inventory management -...
TRANSCRIPT
Inventory Management
Inventory
•Inventory is the stock of any item or resource used in an organization.
•Inventory include: raw materials, finished products, component parts, supplies, and work-in-process
Purposes of Inventory1. 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/Quantity discounts
Types of Inventory
•Raw materials
•Purchased parts and supplies
•Work-in-process (partially completed) products (WIP)
•Items being transported
•Tools and equipment
Inventory Costs
•Holding (or carrying) costs•Costs for storage, handling, insurance, obsolescence, depreciation, opportunity cost of capital,etc•Holding costs tend to favor low inventory levels and frequent replenishment
•Ordering costs•Costs of placing an order, etc
•Shortage costs• temporary or permanent loss of sales when demand cannot be met
Two Forms of Demand
• Dependent• Demand for items used to produce final
products • Tires for autos are a dependent demand item
• Independent• Demand for items used by external customers• Cars, appliances, computers, and houses are
examples of independent demand inventory
E(1)
Independent Demand (Demand for the final end-product or demand not related to other items)
Dependent Demand(Derived demand items for component parts, subassemblies, raw materials, etc)
Finished
product
Component parts
Independent vs. Dependent Demand
The Role of Inventory In Supply Chain Management
•Since demand is usually not known with certainty, it is not possible to produce exactly the amount demanded
•So an additional amount of inventory, called safety or buffer is kept on hand to meet variations in product demand
•The bullwhip effect: The distortion of demand information as it moves away from end-user customer
•This effect causes distributers, manufacturers and suppliers to stock increasingly higher safety stocks
Inventory and Quality Management
•Level of customer service: The ability to meet effectively internal or external customer demand in a timely and efficient manner
•Customer for finished goods perceive quality service as availability of goods they want at the time when they want them
•To provide this level of quality customer service, the tendency is to maintain large stocks of all types of items
•However, there is a cost associated with carrying items in inventory, which creates a trade-off between the quality level of customer service and the cost of that service
Conti..
•As the level of inventory increases to provide better customer service, inventory costs increase, whereas quality-related customer service costs, such as lost sales and loss of customers decrease
•The conventional approach to inventory management is to maintain a level of inventory that reflects a compromise between inventory costs and customer service
•But according to the contemporary “zero defects” philosophy of quality management, the long term benefits of quality in terms of large market share outweigh lower shot-term production-related costs such as inventory costs
Inventory Control System
•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
•There are two basic inventory systems:•Continuous system•Periodic system
Continuous Inventory Systems
•In a continuous inventory system, a continual record of the inventory level for every item is maintained•It is also referred to as a “perpetual system” or a “fixed-order-quantity system”•Whenever the inventory at hand decreases to a predetermined level, referred to as the “reorder point”, a new order is placed to replenish the stock of inventory
Continuous Inventory Systems
•The order that is placed is for a fixed amount that minimizes the total inventory costs
•This amount of order placed is called the “economic order quantity”
•Continuous inventory systems often incorporate information technology tools to improve the speed and accuracy of data entry. E.g. Barcodes
Continuous Inventory Systems
•Since inventory level is continuously monitored, so management always knows the inventory status
•This is advantageous for critical items such as replacement parts or raw material supplies
•However, maintaining a continual record of the amount of inventory on hand can also be costly
Periodic Inventory Systems
•It is also referred to as “fixed-time-period system” or “periodic review system”
•In a periodic inventory system, the inventory on hand is counted at specific time intervals-every week or at the end of each month
•After the inventory in stock is determined, an order is placed for an amount that will bring inventory back up to a desired level
•Since inventory level is not monitored at all during the time interval between orders, little or no record keeping is required
Periodic Inventory Systems
•Disadvantage is less direct control
•Results in larger inventory levels to guard against unexpected stock outs early in the fixed period
•Also requires that a new order quantity be determined each time a periodic order is made
•Used in college library, small retail stores, drug stores, grocery stores, and offices
