Inventory


Control Systems 1

BM317 Warehousing and


Inventory Management



Lecture 10



Inventory System – Defined



 


Inventory is the stock of any item or resource

used in an organization and can include: raw


materials, finished products, component parts,


supplies, and work-in-process


 


An inventory system is the set of policies and

controls that monitor levels of inventory and


determines what levels should be maintained,


when stock should be replenished, and how


large orders should be



Cost trade-offs in Marketing


s

LOGISTICS


MARKETING



Cost Trade-offs Required in a


Logistics System



Relationship Between Customer


Service and Inventory Investment



0


400


800


1200


1600


2000


75 80 85 90 95 100


Service %


Inventory Investment in units



Selected Financial Data for Manufacturers,


Wholesalers, and Retailers for 1997 ($Millions)



Companies Sales Net Profits Net Profits as a Total Assets Inventory Investment Inventories as a


Percent of Sales Percent of Assets


Manufacturers


Abbott Laboratories ,883 ,094 18% ,061 ,280 11%


Borden, Inc. 1,488 221 15% 2,206 302 14%


The Clorox Company 2,741 298 11% 3,030 212 7%


Dresser Industries, Inc. 7,458 318 4% 5,099 972 19%


Ford Motor Company 153,627 6,920 5% 279,097 5,468 2%


General Electric Company 90,840 8,203 9% 304,012 5,895 2%


General Mills 6,033 422 7% 3,861 389 10%


Goodyear Tire & Rubber Co. 13,065 559 4% 9,917 1,835 19%


Harris Corp. 3,939 133 3% 3,784 604 16%


Honeywell Co. 8,028 471 6% 6,411 1,028 16%


NCR Corp. 6,598 7 0.11% 5,293 489 9%


Newell Co. 3,234 290 9% 3,944 625 16%


Pfizer, Inc. 12,188 2,213 18% 15,336 1,773 12%


Sara Lee Corp. 20,011 ( 523) -3% 10,989 2,882 26%


Xerox Corp. 18,166 1,452 8% 27,732 2,792 10%


Wholesalers and Retailers


Baxter International 6,138 300 5% 8,707 1,208 14%


Bergen Brunswig Corp. 11,661 8 2 1% 2,707 1,309 48%


Dayton Hudson Corp. 27,757 751 3% 14,191 3,251 23%


Fleming Companies, Inc. 15,372 2 5 0.16% 3,924 1,019 26%


Kmart Corporation 32,183 249 1% 13,558 6,367 47%


Nordstrom 4,852 186 4% 2,865 826 29%


Sears, Roebuck & Company 41,296 1,188 3% 38,700 5,044 13%


Supervalu Inc. 17,201 231 1% 4,093 1,116 27%


Wal-Mart Stores, Inc. 117,958 3,526 3% 45,384 16,497 36%


Winn-Dixie 13,219 204 2% 2,921 1,249 43%


Note: Ending inventory figures are used for inventory investment. All figures are for 1997.



Purposes of Inventory



1.


To maintain independence of operations

2.


To meet variation in product demand

3.


To allow flexibility in production scheduling

4.


To provide a safeguard for variation in raw

material delivery time



5.


To take advantage of economic purchase-order

size



6.


To act as a buffer between critical interfaces

within the supply chain



Finished goods


inventory


in field


Finished goods


inventory


at plant


Raw


materials


inventory


In-process


inventory



Purposes of Holding Different Types


of Inventory



Types of Inventory Purpose of holding inventory


Raw material inventory /


Component Parts


Reducing ordering costs or setup costs


Work-in-process


Reducing setup costs, reducing inter-dependencies


between operations


Finished products


Reducing ordering costs or setup costs, allowing


flexibility in production scheduling, protecting


against uncertainites in demand


Facilitating goods in


service systems


Reducing ordering costs or setup costs, protecting


against uncertainites in supply & demand



Independent vs. Dependent Demand



Independent Demand (Demand for the final endproduct


or demand not related to other items)


Dependent


Demand


(Derived demand


items for


component


parts,


subassemblies,


raw materials,


etc)



Finished


product


Component parts



Inventory Costs




Holding (or carrying) costs


Costs for storage, handling, insurance, etc


Setup (or production change) costs


Costs for arranging specific equipment setups, etc


Ordering costs


Costs of someone placing an order, etc


Shortage costs


Costs of canceling an order, etc

Components of Inventory Carrying Costs




Capital


Inventory service


Storage space


Inventory risk

Inventory


carrying


costs


Inventory investment


Insurance


Taxes


Obsolescence


Pilferage


Storage


space costs


Capital


costs


Inventory


service


costs


Inventory


risk costs


Plant warehouses


Public warehouses


Rented warehouses


Company-owned


warehouses


Damage


Relocation costs



Inventory Carrying Costs



 



Two Major Decisions



1.


