1 inventory management chapter 13 mis 373: basic operations management additional content from l....

1

INVENTORY MANAGEMENTChapter 13

MIS 373: Basic Operations Management

Additional content from L. Beril Toktay

MIS 373: Basic Operations Management 2

LEARNING OBJECTIVES

• After this lecture, students will be able to 1. Define the term inventory2. List the different types of inventory3. Describe the main functions of inventory4. Discuss the main requirements for effective inventory management5. Describe the A-B-C approach and explain how it is useful6. Describe the basic EOQ model and its assumptions and solve typical

problems.7. Describe reorder point models and solve typical problems.8. Describe situations in which the fixed-order interval model is

appropriate, and solve typical problems.9. Describe service level and risk of stockout and use Z table to identify

the z value for a service level or a risk of stockout

INVENTORY MANAGEMENT AT COX HARDWARE

• From the video, what are the elements relevant to inventory management?


INVENTORY

• An inventory is a stock or store of goods.

• Inventories are a vital part of business: • necessary for operations• contribute to customer satisfaction

• A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory

• But• Costly• May have limited shelf-life• Carrier may have limited space


TYPES OF INVENTORY

• Raw materials and purchased parts

• Work-in-process (WIP)

• Finished goods inventories or merchandise

• Tools and supplies

• Maintenance and repairs (MRO) inventory

• Goods-in-transit to warehouses or customers (pipeline inventory)


COSTS OF INVENTORY

• Physical holding costs:• out of pocket expenses for storing inventory (insurance,

security, warehouse rental, cooling)• All costs that may be entailed before you sell it

(obsolescence, spoilage, rework...)

• Opportunity cost of inventory: foregone return on the funds invested.

With all these costs, why most companies still like to

hold inventories?


INVENTORY FUNCTIONS

• Inventories serve a number of functions such as:1. To meet anticipated customer demand2. To smooth production requirements

• Firms that experience seasonal patterns in demand often build up inventories during preseason periods to meet overly high requirements during seasonal periods.

3. To decouple operations• Buffers between operations

4. To protect against stockouts• Delayed deliveries and unexpected increases in demand increase the

risk of shortages.


INVENTORY FUNCTIONS

• Inventories serve a number of functions such as:5. To take advantage of order cycles

• It is usually economical to produce in large rather than small quantities. The excess output must be stored for later use.

6. To hedge against price increases• Occasionally a firm will suspect that a substantial price increase is

about to occur and purchase larger-than-normal amounts to beat the increase

7. To permit operations• The fact that production operations take a certain amount of time (i.e.,

they are not instantaneous) means that there will generally be some work-in-process inventory.

8. To take advantage of quantity discounts• Suppliers may give discounts on large orders.


OBJECTIVES OF INVENTORY CONTROL

• Inventory management has two main concerns:1. Level of customer service

• Having the right goods available in the right quantity in the right place at the right time

2. Costs of ordering and carrying inventories• The overall objective of inventory management is to achieve satisfactory

levels of customer service while keeping inventory costs within reasonable bounds


MEASURES OF PERFORMANCE

• Measures of performance:• Customer satisfaction

• Number and quantity of backorders• Customer complaints

• Inventory turnover = a ratio of

during a period

(average) cost of goods sold

(average) inventory investment


INVENTORY MANAGEMENT

• Management has two basic functions concerning inventory:

1. Establish a system for tracking items in inventory

2. Make decisions about• When to order• How much to order


EFFECTIVE INVENTORY MANAGEMENT

• Requires:1. A system keep track of inventory2. A reliable forecast of demand3. Knowledge of lead time and lead time variability4. Reasonable estimates of

• holding costs• ordering costs• shortage costs

5. A classification system for inventory items


INVENTORY COUNTING SYSTEMS• Periodic System

• Physical count of items in inventory made at periodic intervals

• Perpetual Inventory System• System that keeps track of removals from inventory continuously, thus

monitoring current levels of each item

• Point-of-sale (POS) systems• A system that electronically records actual sales

• Radio Frequency Identification (RFID)


ONE-BIND & TWO-BIN SYSTEMS

• One-Bin System • Two-Bin System

Bin A

Bin B


INVENTORY COSTS

• Purchase cost• The amount paid to buy the inventory

• Holding (carrying) costs• Cost to carry an item in inventory for a length of time, usually a year

• Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security).