The ABC Classification System
•The ABC system is a method for classifying inventory according to several criteria including its dollar value to the firm
•About 5 % - 15% of all inventory item account for 70% to 80% of the total dollar value of inventory. These are classifies as class A items•B items represent approximately 30% of total inventory units but only about 15% of the total inventory dollar value
•C items account for 50% - 60% of all inventory units but represent only 5% - 10% of total dollar value
The ABC Classification System
• In ABC analysis each class of inventory requires a different levels of inventory monitoring and control-the higher the value of the inventory, the tighter the control
•Class A items require tight inventory control, minimized safety stocks, accurate demand forecasting and detailed record keeping
•B and C items require less stringent inventory control
•Since carrying costs are usually lower for C items, higher inventory levels can sometimes be maintained with larger safety stocks
The ABC Classification System
•A items require a continuous control system, while for B and C items periodic review system with less monitoring•Items kept in inventory are not of equal importance in terms of:• Dollars invested
• Profit potential
• Sales or usage volume
• Stock-out penalties
Illustration of ABC
Part Unit Cost $ Annual Usage1 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120
The maintenance department for a small manufacturing firm has responsibility for maintaining an inventory of spare parts for the machinery it services. The parts inventory, unit cot and annual usage are as follow:
Part Total Value
% of Total Value
% of Total Quantity
% Cumulativ
e
9 30,600 35.9 6.0 6.0
8 16,000 18.7 5.0 11.0
2 14, 000 16.4 4.0 15.0
1 5,400 6.3 9.0 24.0
4 4,800 5.6 6.0 30.0
3 3,900 4.6 10.0 40.0
6 3,600 4.2 18.0 58.0
5 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.0
7 1,700 2.0 17.0 100.0
The department manager wants to classify the inventory parts according to the ABC system to determine which stocks of parts should most closely be monitored
Conti..
Class Items % of Total Value
% of Total Quantity
A 9, 8, 2 71 15
B 1, 4, 3 16.5 25
C 6, 5, 10, 7 12.5 60
ABC Classification of the items:
The Basic EOQ Model
•In a continuous system, when inventory reaches a specific level, referred to as the reorder point, a fixed amount is ordered•The most widely used and traditional means of determining how much to order in a continuous system is the “Economic Order Quantity (EOQ) Model”•The function of EOQ Model is to determine the optimal order size that minimizes total inventory costs
The Basic EOQ Model - Assumptions
1. Demand is known with certainty and is constant over time
2. No shortages are allowed3. Lead time for the receipt of orders
is constant4. The order quantity is received all at
once
Basic Fixed-Order Quantity Model and Reorder Point Behavior
R = Reorder pointQ = Economic order quantityL = Lead time
L L
Q QQ
R
Time
Numberof unitson 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.
Cost Minimization Goal
Ordering Costs
HoldingCosts
Order Quantity (Q)
COST
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 Qopt 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 Qopt inventory order point that minimizes total costs
EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =CoD
Q
Annual carrying cost =CcQ
2
Total cost = +CoD
Q
CcQ
2
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =CoD
Q
Annual carrying cost =CcQ
2
Total cost = +CoD
Q
CcQ
2
EOQ Cost Model
TC = +CoD
Q
CcQ
2
= – +CoD
Q2
Cc
2
TCQ
0 = – +C0D
Q2
Cc
2
Qopt =2CoD
Cc
Deriving Qopt Proving equality of costs at optimal point
=CoD
Q
CcQ
2
Q2 =2CoD
Cc
Qopt =2CoD
Cc
EOQ Cost Model
Order Quantity, Q
Annual cost ($) Total Cost
Carrying Cost =CcQ
2
Slope = 0
Minimum total cost
Optimal order Qopt
Ordering Cost =CoD
Q
EOQ Example
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
Qopt =2CoD
Cc
Qopt =2(150)(10,000)
(0.75)
Qopt = 2,000 gallons
TCmin = +CoD
Q
CcQ
2
TCmin = +(150)(10,000)
2,000(0.75)(2,000)
2
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5= 62.2 store days
Sum 1
•The ePaint stocks paint in its warehouse and sells it online on its Internet Website. The store stocks several brands of paints; however, its biggest seller is Sharman-Wilson Ironcoat paint. The company wants to determine the optimal order size and total inventory cost for Ironcoat paint given an estimated annual demand of 10,000 gallons of paint, an annual carrying cost of $0.75 per gallon, and an ordering cost of $150 per order. They would also like to know the number of orders that will be made annually and time between orders (i.e. order cycle)
Sum 2
•Electronic Village stocks and sells a particular brand of personal computer. It costs the store $450 each time it places and order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is $170. the store manager estimates that annual demand for the PCs will be 1200 units. Determine the optimal order quantity, total minimum cost and order cycle time.
