SBCO 6240InventoryPlanning&Control HB Student

D. Anthony CheversSBCO 6240 - Production and Operations Management

Lecture 7 – Inventory Planning & Control |

Lecture #5 – Inventory Management

Definitions & Purpose Inventory Costs & Trade-off Inventory Models

• Independent DemandBasic economic order quantity (EOQ) modelQuantity Discount Model

• Safety Stock & Customer Service Level• Fixed-Period (P) System

Exercises

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Inventory Planning & Control

3

Supply

The operation

Operations resources

Delivery of products and services when

required

Need for products and services at a

particular time

Demand

The market

Customer requirements


Definitions

Inventory - A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.

Inventory System - A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be.

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Reasons for Inventories

Improve customer service Economies of purchasing Economies of production Transportation savings Hedge against future Unplanned shocks

(labour strikes, natural disasters, surges in demand, etc.)

To maintain independence of supply chain

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Role of Inventory in Services

Need to inventory goods that facilitate service

Helps to “deliver” service on time Helps to accommodate

seasonal demand Helps to hedge against

increases in cost

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Reasons Against Inventory

Non-value added costs Opportunity cost Complacency Inventory deteriorates,

becomes obsolete, lost, stolen, etc.

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Gaining Competitive Advantage

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•Value added activitiesValue added activities•Cost adding activitiesCost adding activities

VALUE ADDED

COST ADDED


Inventory Costs

Procurement costs Carrying costs Out-of-stock costs

• Interest or Opportunity Costs• Storage and Handling Costs• Insurance and Shrinkage Costs• Ordering and Setup Costs• Transportation Costs

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Identifying Critical Inventory Items with ABC

Analysis Thousands of items are held in inventory Only a small percentage of them deserves

management’s closest attention and tight control

ABC analysis is the process of dividing items into three classes, according to their dollar usage, so that managers can focus on items that have the highest dollar value e.g. – Class A items typically represent only about 20% of the

items but account for 80% of the dollar usage

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Class C

Class A

Class B

ABC Classification

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Per

cen

tag

e o

f d

oll

ar v

alu

e100 —

90 —

80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0 —10 20 30 40 50 60 70 80 90 100

Percentage of items


Classifying Inventory Items

ABC Classification (Pareto Principle)

A ItemsA Items: very tight control, complete and accurate records, frequent review

B ItemsB Items: less tightly controlled, good records, regular review

C ItemsC Items: simplest controls possible, minimal records, large inventories, periodic review and reorder

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Types of Inventory

The stocks held in any organization take a variety of forms but generally can be classified under four main headings:

Raw Material & IngredientsRaw Material & Ingredients – material purchased, but not processed.

Work-in-ProcessWork-in-Process – partially completed inventory.MROMRO – Inventories devoted to maintenance/ repair/

operating supplies. Exist because the need and timing for maintenance and repair of some equipment are unknown.

Finished GoodsFinished Goods – Completed inventory (occurs because customer demands for a given period is unknown)

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Lecture 7 – Inventory Planning & Control | 14


Basic EOQ Model Assumptions

Demand is known, constant & independent Lead time is known & constant Receipt of inventory is instantaneous &

complete Quantity discounts are not possible The only variable costs are the cost of setting

up or placing an order & the cost of holding inventory over time

Stock-outs can be completely avoided if orders are placed at the right time

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Rel

evan

t T

otal

Cos

ts (

Dol

lars

)

2,000

4,000

6,000

8,000

10,000

5,434

600 1,200 1,800 2,400988EOQ

Annual relevant

carrying costs

Annual relevant total costs

Annual relevant ordering costs

Order Quantity (Units)

Economic-Order-Quantity Decision Model Example

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Inventory Models for Independent Demand

Basic Economic Order Quantity (EOQ) Model • EOQ = √(2xDxS)/H Or √(2xDxOC)/H

Production Order Quantity Model• Q*p = √(2xDxS)/{H[1 – (d/p)]}

Quantity Discount Model• Q* = √(2xDxS)/(IxP)

Where D = Annual demand; S = Set-up or ordering cost for each order; H = Holding or carrying cost per unit per year; Q* = Optimum number of pieces per order (EOQ); Q = Number of pieces per order; p = Daily production rate; d = Daily demand rate or usage rate; t = Length of the production run in days; IP is holding cost expressed as a percentage of unit price; OC = Order cost

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Diagram –Perpetual Inventory

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Qu

anti

ty

227 Maximum Level

EOQ/ROQ

ROL/ROP33

Minimum Level

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0 Time


Perpetual Equations

Where D is annual demand, OC is order cost, H is holding cost, CC is carrying cost, UP is unit price, U is usage, LT is lead time, TIC is total inventory cost, EOQ is economic order quantity, ROQ is reorder quantity, ROL is reorder level and Q is EOQ.