• Ordering costs• Costs of ordering and receiving inventory

• determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.

• Shortage costs• Costs resulting when demand exceeds the supply of inventory; often

unrealized profit per unit


ABC CLASSIFICATION SYSTEM

• A-B-C approach• Classifying inventory according to some measure of importance, and

allocating control efforts accordingly• A items (very important)

• 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value

• B items (moderately important)• C items (least important)

• 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value


ABC CLASSIFICATION• How to classify?

1. For each item, multiply annual volume by unit price to get the annual dollar value.

2. Arrange annual values in descending order.

3. A items: the few with the highest annual dollar value

C items: the most with the lowest dollar value.

B items: those inbetween

# Annual demand

Unit price

Annual value

Class % of items

% of value

8 1,000 4,000 4,000,000 A 5.3 52.7

3 2,400 500 1,200,000 B

31.4 40.86 1,000 1,000 1,000,000 B

1 2,500 360 900,000 B

4 1,500 100 150,000 C

63.3 6.5

10 500 200 100,000 C

9 8,000 10 80,000 C

2 1,000 70 70,000 C

5 700 70 49,000 C

7 200 210 42,000 C

18,800 7,591,000 100 100


ABC CLASSIFICATION: CYCLE COUNTING

• Cycle counting• A physical count of items in inventory

• Cycle counting management• How much accuracy is needed?

• A items: ± 0.2 percent• B items: ± 1 percent• C items: ± 5 percent

• When should cycle counting be performed?• Who should do it?


HOW MUCH TO ORDER?ECONOMIC ORDER QUANTITY MODELS

• Economic Order Quantity (EOQ) models:• identify the optimal order quantity

• by minimizing total annual costs that vary with order size and frequency

1. The basic Economic Order Quantity model (EOQ)2. The Quantity Discount model3. The Economic Production Quantity model (EPQ)4. Reorder Point Ordering (uncertainty, when to order)5. Fixed-Order-Interval model6. Single Period model (perishable items)


BASIC EOQ MODEL

• The basic EOQ model:• used to find a fixed order quantity that will minimize total annual

inventory costs• continuous monitoring system

• Assumptions:1. Only one product is involved2. Annual demand requirements are known3. Demand is even throughout the year4. Lead time does not vary5. Each order is received in a single delivery6. 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

Usagerate

Time


TOTAL ANNUAL COST

• Total Cost = Annual Holding Cost + Annual Ordering Cost

(TC)

where

• Q = order quantity in units

• H = holding (carrying) cost per unit, usually per year

• D = demand, usually in units per year

• S = ordering cost per order

=Q

H +D

S2 Q

Number of orders

Average number of units in inventory


GOAL: TOTAL COST MINIMIZATION

• The Total-Cost Curve is U-Shaped• There is a tradeoff between holding costs and ordering costs

Order Quantity (Q)

Ordering Costs

Q*

An

nu

al

Cost

(optimal order quantity)

Holding Costs

SQ

DH

QTC

2


DERIVING EOQ

• Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

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

𝑄∗=√ 2𝐷𝑆𝐻

=√ 2 (𝑎𝑛𝑛𝑢𝑎𝑙𝑑𝑒𝑚𝑎𝑛𝑑 ) (𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 )𝑎𝑛𝑛𝑢𝑎𝑙𝑝𝑒𝑟𝑢𝑛𝑖𝑡 h𝑜𝑙𝑑𝑖𝑛𝑔𝑐𝑜𝑠𝑡

