Operations Management-Ch13-Inventory PDF

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Operational Management POMG2710 Chapter 13: Inventory Management

Inventory  Inventory: a stock or store of goods.  Many of the items a company carries in inventory relate to the kind of business it engages in. Examples:  Manufacturing firm: supplies of raw materials, purchased parts, partially finished products, and finished products  Hospital: drugs, surgical supplies, life-monitoring equipment, sheets, pillows, … etc.  Supermarket: fresh and canned food, packaged and frozen foods, household supplies, magazines, baked goods, dairy products, … etc.)

The Importance of Inventories 

Inventories: are a vital part of business, not only for operations but also for customer satisfaction.



Inventories are Assets  reduction in inventories can result in a significant increase in ROI. ROI =



Profit After Tax Total Assets

Inventories decisions in service organizations can be especially crucial. 

Example: Blood Unit in a hospital: 

Being out of stock  affects the well-being of patients



Being over stock  dispose some of unused (because of limited shelf life)



The major source of revenues for retail and wholesale business is inventories.



Space limitation may pose on restrictions on inventory storage capabilities.

Types of Inventories 

Raw materials and purchased parts



Work-in-process (partially completed goods)



Finished goods inventories (manufacturing firms) or merchandise (service firms)



Tools and supplies



Maintenance and repairs (MRO) inventory



Goods-in-transit to warehouses, distributors, or customers (pipeline inventory) Paper Production Process

Functions of Inventory 1. To meet anticipated customer demand  Anticipated stock (because they are held to satisfy expected (i.e. average demand))

2. To smooth production requirements  Seasonal inventories (e.g. fresh fruits and vegetables, Eid greeting cards)

3. To decouple operations  Buffering inventories (inventories kept between successive operations)

4. To protect against stock-outs  Hold safety stock (stocks in excess of expected demand to compensate for variability in demand & lead time)

5. To take advantage of order cycles  Inventory storage enables a firm to buy or produce in economic lot (large sizes) without having to match purchases or production with demand requirements in the short run in order to minimize purchasing and inventory costs  periodic orders or order cycles.

6. To hedge against price increases 7. To permit operations  Little Law: Average amount of inventory = average demand rate X average time a unit in the system (e.g. if a unit is in the s ystem for 10 days, and the demand rate is 5 units per day, the average inventory is 5 units/day X 10 days = 50 units)

8. To take advantage of quantity discounts

Inventory Management 



Inadequate control of inventories can result in: 

Under-stocking  missed deliveries, lost sales, dissatisfied customers, production bottlenecks



Over-stocking  ties up funds that might be more productive elsewhere.

Concerns of inventory management: 

Level of customer service (to have the right good, in sufficient quantities, in the right place, at the right time)



Cost of ordering and carrying inventories. Overall Objective: Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds  When to order and how much to order!!



Measures for Effectiveness of inventory management: 

Inventory turnover (ratio of average cost of goods sold to average inventory investment)



Days of inventory on hand (expected no. of days of sales that can be supplied from existing inventory)

Requirements for Effective Inventory Mngt 1. A system to keep track of inventory: 



4. Reasonable estimates of:

 Inventory Counting Systems: 

Periodic systems: Physical count of items in inventory made at period intervals (weekly, monthly



Perpetual inventory system: System that keeps track of removals from inventory continuously, thus monitoring current levels of each item (e.g. Two-bin system: two containers of inventory; reorder when the first is empty).

 Inventory Counting Technologies: 

Universal product code (UPC): Bar code



Point-of-sale (POS) systems: record items at time of sale.



Holding costs: Cost to carry an item in inventory for a length of time, usually a year.



Ordering costs: Costs of ordering and receiving inventory



Shortage costs: Costs resulting when demand exceeds the supply of inventory (often unrealized profit per unit)



Other costs: purchase cost, setup cost.