Sum 3
• The EastCoasters Bicycle Shop operates 364 days a year, closing only on Christmas Day. The shop pays $300 for a particular bicycle purchased from the manufacturer. The annual holding cost per bicycle is estimated to be 25% of the dollar value of inventory. The shop sells an average of 18 bikes per week. The ordering cost for each order is $250. Determine the optimal order quantity and the total minimum cost.
The Production Quantity Model
•In this EOQ model the assumption that orders are received all at once is relaxed
•The order quantity is received gradually is over time and the inventory level is depleted at the same time it is being replenished
•This situation is commonly found when the inventory user is also the producer as in a manufacturing operation where a part is produced to use in larger assembly
Sum 4•Assume that the epaint Store has its own manufacturing facility in which it produces Ironcoat paint. The ordering cost is the cost of setting up the production process to make paint. The manufacturing facility remains open for the same number of days as the store is open and produces 150 gallons of paint per day. Determine the optimal order size, total inventory cost, the length of time to receive an order, the number of orders per year and the maximum inventory level.
Sum 5•I-75 Discount Carpets manufactures Cascade carpet, which it sells in its adjoining showroom store near the interstate. Estimated annual demand is 20,000 yards of carpet with an annual carrying cost of $2.75 per yard. The manufacturing facility operates 360 days and produces 400 yards of carpet per day. The cost of setting up the manufacturing process for a production run is $720. determine the optimal order size, total inventory cost, length of time to receive an order and maximum inventory level.
Quantity Discounts
•A “quantity discount” is a price discount on an item if predetermined numbers of units are ordered•Determining if an order size with a discount is more cost effective than optimal Q is the main task•When a discount price is available, it is associated with a specific order size, which may be different from the optimal order size and the customer must evaluate the trade off between possibly higher carrying costs with the discount quantity versus EOQ cost
Quantity Discounts
Price per unit decreases as order quantity increases
TC = + + PDCoD
Q
CcQ
2
where
P = per unit price of the itemD = annual demand
Quantity Discount Model
Qopt
Carrying cost
Ordering cost
Invento
ry c
ost
($)
Q(d1 ) = 100 Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)
Sum 6•Avtek, a distributor of audio and video equipment, wants to reduce a large stock of televisions. It has offered a local chain of stores a quantity discount pricing schedule, as follows:
Quantity Price1-49 $1,400
50-89 1,100
90+ 900
The annual carrying cost for the stores for a TV is $190, the ordering cost is &2,500, and annual demand for this particular model TV is estimated to be 200 units. The chain wants to determine if it should take advantage of this discount or order the basic EOQ order size.
Quantity Discount
QUANTITY PRICE
1 - 49 $1,40050 - 89 1,100
90+ 900
Co =$2,500
Cc =$190 per TV
D = 200 TVs per year
Qopt = = = 72.5 TVs2CoD
Cc
2(2500)(200)190
TC = + + PD = $233,784 CoD
Qopt
CcQopt
2
For Q = 72.5
TC = + + PD = $194,105CoD
Q
CcQ
2
For Q = 90
Sum 7•The bookstore at Tech purchases jackets emblazoned with the
school name and logo from a vendor. The vendor sells the jackets to the store for $38 a piece. The cost to the bookstore for placing an order is $120 and the annual carrying cost is 25% of the cost of jacket. The bookstore manager estimates that 1700 jackets will be sold during the year. The vendor has offered bookstore the following volume discount schedule. What is the bookstore’s optimal order quantity?
Order Size Discount1-299 0%
300-499 2%
500-799 4%
800+ 5%
Reorder Point
•The “Reorder Point” is the determinant of when to order in a continuous inventory system, i.e. the inventory level at which a new order is placed •Reorder point for basic EOQ model with constant demand and a constant lead time is:
R = dL
Where
d = demand rate per period (daily demand)
L = Lead Time
Example of Reorder Point with Constant Demand and Lead Time
•The ePaint Store is open 311 days per year. If annual demand is 10,000 gallons of Ironcoat paint and the lead time to receive an order is 10 days. Determine the reorder point for paint.