𝑇 𝐶′=𝐻2

+(−1 ) 𝐷𝑆𝑄2

=0→𝐷𝑆𝑄2

=𝐻2→

𝐷𝑆𝑄

=𝐻𝑄2


EXAMPLE: DERIVING EOQ

• Tire distributer

• D (Demand)=9,600 tires per year

• H (Holding cost)=$16 per unit per year

• S (Ordering cost) = $75 per order


=√ 2∗9,600∗7516

=300 𝑡𝑖𝑟𝑒𝑠

𝑇𝐶=𝑄2𝐻+

𝐷𝑄𝑆=

3002∗16+

9,600300

∗75=2,400+2,400=4,800


EXAMPLE: DERIVING EOQ

• D (Demand)=9,600 tires per year

• H (Holding cost)=$16 per unit per year

• S (Ordering cost) = $75 per order

• Q*=300 tires

• TCmin = 4,800

880,4880,2000,275250

600,916

2

250

2250 S

Q

DH

QTC

000,5800,1200,375400

600,916

2

400

2400 S

Q

DH

QTC

Let’s verify whether the Q* indeed gives the

lowest cost.


WHEN TO REORDER

• If delivery is not instantaneous, but there is a lead time:When to order?

Receive

order

Time

Inve

nto

ry

OrderQuantity

Q

Lead Time

Placeorder


WHEN TO REORDER

• EOQ answers the “how much” question

• The reorder-point (ROP) tells “when” to order

• Reorder-Point• When the quantity on hand of an item drops to this amount (quantity-

trigger), the item is reordered.

• Determinants of the Reorder-Point1. The rate of demand2. The lead time3. The extent of demand and/or lead time variability4. The degree of stockout risk acceptable to management


REORDER-POINT

ROP = (Demand per day) * (Lead time for a new order in days)

= d * L

where

d = (Demand per year) / (Number of working days in a year)

Example:• Demand = 12,000 iPads per year• 300 working day year• Lead time for orders is 3 working days

In other words, the manager should place the order when only 120 units

left in the inventory.

d = 12,000 / 300 = 40 unitsROP = d * L = 40 units per day * 3 days of leading time = 120 units


THE INVENTORY CYCLEProfile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usagerate

Time

ROP = LxD

D: demand per periodL: Lead time in periods

Q: When shall we order? A: When inventory = ROPQ: How much shall we order? A: Q = EOQ

EXERCISE: EOQ & ROP

• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? (Assuming that the lead time to receive cars is 10 days and that there are 365 working days in a year)

ROP = (Demand per day) * (Lead time for a new order in days)

= d * Lwhere d = (Demand per year) / (Number of working days in a year)


=√ 2 (𝑎𝑛𝑛𝑢𝑎𝑙𝑑𝑒𝑚𝑎𝑛𝑑 ) (𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 )𝑎𝑛𝑛𝑢𝑎𝑙𝑝𝑒𝑟𝑢𝑛𝑖𝑡 h𝑜𝑙𝑑𝑖𝑛𝑔𝑐𝑜𝑠𝑡

EOQ =

Recall:

EXERCISE: EOQ & ROP

• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size?

548500

)000,5)(000,15(2* Q

Since d is given in years, first convert: 5000/365 =13.7 cars per working day

So, ROP = 13.7 * 10 = 137

So, when the number of cars on the lot reaches 137, order 548 more cars.


BUT DEMAND IS RARELY PREDICTABLE!

Time

Inventory Level

OrderQuantity

Demand???

Receive order

Placeorder Lead Time



Time

Inventory Level

OrderQuantity

Receive order


Inventory at time of receipt

ROP

Lead Time Demand

When Actual Demand < Expected Demand



Time

Inventory Level

OrderQuantity

Receive order


ROP

When Actual Demand > Expected Demand

Unfilled demand

Stockout Point



Time

Inventory Level

OrderQuantity

ROP = Expected Demand

Average

If ROP = expected demand, inventory left 50% of the time, stock outs 50% of the time.

Uncertain Demand


SAFETY STOCK

Time

Inventory Level

OrderQuantity

Expected

Lead-time

Demand

To reduce stockouts we add safety stock

Receive order


Order QuantityQ = EOQROP =

Safety Stock +

Expected LT

Demand

ExpectedLT Demand

Safety Stock


HOW MUCH SAFETY STOCK?

