Chapter 12

Independent DemandInventory Management

What is “Independent Demand”

• If demand is not fully predictable, then it is called independent demand. Examples: customer demand, demand for repair and maintenance, demand for production varying with the market, …

• Number of components required in a product is called dependent demand. Example: four tires for a car, or 400 tires required for producing 100 cars.

What is “inventory”

• Your inventory refers to the items you keep at your cost for future use. Or

• Your inventory refers to the items for which you have put your money in but have not got the money back.

Types of Inventory

Functions of Inventory (1)

• As a cushion / buffer.– To absorb uncertainties of demand and

suppliers,– To maintain smooth operations.– Example:

• finished good inventory, • material inventory, • MRO inventory, • WIP inventory

Functions of Inventory (2)

• As the result of scale of economy or lot size.– lot size inventory,– transportation inventory.

• As a speculation.

Bad Side of Inventory

• Inventory is money that is put away.• Inventory costs money to hold.• Inventory does not add value to product.• Inventory risks shrinkage due to

pilferage, obsolescence and deterioration.

More or Less Inventory?

• Higher inventory is good to avoid stockout and to absorb uncertainties, but is bad in high cost of inventory.

• Lower inventory is good in saving money, but is bad in increased risk of stockout, customer dissatisfaction, and process interruption.

Tasks of Inventory Management

• “Customer satisfaction”.– Customers are those who will use the inventoried

items, such as external customers and internal production process.

• Keep inventory cost low.• Maintain inventoried items.

– Keep accurate records,– Items are kept so as to be safe and free of

damage, convenient to be located, …

Measurement of Inventory (1)

• Inventory turnover

• It tells how many times the inventory can be used up in a year.

• The higher the turnover the more efficient the inventory.

$in inventory avg.sold goods ofcost annual

Measurement of Inventory (2)

• Weeks of Supply

• It tells how many weeks on average the inventory can sustain.

• The smaller the more efficient.

$in usage weekly avg.$in handon inventory avg.

Measurement of Inventory (3)

• Relationship between weeks of supply and inventory turnover:

supply of weeksyearper weeksofnumber

Turnover

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Example (p.436)

• Last year, total cost of good sold = $5,200,000

• Average inventory = $1,040,000• 52 weeks in a year.

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Example (p.457-458) (cont.)

weeks10.4 turnovers5

weeks52 supply of Weeks

or (weeks), 10.4 $100,000

$1,040,000supply of Weeks

eek$100,000/w 52

$5,200,000 demand weekly Avg.

(turns/yr) 5$1,040,000$5,200,000 Turnover

Determine Inventory Level

• Inventory level for a product item is measured by number of units on hand.

• “A product item” here is known as stock-keeping-unit (SKU). For example, a pair of same jeans with size 32x34 stored in three storages is viewed as three different SKUs.

Inventory Level Changes All the Time

• For each SKU, number of units on hand would change every day or every minute.

• It goes down when some units are used.• It goes up when some units are received

from the supplier.

Inventory DynamicInventoryon hand (units)

Time (day)0

Q,unitsin anorder

Q/2

Order receiving

Average Inventory

• Average inventory is the measure of inventory level

• Average daily inventory level

2orderan in quantitiy

2inventory of levelhighest

Costs Related to Inventory

• Inventory holding cost• Ordering cost• Shortage cost• Item cost (cost of goods)

Carrying Cost

• Includes:– Capital cost– Opportunity costs, – Storage space rental, and labor and

facilities for storage,– Cost of obsolescence and damage,– Insurance.

• Varies with the amount of inventory.

Ordering Cost

• Includes:– Shipping and handling cost,– Cost of processing orders, such as forms,

papers, labor.• Typically, this cost does not change with

number of units in an order.

Shortage Cost

• Includes:– Lost sale, – Expediting and back ordering expenses,– Cost of reputation and goodwill

Some Basic Calculations (1)

D = Annual demand in unitsS = Ordering cost per orderH = Holding cost per unit per yearQ = Number of units in an order.

• Number of orders required in a year

QD

orderan in units ofnumber unitsin demand annual

Some Basic Calculations (2)• Avg. inventory = • Total annual inv. holding cost = • Number of orders in a year• Total annual inv. ordering cost• Total annual inventory cost

HQ2

SQD

SQD H

2Q

2Q

QD

Example

• Annual demand (D) = 10,000 units• Item cost = $3 per unit• Ordering cost (S) = $75 per order• Holding cost (H) = $6 per unit per year• Current order quantity (Q) = 100 unit /order

Example (continuing)

• If order quantity is 100 units/order, calculate:(a) Average inventory level;(b) Total annual inventory holding cost;(c) Number of orders to place in a year;(d) Total annual ordering cost;(e) Total annual inventory cost;(f) Total annual cost including inventory and item

cost.