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EOQ √(2 x D x OC)/H

ROQ equivalent to EOQ

Mini LT x U

ROL (LT x U) x 1.10 [for 10% buffer stock

Maxi EOQ + (ROL – Mini)

# Orders D/EOQ

Interval Annual work days/# of orders

TIC [(Q/2)(H)] + [(D/Q) x OC]


Exercise – Local TV Distributor

A local TV distributor has found from experience that demand for a certain TV model is fairly constant at a rate of 24 sets per week. Holding cost is $28 per unit per year and ordering cost is estimated to be $50 per order. If lead time is 1 week.

a) How many sets should be ordered to minimize inventory cost?b) What is the reorder level using a 4% safety buffc) What is the total inventory cost?d) How many orders will be processed per year?e) What is the time interval between orders?

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Solution – Inventory –TV Distribitor

[Demand is equivalent to Usage]Given:

Usage (U) = 24/week

LT = 1 week

H = $28

OC= $50

Buffer = 4%

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(a) EOQ = √ (2 x 1,248 x 50)/28 = √124,800/28 = √ 4,457.14 = 66.76 TV sets

(b) ROL = (LT X U) 1.04 = (1 x 24) 1.04 = 24 x 1.04 = 24.96 TV sets

(c ) TIC = [Q/2(H)] + [D/Q(OC)] = [66.76/2(28)] + [1,248/66.76(50)] =

934.64 + 934.50 = $1,869.14

(d) # of Orders = D/EOQ = 1,248/66.76 = 18.69 times per year

(e) Interval = Annual work days / # of orders

Assume 365 days/year Assume 260 days/year365/18.69 = 19.53 days 260/18.69 = 13.91 days

Calculations

D = (24x52) = 1,248

Assumptions


Quantity Discount Model To increase sales, many companies offer quantity

discounts to their customers

Quantity discount is a reduced price for items purchased in large quantities. For e.g.

Table1Table1

Might be tempted to order 2,000 units to take advantage of lower product cost

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Discount # Discount Qty % Price

1 0 – 999 -- $5.00

2 1,000-1,999 4 $4.80

3 2,000 & over 5 $4.75


Trade-Off

As discount quantity goes up, the product cost goes down.

But, holding cost increases because orders are larger Trade off between reduced product cost and increased

holding cost Equation for total annual inventory cost, when cost of

product is included:

• Total cost [TC] = (Ordering + Holding + Product) cost• TC = (D/Q)OC + (QH/2) + PDWhere Q = Quantity ordered; D = Annual demandOC = Ordering cost or Setup cost per order or per setupP = Price per unit; H = Holding cost per unit per year

[Note: Order cost = Setup cost]

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4 Stepsto determine quantity that will minimize total

annual inventory cost

1. For each discount, calculate a value for optimal order size Q*, using:1. Q* = √(2xDxS)/(IP) Or √(2xDxO)/(IxP) Where S is setup & O is

order cost

2. Express the holding cost (I) as a percentage of unit price (P) instead of as a constant cost per unit per year, H.

2. If the order quantity is low to qualify for the discount, adjust the order quantity upwards to the lowest quantity that will qualify for the discount1. [[Total cost (TC) = Order cost +Holding cost +Product cost]]

3. Use total cost equation and compute a total cost for every Q*, Equation: [TC = (D/Q)OC + (QH)/2 + PD]

4. Select the Q* that has the lowest total cost24


Example #1 – Quantity Discount

Work’s Discount stocks toy race cars. Recently, the store has a quantity discount schedule as shown below:

Furthermore, ordering cost is $49.00 per order, annual demand is 5,000 race cars, and inventory carrying charge, as a percentage of cost, I, is 20%.

What order quantity will minimize the total inventory cost?

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Discount Discount NumberNumber

Discount Discount QuantityQuantity

Discount Discount (%)(%)

DiscountDiscountPrice (P)Price (P)

1 0 – 999 No discount $5.00

2 1,000-1,999 4 $4.80

3 2,000 & over 5 $4.75


Solution – [Q* = √(2xDxO)/(IxP)]

Step #2 - Adjust upwards those values of Q* that are below the allowable discount range. Since Q1* is between 0 - 999, it is not adjusted.

Q1* = 700

Q2* = 1,000 - adjusted

Q3* = 2,000 - adjusted

Step #1 - Q1* = √ 2(5,000)(49) = 700 cars

(0.2)(5.00)

Q2* = √ 2(5,000)(49) = 714 cars

(0.2)(4.80)

Q3* = √ 2(5,000)(49) = 718 cars

(0.2)(4.75)


Solution cont’d …

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Step #3 - Use total cost equation and compute a total cost for every order qty.

