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Inventory Management
OPERATIONS MANAGEMENT
BYDR. ASIF MAHMOOD
Institute of Business & Management
University of Engineering and Technology,
Lahore
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