5. A classification system for inventory items 

A-B-C approach: classifying inventory according to some measure of importance, and allocating control efforts accordingly

2. A reliable forecast of demand  Inventories are used to satisfy demand, so it is essential to have estimates of the amount and timing of demand

3. Knowledge of lead time 

(i.e. time interval between ordering and receiving the order) and lead time variability

A-B-C Analysis Classification of Inventory items :

Annual $ value of items

A B C

Low Few

Number of Items



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



Another application of ABC concept is as a guide for cycle counting, which is a physical count of items in inventory

Many



Divides on-hand inventory into 3 classes  A class, B class, C class



Basis is usually annual $ volume $ volume = Annual demand x Unit cost



Policies based on ABC analysis 

Develop class A suppliers more



Give tighter physical control of A items



Forecast A items more carefully

% Annual $ Usage

High

100 80 60 A 40 20 0 0

Class A B C

B

% $ Vol 60-70 15 10-15

% Items 10-20 30

C 50

% of Inventory Items

100

50-60

A-B-C Analysis – Cont. Example: The manager of an automobile repair shop hopes to achieve a better allocation of inventory control efforts by adopting an A-B-C approach to inventory control. A.

Given the monthly usages in the following table, classify the items in A, B, and C categories according to RO usage:

B.

Determine the percentage of items in each category and the annual RO value for each category. Item

Usage

Unit Cost (RO)

4021

90

1400

9402

300

12

4066 6500

30

700

150

20

9280

10

1020

4050

80

140

6850

2000

10

3010

400

20

4400

5000

5



Solution Steps:  Compute (Usage x Unit Cost)  Sort from largest to smallest  Categorize (A-B-C)  One A, two B, five C.  Compute percent of items and percent of total cost

Item Usage Unit Cost

Item Usage x Cost

4021 9402 4066 6500 9280 4050 6850 3010 4400

4021 4400 4066 6850 9280 3010 9402 6500 4050

90 300 30 150 10 80 2,000 400 5,000

$1,400 12 700 20 1,020 140 10 20 5

Category A B C

Percent of Items 11.1% 33.3% 55.6%

$126,000 25,000 21,000 20,000 10,200 8,000 3,600 3,000 1,120 217,920

Percent of Total Cost 57.8% 30.2% 11.9%

Category A B B B C C C C C

Solve Question 2 on page 602 

The following table contains figures on the monthly volume and unit costs for a random sample of 16 items from a list of 2,000 inventory items at a health care facility:

Item Unit Cost Usage Dollar Usage Category K34 10 200 K35 25 600 K36 36 150 M10 16 25 M20 20 80 Z45 80 200 20 300 F14 F95 30 800 F99 20 60 D45 10 550 D48 12 90 D52 15 110 D57 40 120 N08 30 40 P05 16 500 P09 10 30

•A. Develop an A-B-C classification for these items. •b. How could the manager use this information? To allocate control efforts. •c. Suppose after reviewing your classification scheme, the manager decides to place item P05 into the “A” category. What would some possible explanations be for that decision? It might be important for some reason other than dollar usage, such as cost of a stockout, usage highly correlated to an A item, etc.

Inventory Ordering Policies 

Inventory Ordering Policies: 1.

How much to order?

2.

When to order?



Cycle Stock: The amount of inventory needed to meet expected demand



Safety Stock: Extra inventory carried to reduce the possibility of a stock-out due to demand and/or lead time variation.



How much to order?: 

The basic economic order quantity model



The economic production quantity model



The quantity discount model

Economic Order Quantity (EOQ) Model 

To find a fixed order quantity that will minimize total annual inventory costs

Assumptions: 1.

Only one product is involved

2.

Annual demand requirements are known

3. Demand is even throughout the year 4.

Lead time does not vary

5.

Each order is received in a single delivery

6.

There are no quantity discounts

(EOQ) Model – Cont. 