Equation: [TC = (D/Q)OC + (QH)/2 + PD] [H = IP]5000 49 0.2 Order C Carrying C Annual Dem Total Cost

Discount Number Unit Price Order Quantity

Annual Ordering

Cost

Annual Holding

Cost

Annual Product

Cost Total1 $5.00 700 $350 $350 $25,000 $25,700

2 $4.80 1,000 $245 $480 $24,000 $24,725

3 $4.75 2,000 $123 $950 $23,750 $24,823

Step #4 - Select that order quantity with the lowest total costOrder quantity of 1,000 toy cars will minimize the total cost

Annual Product Cost: ($5 x 5,000) = $25,000

Annual Ordering Cost: Q1* = (5,000/700)49 = $350

Annual Holding Cost: Q1* = (700 x 0.2 x $5)/2 = $350


Further Problem When it is difficult or impossible to determine the cost

of being out of stock, a manager may decide to follow a policy of keeping enough safety stock on hand to meet a prescribed customer service level

Define the service level as meeting 95% of the demand (or conversely, having stock-outs only 5% of the time)

Assuming that demand during lead time (the reorder period) follows a normal curve, only the mean and standard deviation are needed to define the inventory requirements for any given service level.

Sales data are usually adequate for computing the mean (µ) and standard deviation (σ).

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Equations & Z-Values

Safety stock = x - µ [known][known]

But Z = (x - µ)/σThen x - µ = Z σ; So Safety stock = Zσ

ROP = Expected demand during lead time + safety stock

Z value @ 95% = 1.645Z value @ 97% = 1.88Z value @ 99% = 2.33

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Exercise

Member Hospital stocks a “code blue” rescue kit that has a normally distributed demand during the reorder period. The mean (average) demand during the reorder period is 350 kits, and the standard deviation is 10 kits. The hospital administrator wants to follow a policy that results in stock-outs occurring only 5% of the time.

(a)What is the appropriate value of z?

(b)How much safety stock should the hospital maintain?

(c)What reorder point should be used.

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Solution

(a) (a) We use the properties of a standardized normal curve to get a Z value for an area under the normal curve of 0.95 (or 1-0.05). Using a normal table (Appendix 1), we find a Z vague of 1.65 standard deviation form the mean

(b) (b) Safety stock = x –u

Because z = x-u

σ

Then Safety stock = Zσ ---- (1)

Solving for safety stock, as in Equation (1), gives

Safety stock = (1.65(10) =16.5 kits

(c) (c) The reorder point is:

ROP = Expected demand during lead time + safety stock

350 kits + 16.5kits of safety stock =366.5 or 367 kits31


Reorder Point for a Service Level

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Risk of a Risk of a stockoutstockout

(5% of area of(5% of area ofnormal curve)normal curve)

ROP = ? kitsROP = ? kitsMeanMeanDemandDemand

350350

Probability of Probability of No stock 95% of the timeNo stock 95% of the time

QuantityQuantity

SafetySafetyStockStock

Number of Number of standard deviationsstandard deviations

00 zz


Assumptions The following equations:

• ROP = Expected demand during lead time + Zσ• Safety stock = Zσ

Assume that both an estimate of expected demand during lead times and its standard deviation are available

When data on lead time demand are not at hand, these equations cannot be applied

Need to determine if:• Demand is variable and lead time is constant OR• Only lead time is variable OR • Both demand and lead time are variable

For each, a different equation is needed to compute ROP

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Inventory Systems

Fixed-quantity (Q) system• An EOQ ordering system, with the same order

amount each time [models considered so far]

Perpetual inventory system• A system that keeps track of each withdrawal or

addition to inventory continuously, so records are always current [fixed-quantity model]

Fixed-period (P) system• A system in which inventory orders are made at

regular time intervals.