Stockout, Safety Stock and Service Level
•Stockout: An inventory shortage
•Safety Stock: A buffer added to the inventory on hand during lead time
•Service Level: the service level is the probability that the amount of inventory on hand during the lead time is sufficient to meet the expected demand-i.e. that the customer will e served
•For E.g. A service level of 90% means that there is a 0.90 probability that the demand will be met during the lead time, and the probability that a stockout will occur is 10%
Variable Demand With Reorder Point
Reorderpoint, R
Q
LTTime
LT
Inven
tory
level
0
Reorder Point With Safety Stock
Reorderpoint, R
Q
LTTime
LT
Inven
tory
level
0
Safety Stock
Reorder Point With Variable Demand
R = dL + zd L
where
d= average daily demandL= lead time
d= the standard deviation of daily demand z= number of standard deviations
corresponding to the service levelprobability
zd L= safety stock
Reorder Point For a Service Level
Probability of meeting demand during lead time = service level
Probability of a stockout
R
Safety stock
dLDemand
zd L
Reorder Point For Variable Demand
The paint store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 gallons per dayL = 10 days
d = 5 gallons per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= 326.1 gallons
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 gallons
Sum 8 (Reorder Point with Variable Demand)
•Kelly’s Tavern serves Shamrock draft beer to its customers. The daily demand for beer is normally distributed, with an average of 20 gallons and a standard deviation of 4 gallons. The lead time required to receive an order of beer from the local distributor is 12 days. Determine the safety stock and reorder point if the restaurant wants to maintain a 90% service level. What would be the increase in the safety stock if a 95% service level were desired?
Sum 9
•The amount of denim used daily by the Southwest Apparel Company in its manufacturing process to make jeans is normally distributed with an average of 4000 yards of denim and a standard deviation of 600 yards. The lead time required to receive an order of denim from the textile mill is constant 7 days. Determine the safety stock and reorder point if the company wants to limit the probability of a stock out and work stoppage to 5%? What level of service would a safety stock of 2000 yards provide?
Order Quantity For Periodic Inventory System
•A periodic inventory system is one in which the time between the orders is constant and the order size varies
• Small retailers often use this system of inventory management; E.g. Drugstore
• In this case the vendors who provide stock of materials make periodic visits-every few weeks or every month-and count the stock of inventory on hand
• If the inventory is exhausted or at some predetermined reorder point, a new order will be placed for an amount of inventory that will bring the inventory level back up to the desired level
Order Quantity For Periodic Inventory System
• In periodic inventory system, usually the manager does not monitor the inventory level between vendor visits but instead will rely on the vendor to take inventory
•Since the items are generally of low value, larger safety stocks will not pose a significant cost
•However, if the inventory becomes exhausted early in the time period between visits, resulting in a stockout that will not be remedied until the next scheduled order
Order Quantity For Periodic Inventory System
• If the demand rate and lead time are constant, then the fixed-period model will have a fixed-order quantity that will be made at specified time intervals, which is same as the fixed-order (basic EOQ) model
•But the fixed-period model reacts differently than the fixed-order model when the demand is variable
Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd tb + L - I
where
d = average demand ratetb = the fixed time between ordersL = lead time
d = standard deviation of demand
zd tb + L = safety stockI = inventory level
Periodic Inventory System
Fixed-Period Model With Variable Demand
d = 6 packages per dayd = 1.2 packagestb = 60 daysL = 5 daysI = 8 packagesz = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 packages
Sum 10
•KVS Pharmacy fills prescriptions for a popular children’s antibiotic, Amoxycilin. The daily demand for Amoxycilin is normally distributed with a mean of 200 ounces and a standard deviation of 80 ounces. The vendor for the pharmaceutical firm that supplies the drug calls the drugstore’s pharmacist every 30 days and checks the inventory of Amoxycilin. During a call the druggist indicated the store had 60 ounces of the antibiotic in stock. The lead time to receive an order is four days. Determine the order size that will enable the drug store to maintain a 99% service level.
Sum 11
•Food Place Market stocks frozen pizzas in a refrigerated display case. The average daily demand for the pizzas is normally distributed, with a mean of 8 pizzas and a standard deviation of 2.5 pizzas. A vendor for a packaged food distributor checks the market’s inventory of frozen foods every 10 days. During a particular visit there were no pizzas in stock. The lead time to receive an order is 3 days. Determine the order size for this order period that will result in a 98% service level. During the vendor’s following visit there were 5 frozen pizzas in stock. What is the order size for the next order period?