Total Annual Cost:

𝑨𝒏𝒏𝒖𝒂𝒍 𝑪𝒂𝒓𝒓𝒚𝒊𝒏𝒈 𝑪𝒐𝒔𝑡 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑜𝑛 𝐻𝑎𝑛𝑑

𝑨𝒏𝒏𝒖𝒂𝒍 𝑶𝒓𝒅𝒆𝒓𝒊𝒏𝒈 𝑪𝒐𝒔𝒕 = 𝑁𝑜. 𝑜𝑓 𝑂𝑟𝑑𝑒𝑟𝑠 𝑝𝑒𝑟 𝑌𝑒𝑎𝑟

𝑄 X 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑈𝑛𝑖𝑡 𝑝𝑒𝑟 𝑌𝑒𝑎𝑟 𝐻 2

𝐷 × 𝑂𝑟𝑑𝑒𝑟𝑖𝑛𝑔 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑂𝑟𝑑𝑒𝑟 𝑆 𝑄 

The total cost curve reaches its minimum where the carrying and ordering costs are equal: Q* 



2DS  H

Length of Order Cycle (i.e. time between orders): Length of Order Cycle  

Q = order quantity (units) D = Demand (usually units per year)

Q D

Reorder Point: When the quantity on hand of an item drops to this amount, the item is reordered. ROP  ( d  LT )  SS where d  Demand rate (units per period, per day, per week) LT  Lead time (in same time units as d ) SS  Safty Stock



(EOQ) Model – Cont. Example: A large bakery buys flour in 25-pound bags. The bakery uses an average of 1,215 bags every three months. Preparing an order and receiving a shipment of flour involves a cost of $10 per order. Annual carrying costs are $75 per bag. D = 4,860 bags/yr., S = $10, H = $75

2DS  H

2(4,860)10  36 bags 75

A.

Determine the economic order quantity

B.

What is the average number of bags on hand?

C.

How many orders per year will there be?

D.

Compute the total cost of ordering and carrying flour. TC  Q H  D S  36 (75)  4800 (10)  1350 1350  $2700

Q

Q/2 = 36/2 = 18 bags

orders per year 

4860 bags D   135 orders Q 36bags /orders 2

E.

Q

2

36

If ordering costs were to increase by $1 per order, how much would that affect the minimum total annual cost? Q

2DS 2( 4,860)11   37.757 bags 75 H

TC 

4860 37.757 Q D (11)  1415.89 1415.9  $2831.79 (75)  H S 37.757 2 Q 2

Increase by [$2,831.79 – $2,700] = $131.79 F.

If the lead time is 3 days, what is the reorder point? ROP = d X L = (4860/365days) x 3 days

G.

If the safety stock = 5 units, what is the new ROP?

ROP = (d X L) + SS = (4860/365days) x 3 days + 5

Exercise: solve No. 4, Page 602 

a)

A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper. What order size would minimize the sum of annual ordering and carrying costs?

b) Compute the total annual cost using your order size from part a. c)

D = 40/day x 260 days/yr. = 10,400 packages S = $60 H = $30 a. Q0 

2DS 2(10,400)60   203.96  204 boxes H 30

D Q Except for rounding, are annual ordering and b. TC  H  S Q 2 carrying costs always equal at the EOQ?

d) The office manager is currently using an order size of 200 boxes. The partners of the firm expect the office to be managed “in a cost-efficient manner.” Would you recommend that the office manager use the optimal order size instead of 200 boxes? Justify your answer.



10,400 204 (60)  3,060 3,058.82  $6,118.82 (30)  204 2

c. Yes

10,400 200 (60) (30)  200 2 TC200 = 3,000 + 3,120 = $6,120 6,120 – 6,118.82 (only $1.18 higher than with EOQ, so 200 is acceptable.)

d. TC200 

No. 5, p. 602 D = 750 pots/mo. x 12 mo./yr. = 9,000 pots/yr.

Garden Variety Flower Shop uses 750 clay pots a month. The pots are purchased at $2 each. Annual carrying costs per pot are estimated to be 30 percent of cost, and ordering costs are $20 per order. The manager has been using an order size of 1,500 flower pots. a)

What additional annual cost is the shop incurring by staying with this order size?

b) Other than cost savings, what benefit would using the optimal order quantity yield?