When to place an order for an item?

2.


How many to order or to produce of this

item?



Six Types of Inventory



1.


Cycle Stock


is inventory required to meet demand under certainty

2.


In-Transit Inventories


are items that are move from one location to another

3.


Safety or Buffer Stock


is held in excess of cycle stock because of uncertainty in demand or

lead time



4.


Speculative Stock


is inventory held for reasons other than satisfying current demand (e.g.

quantities discounts)



5.


Seasonal Stock


is a form of speculative stock that involves the accumulation of

inventory before a season begins



6.


Dead Stock


is the set of items for which no demand had been registered for some

specified period of time



Inventory Systems




Fixed-Order Quantity Model


Event triggered (Example: running out of stock)


Fixed-Time Period Model


Time triggered (Example: Monthly sales call by

sales representative)



Fixed-Order Quantity Model




Demand for the product is constant and uniform

throughout the period




Lead time (time from ordering to receipt) is constant


Price per unit of product is constant


Inventory holding cost is based on average inventory


Ordering or setup costs are constant


All demands for the product will be satisfied (No back

orders are allowed)



Assumptions



Basic Fixed-Order Quantity Model


and Reorder Point Behavior



R = Reorder point


Q = Economic order quantity


L = Lead time



L L


Q Q Q


R



Time


Number


of units


on hand



1. You receive an order quantity Q.


2. Your start using


them up over time. 3. When you reach down to


a level of inventory of R,


you place your next Q


sized order.


4. The cycle then repeats.



200


400


0


Days 10 20 30 40 50 60


Inventory


Order


placed


Order


arrival


Order


placed Average


cycle


inventory


A. Orderquantity of 400 units


Order


arrival



The Effect of Reorder Quantity on


Average Inventory Investment



With Constant Demand and Lead Time



Inventory


Order


placed


Order


arrival


Average


cycle


inventory


Days 10 20 30 40 50 60


0


100


200


B. Orderquantity of 200 units



The Effect of Reorder Quantity on


Average Inventory Investment



With Constant Demand and Lead Time



Average


cycle


inventory


Order


arrival


Order


placed


C. Orderquantity of 600 units


Days 10 20 30 40 50 60


Inventory


0


300


600



The Effect of Reorder Quantity on


Average Inventory Investment



With Constant Demand and Lead Time



Cost Minimization



Ordering Costs



Holding


Costs



Order Quantity (Q)


C


OST



Annual Cost of


Items (DC)



Total Cost



QOPT



By adding the item, holding, and ordering costs together, we


determine the total cost curve, which in turn is used to find


the Q


opt inventory order point that minimizes total costs

By adding the item, holding, and ordering costs together, we


determine the total cost curve, which in turn is used to find


the Q


opt inventory order point that minimizes total costs

Basic Fixed-Order Quantity


(EOQ) Model Formula



H


2


Q


S +


Q


D


TC = DC +



Total


Annual =


Cost


Annual


Purchase


Cost


Annual


Ordering


Cost


Annual


Holding


Cost



+ +



TC=Total annual cost


D =Demand


C =Cost per unit


Q =Order quantity


S =Cost of placing an


order or setup cost


R =Reorder point


L =Lead time


H=Annual holding and


storage cost per unit


of inventory



TC=Total annual cost


D =Demand


C =Cost per unit


Q =Order quantity


S =Cost of placing an


order or setup cost


R =Reorder point


L =Lead time


H=Annual holding and


storage cost per unit


of inventory



Source: Chase, Aquilano, Jacobs, “Operations Management – For Competitive Advantage” Iran McGraw-Hill



Order


Quantity


Number


of Orders


(D/Q)


Ordering


Cost


S * (D/Q)


