Basics of Supply Chain Management : BSCM

Basics of Supply Chain Management : BSCM

Ch.7 Inventory Management

Chapter 7. Inventory Management.

Main Issues :

· Understand Order Quantities and Its Rules : Lot-for-Lot and Fixed Order Quantity

· Understand Economic Order Quantity(EOQ) Calculation and Its Assumption.

· Explain the Concept of an Reorder Point.

· Understand the Reasons for Carrying Safety Stock. : Uncertainty of Demand and Supply.

· Describe the Idea of Service Level and the Service Factors influencing it.

· Explain the Two-Bin System and the Perpetual Inventory System.

· Recognize the Purpose of Auditing Inventory Records.

· Explain the Cycle Counting Process.

1. Order Quantities.

□ How Much to Order at One Time.

- Management's two objectives in deciding how much to order at one time are

· To minimize the sum of all costs.

· To maximize customer service.

- Methods of deciding how much to order at one time.

· Lot-for-lot.

· Fixed order quantity.

· Economic order quantity.

- Stock keeping unit (SKU)

· An individual item in a specific inventory location.

· Two white shirts in the same inventory but of different sizes or styles would be                   two different SKUs. The same shirt in two different inventories would be two

different SKUs.

□ Lot-size Decision Rules.

- Lot-for-Lot (L4L)

· L4L calls for placing an order for each period that has requirements in the exact

amount of the requirement.

· If there are requirements in every period, then orders will be placed every period.

· This is the equivalent of an "as-required" or "as-needed" rule.

· This method is used

: For dependent demand items.

: For expensive components (A items)

: In a JIT environment.

- Fixed-order quantity

· These types of decision rules specify the number of units to be ordered each

time an order is placed for an individual item or SKU.

· The advantage to this type of rule is that it is easily understood.

· The disadvantage is that it does not minimize the costs involved.

· A variation on the fixed order quantity system is the min-max system.

Figure 1. Lot-for-Lot

Safety Stock = 80			P E R I O D S
Order Quantity = L4L
Lead Time = 2			1	2	3	4	5	6	7	8
Y	Forecast Demand		130	160	120	260	130	120	185	115
	Scheduled Receipts		130	160
	Projected Available	80	80	80	80	80	80	80	80	80
	Planned Receipts				120	260	130	120	185	115
	Planned Order Releases		120	260	130	120	185	115

Figure 2. Fixed Order Quantity

Safety Stock = 80			P E R I O D S
Order Quantity = 500
Lead Time = 2			1	2	3	4	5	6	7	8
Y	Forecast Demand		130	160	120	260	130	120	185	115
	Scheduled Receipts
	Projected Available	370	240	80	460	200	570	450	265	150
	Planned Receipts				500		500
	Planned Order Releases		500		500

Figure 3. Economic Order Quantity

Safety Stock = 80			P E R I O D S
Order Quantity = EOQ
Lead Time = 2			1	2	3	4	5	6	7	8
Y	Forecast Demand		130	160	120	260	130	120	185	115
	Scheduled Receipts
	Projected Available	370	240	80	610	350	220	100	565	450
	Planned Receipts				650				650
	Planned Order Releases		650				650

* Average per period =	130 + 160 + 120 + 260 + 130 + 120 + 185 + 115	= 152.5
	8

*  A = 152.5 × 52 = 7930

*  [eqn: EOQ = root{2AS over {C ×i}} = root{{2×7930×10}over{1.50 ×0.25}} = 650]

2. Economic Order Quantity (EOQ)

□ Assumptions.

- Annual usage is assumed to be level and continuous

- Underlying costs are assumed to be accurate

- Replenishment is assigned to be instantaneous

- Costs are most often expressed as total, or average, rather than marginal

- Single-item replenishment is assumed

Figure 4. Inventory on hand over time

□ The Cost of Carry Inventory

- Capital Costs.

· Money invested in inventory is not available for other uses and as such

represents a lost opportunity cost.

- Storage Costs.

· Storing inventory requires space, workers, and equipment. As inventory increases,

so do these costs.

- Risk Costs.

· Obsolescence.