Price = $2/pot S = $20 P = $50 H = ($2)(.30) = $.60/unit/year

Q

2 DS 2(9000)20   774.60  775 bags H 0.6 Q D 774.6 9000 TC  H  S  (0.6)  (20) Q 2 2 774.6

TC  232.35 232.36  $464.71 

1500 9000 Q D (0.6)  (20) H S  2 2 1500 Q TC  450  120  $570

If Q = 1500, TC 

Therefore the additional cost of staying with the order size of 1,500 is: Additional cost = $570 – $464.71 = $105.29 b. Only about one half of the storage space would be needed.

No. 6 , p. 602 

A produce distributor uses 800 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35 percent of the purchase price per crate. Ordering costs are $28. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using the EOQ?

6. u = 800/month, so D = 12(800) = 9,600 crates/yr. H = .35P = .35($10) = $3.50/crate per yr. S = $28

TC at EOQ: Savings approx. $364.28 per year.

Quantity Discount Model  

Quantity discount: Price reduction offered to customers for placing large orders QD model is same as EOQ model, except: unit price depends upon the quantity ordered Total Cost Carrying Cost Ordering Cost  Purchasing Cost 

Q D H  S  PD Q 2

where P  Unit price  Why not include P in EOQ?: EOQ assumes no quantity discount (i.e. price per unit is the same for all order sizes)  Adding PD doesn’t change EOQ!!

Quantity Discount Model – Cont.  

With quantity discount: Suppose: Order Quantity 1 to 44 45 to 69 70 or more

Price per Box ($) 2.00 1.70 1.40

 Total cost curve with quantity discounts is composed of a proportion of the total-cost curve for each price (i.e. smaller unit prices will raise the curve lower than larger unit prices)  Even though each curve has a minimum, those points are NOT necessarily feasible!!!

Quantity Discount Model – Cont.  

Objective of QD model  to identify the order quantity that will represent the lowest total cost for the entire set of curves. Two general cases of QD model:

1. Carrying costs are constant  all curves have their minimum points at the same quantity

2. Carrying costs are percentage of unit price  the minimum points do not line up

Quantity Discount Model – Cont. 

QD Model Procedures: 1.

Calculate the EOQ (i.e. the common minimum point)

2.

Determine whether the EOQ is feasible at that price (i.e. will the supplier sell that quantity at that price?)

3.

If yes, STOP and optimal order quantity is found. If not, continue

4.

Check the feasibility of EOQ at the next higher price

5.

Continue until you identify a feasible EOQ.

6.

Calculate the total costs (including total item cost) for the feasible EOQ model.

7.

Calculate the total costs of buying at the minimum quantity required for each of the cheaper unit prices

8.

Compare the total cost of each option & choose the quantity with the lowest cost alternative.

Quantity Discount Model – Cont. 

Example: A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Determine A. B.

the optimal order quantity. The number of orders per year.

Number of boxes 1,000 to 1,999 2,000 to 4,999

Price per Box ($) 1.25 1.20

5,000 to 9,999

1.15

10,000 or more

1.10

Quantity Discount Model – Cont. a.Compute the common minimum Q*  2DS  H

2400 boxes

Since this quantity is feasible in the range 2000 to 4,999, its total cost and the total cost of all lower price breaks (i.e., 5,000 and 10,000) must be compared to see which is lowest. When: Q = 2400, TC = 23,040 Q = 5000, TC = 22545.6  lowest Q = 10000, TC = 22,972.8 Therefore, best order quantity is 5,000 boxes. b. No. orders = D/Q = 18000/5000 = 3.6 orders per year.

Quantity Discount Model – Cont. Exercise: A company will begin stocking remote control devices. Expected monthly demand is 800 units. The controllers can purchased from either supplier A or supplier B. Their prices lists are as follows:

Supplier A Quantity Unit Price ($) 1 – 199 14.00 13.80 200 – 499 13.60 500 + 

Supplier B Quantity Unit Price ($) 1 – 149 14.10 150 – 349 13.90 350 + 13.70

Ordering cost is $40 and annual holding cost is 25 percent of unit price per unit. Which supplier should be used and what order quantity is optimal if the intent is to minimize total annual cost?

Quantity Discount Model – Cont. D = (800) x (12) = 9600 units S = $40 H = (25%) x P