Inventory


Carrying


Cost


1/2 Q * H


Total


Cost



40


60


80


100


120


140


160


200


300


400


120


80


60


48


40


35


30


24


18


12


$ 4,800


3,200


2,400


1,920


1,600


1,400


1,200


960


720


480


$ 500


750


1,000


1,250


1,500


1,750


2,000


2,500


3,750


5,000


$ 5,300


3,950


3,400


3,170


3,100


3,150


3,200


4,460


4,470


5,480



Cost Trade-offs Required to Determine


the Most Economic Order Quantity



Deriving the EOQ



Using calculus, we take the first derivative of the


total cost function with respect to Q, and set the


derivative (slope) equal to zero, solving for the


optimized (cost minimized) value of Q


opt

Using calculus, we take the first derivative of the


total cost function with respect to Q, and set the


derivative (slope) equal to zero, solving for the


optimized (cost minimized) value of Q


opt

Q =


2DS


H


=


2(Annual Demand)(Order or Setup Cost)


Annual Holding Cost


OPT

Q =


2DS


H


=


2(Annual Demand)(Order or Setup Cost)


Annual Holding Cost


OPT

Reorder point, R = d L



_



Reorder point, R = d L



_



d = average daily demand (constant)


L = Lead time (constant)



_



We also need a


reorder point to


tell us when to


place an order



We also need a


reorder point to


tell us when to


place an order



EOQ Example



Annual Demand = 1,000 units


Days per year considered in average


daily demand = 365


Cost to place an order =


Holding cost per unit per year = .50


Lead time = 7 days


Cost per unit =



Given the information below, what are the EOQ and


reorder point?



Given the information below, what are the EOQ and


reorder point?



EOQ Example – Solution



Q =


2DS


H


=


2(1,000 )(10)


2.50


= 89.443 units or


OPT 90 units

d =


1,000 units / year


365 days / year


= 2.74 units / day



Reorder point, R = d L = 2.74units / day (7days) = 19.18 or



_



20 units



In summary, you place an optimal order of 90 units. In


the course of using the units to meet demand, when


you only have 20 units left, place the next order of 90


units.



In summary, you place an optimal order of 90 units. In


the course of using the units to meet demand, when


you only have 20 units left, place the next order of 90


units.



Price-Break Model Formula



Annual Holding Cost


2(Annual Demand)(Order or Setup Cost)


=


iC


2DS


Q =


OPT

Based on the same assumptions as the EOQ model,


the price-break model has a similar Q


opt formula:

i = percentage of unit cost attributed to carrying inventory


C = cost per unit


Since “C” changes for each price-break, the formula


above will have to be used with each price-break cost


value



Price-Break Example



A company has a chance to reduce their inventory


ordering costs by placing larger quantity orders using


the price-break order quantity schedule below. What


should their optimal order quantity be if this company


purchases this single inventory item with an e-mail


ordering cost of , a carrying cost rate of 2% of the


inventory cost of the item, and an annual demand of


10,000 units?



A company has a chance to reduce their inventory


ordering costs by placing larger quantity orders using


the price-break order quantity schedule below. What


should their optimal order quantity be if this company


purchases this single inventory item with an e-mail


ordering cost of , a carrying cost rate of 2% of the


inventory cost of the item, and an annual demand of


10,000 units?



Order Quantity(units) Price/unit($)


0 to 2,499 .20


2,500 to 3,999 1.00


4,000 or more .98



Price-Break Example Solution



= 1,826 units


0.02(1.20)


2(10,000)( 4)


=


iC


2DS


Q =


OPT

Annual Demand (D)= 10,000 units


Cost to place an order (S)=



First, plug data into formula for each price-break value of “C”


= 2,000 units


0.02(1.00)


2(10,000)( 4)


=


iC


2DS


Q =


OPT

= 2,020 units


0.02(0.98)


2(10,000)( 4)


=


iC


2DS


Q =


OPT

Carrying cost % of total cost (i)= 2%


Cost per unit (C) = .20, .00, .98



Interval from 0 to 2499, the


Qopt value is feasible


Interval from 2500-3999, the


Qopt value is not feasible


Interval from 4000 & more,


the Qopt value is not feasible



Next, determine if the computed Q


opt values are feasible or not

Since the feasible solution occurred in the first pricebreak,


it means that all the other true Q


opt values occur

at the beginnings of each price-break interval. Why?



Since the feasible solution occurred in the first pricebreak,


it means that all the other true Q


opt values occur

at the beginnings of each price-break interval. Why?