: Loss of product value resulting from a model or style change or

: technological development.

: Engineering changes, Spoilage, Technical Obsolescence, Defects.

· Damage : Inventory damaged while being held or moved.

· Pilferage : Goods lost, strayed, or stolen.

· Deterioration.

: Inventory that rots or dissipates in storage or whose shelf life is limited.

□ The Cost for Placing Orders

- Purchase Order Costs

· Supplier selection, follow-up, and other contacts

· Accounts payable and collection

· Receiving, inspection, and handling

· Preparation and handling of an authorization document

- Production Order Costs

· Setup of equipment or assembly-line changeover

· Preparation of production order paperwork

· Tracking and reporting work orders in the plant

· Scrap that results from start-up after a new setup

□ Total Inventory Cost vs. Order Quantity.

- Example.

A hardware supply distributor carries boxes of 3-inch bolts in stock. The annual usage

is 1000 boxes, and demand is relatively constant throughout the year. Ordering costs

are $20 per order, and the cost of carrying inventory is estimated to be 20%. The cost

per unit is $5.

· Annual Demand (A) = 1000 units.

· Ordering Cost in dollar per order(S) = $ 20 per order.

· Unit Cost in dollars (C) = $ 5 per units.

· Annual Carrying Cost Rate = 20 %

· Annual Carrying Cost

CC =	Order Quantity	× Unit Cost × Carrying Cost Rate = [eqn: Q over 2] × 5 × 0.2
	2

· Annual Ordering Cost

OC =	Annual Usage	× Ordering Cost = [eqn: 1000 over Q] × 20
	Order Quantity

· Total Cost = Annual Carrying Cost + Annual Order Cost.

TC = [eqn: Q over 2] × 5 × 0.2  +  [eqn: 1000 over Q] × 20

· Cost for different lot sizes.

Figure 5. Total Cost vs. EOQ

Order Quantity	Ordering Cost	Carrying Cost	Total Cost
50	$ 400	$ 25	$ 425
100	200	50	250
150	133	75	208
200	100	100	200
250	80	125	205
300	67	50	217
350	57	175	232
400	50	200	250

□ Economic Order Quantity (EOQ)

- A type of fixed order-quantity model that determine that amount of an item to be

purchased or manufactured at one time.

- The intent is to minimize the combined costs of ordering and carrying inventory.

- The basic formula :

· EOQ = [eqn: root{{2AS} over {C×i}}]

□ Significant Relationships

- The more demanded per year, the larger the order quantity

- The higher the order, or setup cost, the larger the order quantity

- The more expensive the item, the smaller the order quantity

- The higher the carrying cost, the smaller the order quantity

- Aggregate inventory levels can be manipulated be varying the assumptions about

carrying cost.

□ EOQ Excercise

- Item cost  = $ .50

- Order cost = $ 10.00

- Average annual usage = 15,000 units

- Annual carrying cost percentage = 20%

(a) Calculate EOQ

(b) What change occurs to the EOQ if the carrying cost percentages is 22 %  instead of 25% ?

What about 15% ?  What do you conclude about the sensitivity of the EOQ with

respect to carrying cost ?

(c) What change occurs to the EOQ if the annual usage is 20,000 units instead of 15,000 ?

What about 60,000 units ?  What do you conclude about the sensitivity of the EOQ with

respect to annual usage ?

(d) Assume that an arbitrary order quantity of 1000 units has been selected. Use the EOQ

formula to determine the carrying cast percentage implied by this order quantity. Is it

reasonable ?

3. Order Point System.

□ Introduction.

- When the quantity of an item on hand in inventory falls to a predetermined level, called

an order point, an order is placed.

- Using this system, an order must be placed when there is enough stock on hand to

satisfy demand from the time the order is placed until the new stock arrives called the

lead time.

- If it is necessary to provide some protection against a stockout, safety stock can be added.

□ Order Point Formula.

- OP = DDLT + SS

where OP = order point.

DDLT = demand during the lead time.

SS = safety stock.

Figure 6. Quantity on hand versus time

: Independent demand item

- With order point system :

· Order quantities are usually fixed.