Q and P Systems

Q SystemsQ Systems Based on reorder point –

when inventory is depleted to ROP, order replenishment of quantity EOQ

Individuals review frequencies Possible quantity discounts Lower, less-expensive safety

stocks

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P SystemsP Systems Alternative ROP/Q-System

control is periodic review method Q-System – each stock item rendered at different times – complex, no economies of scale or common prod./transport runs P-system – inventory levels for multiple stock items reviewed at same time – can be reordered together higher carrying costs – not optimum, but more practical

Convenient to administer Orders may be combined IP may require review


Fixed-Period (P) System

Inventory is ordered at the end of a given period At that time, on-hand inventory is counted Only the amount necessary to bring total inventory up

to a pre-specified target level is ordered

Assumptions (similar to basic EOQ fixed-quantity system)

• Only relevant cost are ordering & holding costs• Lead times are known & constant• Items are independent of one another

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Fixed-Period (P) SystemVarious amounts (Q1, Q2, etc) are ordered at regular

time intervals (P) based on the qty. necessary to bring inventory up to target maxi. (T)

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On-

hand

Inv

ento

ry

Time

Target maximum (T)


Fixed-Period (P) System

Hard Rock Little London has a back order for three (3) leather jackets in its retail store. There are no jackets in stock, none are expected from earlier orders, and it is time to place an order. The target value is 50 jackets. How many jackets should be ordered?

SolutionOrder amount (Q) = Target (T) – OnHand inventory – Earlier orders not yet received + Back ordersQ = 50 – 0 – 0 + 3 = 53 jackets

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Advantages: Fixed-Period No physical count of inventory items after an item is

withdrawn Count occurs only when the time for the next review

comes up Procedure is convenient to administer, especially if

employee has several duties Appropriate when vendors make routine visits to

customers to take fresh orders Appropriate when purchasers want to combine orders

to save ordering & transportation costs. E.g., a vending machine company may refill its machine every Tuesday

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(Heizer, 2004)


Disadvantages: Fixed-Period

No tally of inventory during review period can cause stock-out during period

A large order (pick list) can draw the inventory level down to zero

Hence, higher level of safety stock (as compared to a fixed-quantity system) needs to be maintained to provide protection against stock-out during both the time between reviews and lead time.

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(Heizer, 2004)


Summary

Inventory represents a major investment for many firmsThis investment is often larger than it should be because firms find it easier to have “Just-in-case” inventory rather than “Just-in-time” inventory.

A basic inventory management question is whether to order large quantities infrequently or to order small quantities frequently. The EOQ provides guidance for this choice by indicating the lot size that minimizes the sum of holding and ordering costs over some period of time, such as a year.

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Normal Distribution

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Equations

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Exercises – Lot Size

A museum of natural history opened a gift shop two years ago. Managing inventories has become a problem. Low inventory turnover is squeezing profit margins and causing cash-flow problems. One of the top-selling items in the container group at the museum’s gift shop is a bird feeder. Sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order with the supplier is $45. Annual holding cost is 25% of a feeder’s value and the museum operates 52 weeks per year. Management chose a 390-unit lot size so that new orders could be placed less frequently. What is the annual cost of the current policy of using a 390-unit lot size?

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Solution – Lot Size D = (18 units/wk)(52 wks/yr) = 936 units H = 0.25($60/unit) = $15 Total annual cost for the current policy is:

• C = [Q/2(H) + D/Q(S)]• C = [390/2($15) + 936/390($45)]• C = $2,925 + $108 = $3,033

Total annual cost for alternative lot size is:• C = [468/2($15) + 936/469($45)]• C = $3,510 + $90 = $3,600

The lot size of 468 units, which is a half-year supply, would be a more expensive option than the current policy. The savings in order costs are more than offset by the increase in holding costs. Management should use the total annual cost equation to explore other lot-size alternatives.

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Exercise – Basic EOQ Model

The economic order quantity, EOQ, is 75 units when annual demand, D, is 936 units/year, setup cost, S, is $45, and holding cost, H, is $15/unit/year. Suppose that we mistakenly estimate inventory holding cost to be $30/unit/year.

• (a) What is the new order quantity, Q, if D = 936 units/year, S, = $5 and H = $30/unit/year?

• (b) What is the change in order quantity, expressed as a percentage of the economic order quantity (75 units)?

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Solution – Basic EOQ Model

(a) The new order quantity isEOQ = √(2DS)/H = √[2(936)($45)]/$30√2,808 = 52.99 or 53 units

(b) The change in percentage is[(53 – 75)/75] x (100) = -29.33%

The new order quantity (53) is about 29 percent smaller than the correct order quantity (75)

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Discussion Questions

What is the relationship between inventory and the nine competitive priorities (low-cost operations, top quality, consistent quality, delivery speed, on-time delivery, development speed, customization, variety and volume flexibility)?

Suppose that two competing manufacturers, Company H and Company L, are similar except that Company H has much higher investments in raw materials, work-in-process, and finished goods inventory than Company L. In which of the nine competitive priorities will Company H have an advantage?

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Case Discussion

Next Class – Case Study Analysis• Catherine’s Confectionaries (Notes #1)

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NEXT LECTURE:

Supply Chain

D. Anthony Chevers

[email protected], Room #28

SBCO 6240InventoryPlanning&Control HB Student

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