• The amount of safety stock that is appropriate for a given situation depends upon:1. The average demand rate and average lead time2. Demand and lead time variability3. The desired service level

• Service level = probability of NOT stocking out

• Reorder point (ROP) =

Expected demand during lead time + z*σdLT

Where

z = number of standard deviations

σdLT = the standard deviation of lead time demand


REORDER POINT

• The ROP based on a normal distribution of lead time demand

Safety Stock

Risk of stockout

ROP

Quantity

Expected demand

Service level

(probability of not stockout)

Z scaleZ0

Z TABLE

• http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf• Other variations of Z table

• http://2.bp.blogspot.com/-afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeg

• https://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/files/lesson17/TopOfNormalBTable.gif

• How to use Z table:1. Decide the desired service level2. Look up the smallest number in the Z table that is greater than the service level3. Use the row of the number to identify the first two digits of the z4. Use the column of the number to identify the second decimal point

• Q1: what is the z for a 99% service level?

• Q2: what is the z for a 10% risk of stockout?

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

http://2.bp.blogspot.com/-afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeg

http://2.bp.blogspot.com/-afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeg

https://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/files/lesson17/TopOfNormalBTable.gif




FIXED-ORDER-INTERVAL MODEL

• The fixed-order-interval (FOI) model is used when orders must be placed at fixed time intervals (weekly, twice a month, etc.): The timing of orders is set. The question, then, at each order point, is how much to order.

• Fixed-interval ordering systems are widely used by retail businesses.• If demand is variable, the order size will tend to vary from cycle to

cycle.

• This is quite different from an EOQ/ROP approach in which the order size generally remains fixed from cycle to cycle, while the length of the cycle varies.



• Reasons for Using the Fixed-Order-Interval Model• A supplier's policy might encourage orders at fixed intervals. • Grouping orders for items from the same supplier can produce

savings in shipping costs.

• Some situations do not readily lend themselves to continuous monitoring of inventory levels.

• Many retail operations (e.g., drugstores, small grocery stores) fall into this category.

• The alternative for them is to use fixed-interval ordering, which requires only periodic checks of inventory levels.


fixed-quantity ordering

fixed-interval ordering

LT: Lead Time

LT: Lead TimeOI: Order Interval

The same quantity

same length same length

Different quantity



• Order size in the fixed-interval model is determined by the following computation:

Amount to order

Expected demand during protection

interval

Safety stock

Amount on hand at reorder time

= + −

Q 𝑧 𝜎𝑑√𝑂𝐼+𝐿𝑇= + − A𝑑 (𝑂𝐼+𝐿𝑇 )

where d = demand in a time unit, e.g., 100 units per dayOI = Order interval (length of time between orders), e.g., 10 daysLT = Lead time, e.g., 3 days = the standard deviation of the demand, e.g., 20 unitsz = z score for a desired service level, e.g., 2.33 for a 99% service levelA = Amount on hand at reorder time


EXAMPLE: FIXED-ORDER-INTERVAL MODEL

• Given the following information, determine the amount to order.

• d = 30 units per day

• OI = 7 days

• LT = 2 days

• = 3 units per day

• Service level = 99% z = 2.33 (by looking up the z table)

• A = 71 units

• Q 𝑧 𝜎𝑑√𝑂𝐼+𝐿𝑇= + − A𝑑 (𝑂𝐼+𝐿𝑇 )

2.33×3×√7+2= + − 7130 (7+2 )

= 222 units


KEY POINTS

• All businesses carry inventories, which are goods held for future use or potential future use.

• Inventory represents money that is tied up in goods or materials.

• Effective inventory decisions depend on having good inventory records, good cost information, and good estimates of demand.

• The decision of how much inventory to have on hand reflects a trade-off, for example, how much money to tie up in inventory versus having it available for other uses. Factors related to the decision include purchase costs, holding costs, ordering costs, shortage and backlog costs, available space to store the inventory, and the return that can be had from other uses of the money.

• As with other areas of operations, variations are present and must be taken into account. Uncertainties can be offset to some degree by holding safety stock, although that adds to the cost of holding inventory.

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