· The order point is determined by the average demand during the lead time.

· The interval between replenishment are not constant but vary dependent on the

actual demand during the reorder cycle.

· Average inventory :

Order Quantity	+ Safety stock =	[eqn: Q over 2] + SS
2

4. Safety Stock.

□ Why Safety Stock ?

- Safety stock is intended to protect against uncertainty in supply and demand.

- Uncertainty may occur in two ways : Quantity uncertainty and Timing uncertainty.

· Quantity uncertainty occurs when the amount of supply or demand varies.

· Timing uncertainty occurs when the time of receipt of supply or demand differs

from that expected.

- There are two ways to protect against uncertainty : Safety stock and Safety lead time.

- Safety stock is the most common way of buffering against uncertainty. The safety stock

required depends on the following.

· Variability of demand during the lead time.

· Frequency of reorder.

· Service level of desired.

· Length of the lead time.

Figure 7-1 Demand Uncertainty

Figure 7-2 Supply Uncertainty

□ Service Levels.

- Factors for calculating service levels.

1. Variation in demand during lead time.

[eqn: bar x = {sum from i=1 to n x_i } over n],       [eqn: sigma = root{{ sum from i=1 to n ( x_i - bar x )^2} over n}] or MAD

2. Normal distribution.

3. Safety factor.

: The service level is directly related to the number of standard deviation

: provided as safety stock and is usually called the safety factor.

: The service level is the percentage of order cycles without a stockout.

Service level (%)	Safety factor
50 75 80 85 90 94 95 96 97 98 99 99.86 99.99	0.00 0.67 0.84 1.04 1.28 1.56 1.65 1.75 1.88 2.05 2.33 3.00 4.00

□ Service Levels.

1. SS = Sigma([eqn: sigma]) × safety factor              (if [eqn: LTI]  = [eqn: FI])

2. SS = Sigma([eqn: sigma]) × [eqn: root {LTI over FI }] × safety factor   (if [eqn: LTI] ≒ [eqn: FI])

where [eqn: LTI] = Lead time interval.

[eqn: FI]  = Forecast interval.

□ Determining the Safety Stock and Order Point.

- Example 1.

If the standard deviation is 200 units, what safety stock should be carried to provide

a service level of 90% ? If the expected demand during the lead time is 1500 units.

What is the order point ?

Answer)

· Safety Stock = sigma × safety factor = 200 × 1.28 = 256 unts.

· Order Point = DDLT + SS = 1500 + 256 = 1756 units.

- Example 2.

The safety stock for an item is 150 units, and the lead time is two weeks. if the

lead time changes to three weeks, calculate the new safety stock.

Answer)

· New safety stock = old safety stock × [eqn: rm{root{{N e w ~i n terval} over {Old ~i n terval}}}]

.     = 150 × [eqn: root{3 over 2}]  = 150 × 1.22 = 183 unts.

- Example 3.

Suppose management stated that it could tolerate only one stockout per year for a                specific item. For this particular item, the annual demand is 52,000 units, it is                     ordered in quantity of 2600, and the standard deviation of demand during the lead                 time is 100 units. The lead time is one week. Calculate :

a. Number of order per year.

b. Service level.

c. Safety stock.

d. Order point.

Answer)

· Number of orders per year  = Annual demand / order quantity

= 52,000 / 2600 = 20 times per year.

· Since one stockout per year is tolerance, there must be no stockouts 19 (20-1)

times per year.

: Service level = [eqn: 20-1 over 20] = 95 %

· Calculate safety stock.

: Safety factor = 1.65

: Safety stock = sigma × safety factor = 100 × 1.65 = 165 units.

· Order point

: Demand during lead time = (1 week) [eqn: 52,000 over 52] = 1000 units.

: Order point = demand during lead time + SS

= 1000 + 165 = 1165 units.

5. Determining When the Order Point is Reached.

□ Two-Bin System.

Figure 8. A Two-bin System

- A quantity of an item equal to the order point quantity is set aside (frequently in a

separate or second bin) and not touched until all the main stock is used up.

- The two-bin system is a simple way of keeping control of C items.

□ Perpetual Inventory Record System.

