5 1 Inventory management

Inventory Management Inventory meaning Independent demand VS Dependent demand Types of inventory Functions of inventory Objectives of inventory Requirements for effective inventory

management. Inventory model

Basic EOQ model EPQ model Fixed Time period model Re-order model Single period model

Inventory Is the stock of any item or resources used in an

organization An inventory system is the set of policies and

controls that monitor levels of inventory and determine

what level should be maintained, when stock should be replenished and how large order should be.

In mfg inventory refers to items that contribute to or become part of a firm’s product output

In service inventory refers to the tangible goods to be sold and the supplies necessary to administer the service

Inventory a stock or store of goods

Independent Demand

A

B(4) C(2)

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

Dependent Demand

Independent demand is uncertain. Dependent demand is certain.

Independent vs dependent

Independent demand – finished goods, items that are ready to be sold E.g. a computer

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

Types of Inventories

Raw materials & purchased parts Partially completed goods called

work in progress Finished-goods inventories

(manufacturing firms) or merchandise (retail stores)

Types of Inventories Replacement parts, tools, &

supplies

Goods-in-transit to warehouses or customers

Functions of Inventory

To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stock-outs

Functions of Inventory (Cont’d)

To take advantage of order cycles

To hedge against price increases

To permit operations

To take advantage of quantity discounts

Objective of Inventory Control To achieve satisfactory levels of

customer service while keeping inventory costs within reasonable bounds Level of customer service

Costs of ordering and carrying inventoryInventory turnover is the ratio of average

cost of goods sold to average inventory investment.

Effective Inventory Management

A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of

Holding costs Ordering costs Shortage costs

A classification system

Inventory Counting Systems

Periodic SystemPhysical count of items made at

periodic intervals Perpetual Inventory System

System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

Inventory Counting Systems

Two-Bin System - Two containers of inventory; reorder when the first is empty

Universal Bar Code - Bar code printed on a label that hasinformation about the item to which it is attached 0

214800 232087768

Key Inventory Terms

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

ABC Classification System

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 Models

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

annual cost

Economic production model

Quantity discount model

Assumptions of EOQ Model Only one product is involved

Annual demand requirements known

Demand is even throughout the year

Lead time does not vary

Each order is received in a single delivery

There are no quantity discounts

The Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

Total Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2H D

QS+

Let differentiate TC with respect to Q. Setting the result =0, & solving QdTC/dQ= d QH/2 +d DS/Q = H/2- DS/Q2

H/2- DS/Q2 = 0 or DS/Q2 = H/2 or Q2 H= 2DS or Q= 2DS/HNote the second derivative is positive which indicates a minimum has been obtained.

Cost Minimization Goal

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQH

D

QS

2

Deriving 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.

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

Minimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q2H D

QS=

Economic Production Quantity (EPQ)

Production done in batches or lots Capacity to produce a part

exceeds the part’s usage or demand rate

Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

Economic Run Size

QDS

H

p

p u0

2

Derivation of EPQ Annual carrying cost = I max* H/2 , Imax= Q/P ( p - u) where p = production and u= usage

rate and Q/P is the run time or no of days. Annual carrying cost= QH(p-u)/2p Set up cost = DS/Q As we know the optimum size Q or EPQ occurs in the

trade off between carrying cost and order cost. In other words when

Carrying cost = Order cost.

QH (p-u)/2p = DS/Q

Q = 2DSp/H(p-u)

When to Reorder with EOQ Ordering Reorder Point - When the quantity on

hand of an item drops to this amount, the item is reordered

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

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

Determinants of the Reorder Point

The rate of demand The lead time Demand and/or lead time

variability Stock out risk (safety stock)

Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stockSafety stock reduces risk ofstockout during lead time

Reorder Point

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

ROP

For constant Demand & Lead Time ROP= d L d= Average daily demand L = Lead Time

ROP with safety stock When demand is uncertain ? Of saftey

stock comes Reorder point is ROP= d L+zL

d= Average daily demand L= Lead time Z= number of std deviation L = Std deviation of usage during lead time

zL = amount of safety stock

ROP with safety stock d = di /n Standard deviation of daily demand is d = (di-d) 2/n

d refers to one day if lead time extends over several days we can use statistical premises that the std deviation of a series of independent occurrences is equal to the square root of the sum of the variances.ie

L = 21+ 2

2+ 23+….+ 2

L

To find out Z use formula NORMSINV() or see appendix D

Example Daily demand for a certain product is normally

distributed with a mean of 60 and standard deviation of 7.The source of supply is reliable and maintains a constant lead time of six days.The cost of placing the order is $10 and annual holding cost are $.50 per unit.There are no stock out cost and unfilled orders are filled as soon as order arrives.Assume sales occur over the the entire 365 days of a year.Find the order quantity and rop to satisfy a 95% probability of not stocking out during lead time.

Solution d=60 S= $10 H= $.50 L=6 D= 60*365 d = 7

EOQ = 2DS/H = 2*60*365*10/.5= 876000= 936 units

ROP= d L+zL = 60*6 +1.64*17.15=388 units

L = 21+ 2

2+ 23+….+ 2

L

L = 6*72 =17.15

Fixed-Order-Interval Model Orders are placed at fixed time intervals Fixed time period model generates order

quantities that vary from period to period, depending on usage rate

This generally requires higher safety stock FOIMQ = Average demand over the vulnerable

period+Safety Stock- Inventory currently on hand

Q= d(T+L) + zT+L -I

T= Number of days b2n reviews, T+L = std deviations of demand over the review and lead time

FOIM Daily demand for a product is 10 units with a standard

deviation of 3 units.The review period is 30 days and lead time is 14 days.Mgt has set a policy of satisfying 98 % demand from items in stock.At the beginning of this review period there are 150 units in inventory.How many units should be ordered?

Q= d(T+L) + zT+L -I = 10(30+14) +2.05 (T+L) 2

d –150 =10*44+2.05 (30+14)(3)2-150 440+2.05*19.9-150=331 units

Fixed-Interval Benefits 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 Disadvantages

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

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 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

Optimal Stocking Level

Service Level

So

Quantity

Ce Cs

Balance point

Service level =Cs

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

Example

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

Operations Strategy 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