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Page 1: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

Inventory Management

Page 2: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 3: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 4: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

Types of Inventory

•Raw materials

•Purchased parts and supplies

•Work-in-process (partially completed) products (WIP)

•Items being transported

•Tools and equipment

Page 5: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 6: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 7: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 8: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 9: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 10: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 11: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 12: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory 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

Page 13: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 14: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 15: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 16: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 17: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 18: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 19: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 20: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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:

Page 21: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 22: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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:

Page 23: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 24: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 25: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 26: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 27: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 28: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 29: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 30: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 31: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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)

Page 32: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 33: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 34: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 35: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 36: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 37: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 38: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 39: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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)

Page 40: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 41: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 42: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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%

Page 43: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 44: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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.

Page 45: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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%

Page 46: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

Variable Demand With Reorder Point

Reorderpoint, R

Q

LTTime

LT

Inven

tory

level

0

Page 47: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

Reorder Point With Safety Stock

Reorderpoint, R

Q

LTTime

LT

Inven

tory

level

0

Safety Stock

Page 48: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 49: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 50: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 51: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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?

Page 52: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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?

Page 53: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 54: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 55: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 56: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

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

Page 57: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a periodic inventory system,

Periodic Inventory System

Page 58: Inventory Management - docshare01.docshare.tipsdocshare01.docshare.tips/files/29727/297274307.pdf · replenish the stock of inventory . ... •In a 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

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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.

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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?