- A perpetual inventory record is a continual account of inventory transactions as they occur.

- At a minimum, it contains the balance on hand, but it may also contain the quantity on

order but not received, the quantity allocated but not issued, and the available balance.

Figure 9. Perpetual Inventory Record.

426254 SCREW				Order Quantity 500		Order Point 100
Date	Ordered	Received	Issued	On hand	Allocated		Available
01				500			500
02				500	400		100
03	500			500
04			400	100	0		100
05		500		600	0		600

- An inventory record contains variable and permanent information.

· Permanent information

: Part number, name, and description.

: Storage location.

: Order point.

: Order quantity.

: Lead time.

: Safety stock.

: Suppliers.

· Variable information

: Quantities ordered : dates, order numbers, and quantities.

: Quantities received : dates, order numbers, and quantities.

: Quantities issued : dates, order numbers, and quantities.

: Balance on hand.

: Allocated : date, order numbers, and quantities.

: Available balance.

6. Periodic Review System.

□ Periodic Review System.

- In the periodic review system, inventory levels are reviewed periodically ; and orders

are placed all at one time, often for all items in stock, to replenish the inventories up

to some target level.

- This approach is applicable especially in retail business where nearly all goods are

ordered from a common source and where it is not feasible to keep perpetual

inventory records.

- Modern point-of-sale devices make possible perpetual inventory records for retailers in

many situations. Therefore, periodic review systems are less prevalent now than they

used to be.

□ A Periodic Review Model

- The review periods are spaced equally, whereas the order quantities vary based on the

actual demands.

- An order is placed at the time of the review and is received into inventory after

expiration of the delivery lead time.

- A primary step with a periodic review inventory systems is to determine the intervals

for reviews, such as daily, weekly, or semimonthly.

□ Review Periods

- An optimal review period might be determined in a manner similar to the POQ.

- However, the interval is determined by more practical considerations, so that a large

group of items, which are stocked in adjacent locations or ordered from the same

source, are reviewed at the same time regardless of usage.

Figure 8. Periodic Review System

□ Target Level or Maximum-Level Inventory.

- The quantity equal to the demand during the lead time plus the demand during the

review period plus safety stock is called the target level or maximum-level inventory.

- Target Level Inventory.

·[eqn: T ~=~ D(R+L) + SS]

where [eqn: T] = target inventory level.

.[eqn: D] = demand per unit of time.

.[eqn: L] = lead-time duration.

.[eqn: R] = review period duration.

.[eqn: SS] = safety stock.

□ Used where

- Where there are many small issues from inventory, and posting transactions to

inventory records are very expensive. (ex. supermarkets, retailer.)

- Where ordering costs are small. This occurs when may different items are ordered

from one source.

- Where many items are ordered together to make up a production run or fill a

truckload.

- Example.

A hardware company stocks nuts and bolts and orders them from a local supplier                 once every two weeks (ten working days). Lead time is two days. The company                  has determined that the average demand for 1/2-inch bolts is 150 per week (five                  working days), and it wants to keep a safety stock of three days' supply on hand.                An order is to be planed this week, and stock on hand is 130 bolts.

Answer)

· Demand per unit of time (D) = 150 ÷ 5 = 30 per working day.

· Lead-time duration (L) = 2 days.

· Review period duration (R) = 10 days.

· Safety stock (SS) = 3 days' supply = 90 units.

· Inventory on hand (I) = 130 units.

· Target Level T = D(R ／ L) ／ SS = 30 (10 + 2) ／ 90 = 450 units.

· Order Quantity Q = T - I =  450 - 130 = 320 units.

7. Auditing Inventory Records.

□ Auditing Inventory Records.

- Errors in record keeping occur, and inventories have to be checked.

- There are two basic methods of checking inventory record accuracy :

· Periodic, usually annual, counts of all the items.

· Cycle, usually daily counts of specific items.

□ Periodic Inventory Audit.

- The primary purpose is to verify the financial value of the inventory.

- Production is disrupted while inventory takes place.

- Labor and paperwork are expensive.

- Accuracy is poor.

· People taking the inventory are usually inexperienced and error prone.