Example (continuing)

• If order quantity is 1,000 units/order, calculate:(a) Average inventory level;(b) Total annual inventory holding cost;(c) Number of orders to place in a year;(d) Total annual ordering cost;(e) Total annual inventory cost;(f) Total annual overall cost that includes inventory

and item cost.

Economic Order Quantity (EOQ)

• EOQ is the order quantity at which the total annual inventory cost (annual holding cost + annual ordering cost) is minimized.

EOQ Total CostsTotal annual costs

= annual ordering costs + annual holding costs

Formula for EOQLet Q* be Economical Order Quantity (EOQ):

HDSQEOQ 2*

Example (Revisit)

• Calculate EOQ amount Q*.• Calculate the total annual inventory cost

associated with Q*.• Calculate the overall annual total cost

associated with Q*, which includes inventory cost and cost of good.

Cost of Goods• Cost of good of inventoried items is

not in the EOQ formula, since total item cost remains a constant Dprice, no matter what size of order is.

• Sometime, unit carrying cost is a percent of the purchase cost of the item.

• Item cost must be considered if volume discount presents.

Features of EOQ

• EOQ is the ‘optimal’ lot size, which means any lot size other than EOQ would cause higher total inventory cost than EOQ.

• Greater D would cause a greater EOQ.• Greater S would cause a greater EOQ.• Greater H would cause a smaller EOQ.• At EOQ, total annual holding cost = total

annual ordering cost.

How Much?How Much? When!When!

Basic Decisions in Inventory Management:

Reorder Point (1)

• It tells when to place an order.• Reorder point is in terms of number of

units on hand, at which an order should be placed.

• Reorder point must be at least the demand during the delivery time (lead time).

Reorder Point (2)

• Demand during the lead time = (avg. daily demand)(lead time)

Safety Stock and Uncertainties

Reorder Point (3)

• If demand and lead time are uncertain, then reorder point is calculated as:R = (Demand during the lead time) + (safety stock)

= (avg. daily demand)(lead time)+ (Safety Stock)

= (d)(L)+SS

Example

• Procomp’s annual demand is 8,000 units. There are 200 work days per year. Lead time = 3 days, and safety stock = 20 units

• What is the reorder point?

Safety Stock• Safety stock is the extra stock to help

deal with uncertainties after order is placed so as to reduce the risk of stockout.

• The more uncertain the higher the safety stock.

• The more you care stockout, the higher the safety stock you apply.

Determining Safety Stock

• SS=zdL

where z = number of standard deviations derived with

the % risk you could take for stockout from Appendix B p.671;

dL = standard deviation (in units) of demand during the lead time.

Example (p.485)

• Demand during the lead time averages 5,000 units with a standard deviation 300 units.

• Manager can take up to 4% of stockout risk.• What is the safety stock? Reorder point?

• Note: Taking at most 4% of stockout risk means at least 96% of chance with no stocktout is tolerable. In the half-Normal-graph as in Appendix B on p.671, the corresponding shaded area is thus 96%-50%=46%=0.46. Find 0.46 in the table, then z value is on the left and top.

Trial-and-Error Method for SS

• Progressive adjustment.– Managers may adjust safety stock by trial-

and-error, based on the historical data and their experience.

Average Inventory with Safety Stock

• If safety stock is SS, then the average inventory formula is:

Avg. Inventory = SSQ

2

How Does EOQ Work in Inventory Control?

• For each item k, calculate its economic order quantity Qk

* and its reorder point Rk.

• Keep watching the inventory on hand. If the stock of item k drops to Rk, order Qk

* units of item k.

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EOQ Assumptions• Demand rate is constant.• No quantity discounts are available• Ordering (or setup) costs are constant• All demand is satisfied (no shortages)• The ordered units are delivered in a

single shipment

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Quantity Discount EOQ Model

• Assumptions are same as EOQ except that unit price depends upon the quantity ordered

• The best order quantity must make the overall total cost (total inventory cost plus total cost of good) minimized.

D*PriceH2QS

QDTCoverall

Example on p.477-478

• D = 5,200 lbs / year• S = $50 / order; H = 30% of unit price

Discount brackets Unit price (P) H = P * 30%

0 – 499 lbs / order $7.50500 – 999 lbs / order $6.901,000 lbs up / order $6.20

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To Determine Order Quantity under Volume Discount

• Calculate EOQ Q* (If holding cost H is a % of unit price, use the lowest possible unit price P first; if Q* is not in the discount bracket for price P, then re-calculate EOQ using the next lowest possible unit price; until Q* is consistent with the assumed price P. (see ex. p.477-479))

• Compare the TCoverall for Q* and TCoverall for each of discount break points that are more than Q*. (see ex. p. 480, and Prob. 3, p.496-497)

• The order quantity is with the lowest TCoverall.

