total annual cost of ordering and carrying the inventory.

Q0 = 131 picture tubes TC = $852+$852 = $1,704

When to Reorder with EOQ When to Reorder with EOQ OrderingOrdering

Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

. Expected Demand during Lead time

+ Safety StockROP =

Optimal Stocking LevelOptimal Stocking Level

Service Level

So

Quantity

Ce Cs

Balance point

Service level =Cs

Cs + CeCs = Shortage cost per unitCe = Excess cost per unit

Order Cycle Service Level - Probability that demand will not exceed supply during lead time.

Example 15Example 15

Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75

Service Level = 75%

Quantity

Ce Cs

Stockout risk = 1.00 – 0.75 = 0.25

Reorder PointReorder Point

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand

Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered

• ROP = Demand (per day/week) X Lead time (day/week)

Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed

intervals May require only periodic checks of

inventory levels Risk of stockout Fill rate – the percentage of demand

filled by the stock on hand

Fixed-Order-Interval ModelFixed-Order-Interval Model

Tight control of inventory items Items from same supplier may yield

savings in: Ordering Packing Shipping costs

May be practical when inventories cannot be closely monitored

Fixed-Interval BenefitsFixed-Interval Benefits

Requires a larger safety stock Increases carrying cost Costs of periodic reviews

Fixed-Interval DisadvantagesFixed-Interval Disadvantages

Single period model: model for ordering of perishables and other items with limited useful lives

Shortage cost: generally the unrealized profits per unit

Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

Single Period ModelSingle Period Model

Continuous stocking levels

Identifies optimal stocking levels

Optimal stocking level balances unit shortage and excess cost

Discrete stocking levels

Service levels are discrete rather than continuous

Desired service level is equaled or exceeded

Single Period ModelSingle Period Model

Too much inventory Tends to hide problems Easier to live with problems than to

eliminate them Costly to maintain

Wise strategy Reduce lot sizes Reduce safety stock

Operations StrategyOperations Strategy