□ Cycle Counting.

- Inventory is counted continually throughout the year.

- Some items are counted each day.

- All item are counted a predetermined number of times per year depending on their importance.

- Cycle counting uses trained and dedicated personnel.

- Advantages of cycle counting.

· Timely detection and correction of problems.

· Little or no loss of production time.

· Identification and elimination of causes of error.

- Determining Count Frequency.

· The count frequency is the number of times an item is counted in a year.

· There are different methods of determining the count frequency. One of the most

common is the ABC method.

1. Classify items by their importance into A, B, and C categories.

2. Establish rules for count frequency of each classification.

3. Establish count schedule.

- Count Frequency Example.

Classification	Number of items	Count Frequency	Number of Counts
A	2,000	12	24,000
B	3,000	4	12,000
C	5,000	2	10,000
Total Counts			46,000
Workdays per year			250
Counts per day			184

- When to count : It can be scheduled at regular intervals or on special occasions.

· When an order is placed.

: Items are counted just before an order is placed.

: This has the advantages of detecting errors before the order is placed and

reducing the amount of work by counting at a time when stock is low.

· When an order is received.

: Inventory is at its lowest level.

· When the inventory record reaches zero.

: This method has the advantage of reducing work.

· When a specified number of transactions have occurred.

: Error occur when transactions occur.

: Fast-moving items have more transactions and are more prone to error.

· When an order occurs.

: A special count is appropriate when an obvious error is detected.

: This may be a negative balance on the stock record or when no items can

: be found although the record shows some in stock.

■  Performance Check

1. Which of the following statements best describes stockkeeping units ?

A. Sodas in a 6-pack and 12-pack are the same SKU because the cans are the same SKU.

B. White shirts of different size but in the same size box are the same SKU.

C. Wires of different gauges that are stocked in reels are the same SKU.

D. Two white shirts in the same inventory but of different sizes or styles would be different SKUs.

2. If the order quantity is increased, which of the following occurs ?

A. The cost of carrying inventory decrease, and the cost of ordering increase.

B. The cost of carrying inventory increase, and the cost of ordering decrease.

C. The cost of carrying inventory increase, and the cost of ordering increase.

D. The cost of carrying inventory decrease, and the cost of ordering decrease.

3. In developing the standard economic order quantity (EOQ) formula, which of the following assumptions are made ?

A. Demand for the item is relatively uniform.

B. Replenishment is in lots or batches that arrive all at once.

C. Ordering and carrying costs are constant.

D. All the above are assumed.

4. Which of the following statements is best ?

A. Order point = DDLT + SS.              B. Average inventory = (Q + SS) ÷ 2.

C. Safety stock is always needed.          D. Safety stock = order point + order quantity.

5. Safety stock will depend on which of the following ?

A. Variability of demand.                    B. Cost of carrying inventory.

C. Cost of placing an order.                D. Product obsolescence.

6. Assuming that the cost per order and the demand are constant, what effect will increasing the order quantity have on the annual ordering cost ?

A. Ordering cost will decrease.

B. Ordering cost will increase.

C. Ordering cost will remain the same.

D. Ordering cost will increase at a decreasing rate.

7. What effect will increasing the order quantity have on the annual cost of carrying inventory ?

A. Annual cost of carrying inventory will increase.

B. Annual cost of carrying inventory will decrease.

C. Annual cost of carrying inventory will remain the same.

D. Annual cost of carrying inventory is not affected by the order quantity.

8. What type of inventory record system keeps a continuous account of transactions as they occur ?

A. Perpetual inventory system.

B. Periodic inventory system.

C. Two-bin system.

D. Safety stock system.

9. If the lead time is one week, the review period one week, the average demand 100 units per week, and the safety stock 50 units, the target level will be

A. 150 units.      B. 200 units.       C. 250 units.       D. 300 units.

10. Which of the following is an advantage of cycle counting ?

A. Timely detection and correction of problems.

B. Reduction of direct labor cost.

C. Use of spare labor.

D. Replenishment of inventory.

Solutions :

1  2  3  4  5  6  7  8  9  10

D B D A A A A A C A