Example (p.480)

• Annual demand (D) = 780 units.• Ordering cost (S) = $15 / order.• Holding cost (H) = $3 per unit per year.• Prices discounted with volume:

1-73 units $60 / unit,74-144 units $56 / unit,

145 or more $53 / unit.• Determine the best order quantity.

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Economic Production Quantity (EPQ)

• The assumptions of EPQ are same as EOQ except that the ordered units arrive piece by piece.

• Application example: • a company's finished good inventory that is

supplied by the company's production department.

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EPQ Profile

53

EPQ Formula

d = daily demand in units,p = daily production capacity in units,D, H, S are defined same as before,then

)1(

2*

pdH

DSQ

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Meaning of Q* in EPQ• Q* here is still the “order quantity”

(number of units in an order), but now the “order” is issued to the production department of the same company.

• Therefore, Q* is actually the production batch size or lot size.

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Formulas in EPQ (1)• Maximum Inventory Level, Imax:

• Average Inventory Level

=

)1(*max pd

QI

2maxI

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Formulas in EPQ (2)

• Total annual ordering cost = (same as for EOQ)• Total annual holding cost

• Total annual inventory cost

SQD

H )(12Q

pd

H )(12Q

SQD

pd

HI

2max

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Example (p.476)

Monthly demand = 1,500 units;Setup (ordering) cost = $800/orderHolding cost = $18/unit/yearThere are 20 work days in a month. The

company can produce 2,500 units per month. Once a unit is finished, it is counted into the inventory. Lead time is 5 days.

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Example (cont.)

(a) Calculate the best production batch size (economic production quantity).

(b) Calculate the total annual inventory cost associated with the EPQ you just found.

(c) If the current production batch size is 1,200 units, what is the current total annual inventory cost?

(d) Calculate the reorder point.

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Other Order Quantity Approaches

• Lot-for-lot:

– Order exactly what is needed• Min-max system:

– When inventory falls to a pre-set minimum level, place an order to the predetermined maximum level

• Order enough for n periods• Periodic review

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Periodic Review System• At specified intervals, order up to a

predetermined target level• Target inventory • Order quantity

where TI=target inventory (in units) d=average daily demand (in units) RP=review period (in days)

L=Lead time (in days) SS=safety stock (in units)

OH=inventory on hand (in units)

SSLRPdTI

OHTIQ

Single-Period Inventory

• Inventoried items are for a short season, such as holiday decorations, Christmos trees, newspapers, vegetable salad.

• Generate a decision table, order amounts vs. demands, and determine the best order quantity by using Decision Making theory (learned in BSNS2120).

Example (p.489)• Possible demands for a T-shirt in Walk for Diabetes:

80 shirts 0.2 probability90 shirts 0.25 probability100 shirts 0.3 probability110 shirts 0.15 probability120 shirts 0.1 probability

• A T-shirt will be priced at $20 and cost at $8 per unit. Unsold shirts will be sold for rags at $2 per unit.

• How many T-shirts should be ordered?

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ABC Classification• There is a critical few and trivial many.• Pareto’s law:

– Roughly 20% of inventories will account for 80% of inventory value

• Divide inventories into A, B, and C categories based on value, risk, ... More management efforts will be given to more important items.

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Annual Dollar Usage• An item’s inventory value (in $) tends to

be high if its unit cost is high, and/or it has a large demand.

• Annual dollar usage (ADU) is a measure of the combination of unit cost and demand of an item :

ADU = annual demand X unit cost

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Steps of ABC Classification• Calculate ADU for each item;• Sort items on ADUs in descending order;• Calculate %-of-ADU and cumulative-%-of-

ADU for each item;• Classify the items into groups (class A items

takes 60% to 80% of total ADU, class C items take 3% to 15% of total ADU)

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Example (p.462)

• Follow the steps of ABC classification in the last slide.

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An Application of ABC• Inventoried items should be counted

periodically to reconcile the records with actual on-hand.

• When ABC analysis is applied, one may count, for example, class A items once a day, class B items once a week, and class C once a month or a year.

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Towards JIT• In a JIT system, order quantity and

production batch size are as small as possible.

• Reviewing the formulas for EOQ and EPQ, the best way to reduce order quantity and production batch size is to reduce ordering cost or setup cost.