0 1826 2500 4000 Order Quantity



Total


annual


costs



So the candidates


for the pricebreaks


are 1826,


2500, and 4000


units



So the candidates


for the pricebreaks


are 1826,


2500, and 4000


units



Because the total annual cost function is


a “u” shaped function



Because the total annual cost function is


a “u” shaped function



Price-Break Example Solution



iC


2


Q


S +


Q


D


TC = DC +



Next, we plug the true Q


opt values into the total cost

annual cost function to determine the total cost under


each price-break



Next, we plug the true Q


opt values into the total cost

annual cost function to determine the total cost under


each price-break



TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)


= ,043.82


TC(2500-3999)= ,041



TC(4000&more)= ,949.20



TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)


= ,043.82


TC(2500-3999)= ,041



TC(4000&more)= ,949.20



Finally, we select the least costly Q


opt, which is this

problem occurs in the 4000 & more interval. In summary,


our optimal order quantity is 4000 units



Finally, we select the least costly Q


opt, which is this

problem occurs in the 4000 & more interval. In summary,


our optimal order quantity is 4000 units



Price-Break Example Solution



A.With variable demand


Inventory


Average


cycle


inventory


Ss(


afety


tock


50)


y


Ave ra ge


inve ntor


(150)


200


100


8 10 20 30 40



{ {


Days

Average Inventory Investment


Under Conditions of Uncertainty



B. With variable lead time


Inventory


Average


cycle


inventory


y


Ave ra ge


inve ntor


(140)


200


100



{


10 12 20 30 40

Day


Ss(


afety


tock


40) s


{

Average Inventory Investment


Under Conditions of Uncertainty



C. With variable demand and lead time


Inventory


Average


cycle


inventory


y


Ave ra ge


inve ntor


(200)


200


100



{


10 12 20 30 40

Day


y Ss(


afet


0


tock


10 )



{


s 8

Average Inventory Investment


Under Conditions of Uncertainty


Fixed-Time Period Model with Safety


Stock Formula



I = current inventory level (includes items on order)


= standard deviation of demand over the review and lead time


z = the number of standard deviations for a specified service probabilit y


d = forecast average daily demand


L = lead time in days


T = the number of days between reviews


q = quantitiy to be ordered


Where :


q = d(T + L) + Z – I



T+L


T+L






q


q == Averaee demand ++ Safety stock Inventory currently  on hand

Fixed-Time Period Model:


Determining the Value of


T+L

 


( )


 



T+L d


i 1


T+L


d


T+L d


2



=


Since each day is independent and is constant,


= (T + L)



i


2


=



 


( )


 



T+L d


i 1


T+L


d


T+L d


2



=


Since each day is independent and is constant,


= (T + L)



i


2


=




The standard deviation of a sequence of

random events equals the square root of the


sum of the variances



Symptoms of Poor Inventory




Increasing numbers of back orders


Increasing dollar investment in inventory with back

orders remaining constant.




High customer turnover rate.


Increasing number of orders being canceled.


Periodic lack of sufficient storage space.


Wide variance in inventory turnover among

distribution centers and major inventory items.




Deteriorating relationships with intermediaries


Large quantities of obsolete items

Ways to Reduce Inventory Levels




Multi-level inventory planning – ABC analysis


Lead time analysis


Delivery time analysis – This may lead to a change in

carriers




Elimination of low turnover and/or obsolete items


Analysis of pack size and discount structure


Encouragement/automation of product substitution


Analysis of customer demand characteristics


Development of a formal sales plan and source demand

ABC Classification System




Items kept in inventory are not of equal

importance in terms of:




dollars invested


profit potential


sales or usage volume


stock-out penalties

0


30


60


30


60



A


B


C



% of


$ Value


% of


Items



So, identify inventory items based on percentage of total


dollar value, where “A” items are roughly top 15 %, “B”


items as next 35 %, and the lower 65% are the “C” items



Relationship Between Customer


Service and Inventory Investment



0


400


800


1200


1600


2000


75 80 85 90 95 100


Service %


Inventory Investment in units



Model of Consumer Reaction


to a Repeated Stockout



Customer


3


Lower


4


Other


size


2


Same


1


Higher


Another


store


6


Ask here


again


5


Special


order


Switch


stores


?


Substitute


?


Switch


brand


?


Substitute


?


Switch


price


?


No


No


Yes


Yes


Yes


Yes


No


No



Inventory Accuracy & Cycle Counting




Inventory accuracy refers to how well the

inventory records agree with physical


count




Cycle Counting is a physical inventory taking

technique in which inventory is


counted on a frequent basis rather than


once or twice a year




Credit:ivythesis.typepad.com



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