BUAD306

Chapter 13 - Inventory Management

Everyday Inventory

Food Gasoline Clean clothes…

What else?

Inventory

Stock or quantity of items kept to meet demand

Takes on different forms Final goods Raw materials Purchased/component parts Labor In-process materials Working capital

Inventory

Static – only one opportunity to buy and sell units

Dynamic – ongoing need for units; reordering must take place

Demand

Dependent DemandItems are used internally to produce a

final product Independent Demand

Items are final products demanded by external customers

Reasons To Hold Inventory

To meet anticipated demand To smooth production requirements To decouple components of the production-

distribution system To protect against stock-outs To take advantage of order cycles To hedge against price increases or to take

advantage of quantity discounts To permit operations

Inventory Costs

Carrying CostsCosts of holding an item in inventory

Ordering CostsCosts of replenishing inventory

Shortage (stockout) CostsTemporary or permanent loss of sales

when demand cannot be met

Inventory Management

Objective: To keep enough inventory to meet customer demand and also be cost-effective

Purpose: To determine the amount of inventory to keep in stock - how much to order and when to order

How much and when to order inventory?

Inventory Management Requirements A system to keep track of the inventory

on hand and on order A reliable forecast of demand Knowledge of lead times Reasonable estimates of inventory

costs A classification system for inventory

items (ABC)

Inventory Control Systems

Control the level of inventory by determining how much to order and whenContinuous (Perpetual) Inventory

System - a continual record of the inventory level for every item is maintained

Periodic Inventory System - inventory on hand is counted at specific time intervals

Other Control Systems/Tools

Two-Bin System - two containers of inventory; reorder when the first is empty

Universal Product Code (UPC) - Bar code printed on a label that has information about the item to which it is attached

RFID Tags 0214800 232087768

Considerations

Lead TimeTime interval between ordering and

receiving the order Cycle Counting

Physical count of items in inventory Usage Rate

Rate at which amount of inventory is depleted

Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

Economic Order Quantity

The EOQ Model determines the optimal order size that minimizes total inventory costs

Inventory Costs

Carrying Costs – cost associated with keeping an item in stockIncludes: storage, warehousing,

insurance, security, taxes, opportunity cost, depreciation, etc.

Ordering Costs – cost associated with ordering and receiving inventoryDetermining quantities needed,

preparing documentation, shipping, inspection of goods, etc.

Optimal Order Quantity

Q = 2DS

H =

2 (Annual Demand) (Order Cost)

Annual Holding Cost per unito

Qo

DLength of order cycle =

DQo

# Orders / Year =

Basic EOQ Model

Annualcarryingcost

Annualorderingcost

Total cost = +

Qo

2 H D

Qo

STC = +

Where: Qo = Economic order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost

Cost Minimization Goal

The Total-Cost Curve is U-Shaped

Ordering Costs

QO Order Quantity (Q)

An

nu

al C

os

t

(optimal order quantity)

SQo

DH

QoTC

2

Carrying Costs

EOQ Example 1

A local office supply store expects to sell 2400 printers next year. Annual carrying cost is $50 per printer, and ordering cost is $30. The company operates 300 days a year.

A) What is the EOQ?

B) How many times per year does the store reorder?

C) What is the length of an order cycle?

D) What is the total annual cost if the EOQ quantity is ordered?

Given:Demand = D = 2400Holding Cost = H = $50 per unit per yearOrdering Cost = S = $30

A. What is the EOQ?

B. How many times per year does the store reorder?

C. What is the length of an order cycle?

Given:Demand = D = 2400Holding Cost = H = $50 per unit per yearOrdering Cost = S = $30

D. What is the total annual cost if the EOQ quantity is ordered?

TC = Carrying cost + Ordering cost

EOQ Example 2

A local electronics store expects to sell 500 flat-screen TVs each month during next year. Annual carrying cost is $60 per TV, and ordering cost is $50. The company operates 364 days a year.

A) What is the EOQ?

B) How many times per year does the store reorder?

C) What is the length of an order cycle?

D) What is the total annual cost if the EOQ quantity is ordered?

Given:Demand = D = 6,000Holding Cost = H = $60 per unit per yearOrdering Cost = S = $50

A. What is the EOQ?

B. How many times per year does the store reorder?

C. What is the length of an order cycle?

Given:Demand = D = 6,000Holding Cost = H = $60 per unit per yearOrdering Cost = S = $50

D. What is the total annual cost if the EOQ quantity is ordered?

TC = Carrying cost + Ordering cost

Other Considerations

Safety Stock Reorder Point Seasonality

Quantity Discounts

A price discount on an item if predetermined numbers of units are ordered

TC =

Carrying cost + Ordering cost + Purchasing cost =

(Q / 2) H + (D / Q) S + PD

where P = Unit Price

Quantity Discount Example

Campus Computers 2Go Inc. wants to reduce a large stock of laptops it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule as shown below. Given the discount schedule and its known costs, the bookstore wants to determine if it should take advantage of this discount or order the basic EOQ order size.

Quantity Price

1 – 49 $1,500

50 – 89 $1,000

90 + $800

Carrying Cost: $200

Ordering Cost $1,000

Annual Demand 400 units

First, determine the optimal size and cost with the basic EOQ model.QO =

This order size is eligible for the discount price of $1,000… now we compute the total costTC =

Compare this cost to an ordering size of 90 @ $800:TC = (Q / 2) H + (D / Q) S + PD =

What if a new discount was offered where they would receive a price of $790 if they were to order 150 or more?

HW #13

A mail-order house uses 18,000 boxes a year. Carrying costs are $.60 per box per year and ordering costs are $96. The following price schedule is offered. Determine the EOQ and the # of orders per year.

# Boxes Unit Price

1000-1999 $1.25

2000-4999 $1.20

5000-9999 $1.15

10000+ $1.10

EOQ with Incremental Replenishment (EPQ)

Used when company makes its own product

Considers a variety of costs/terms:Carrying CostSetup Cost (analogous to ordering costs)Maximum and Average Inventory LevelsEconomic Run QuantityCycle TimeRun Time

EOQ with Incremental Replenishment (EPQ)

DefinitionsS = Setup CostH = Holding CostImax = Maximum Inventory

Iavg = Average InventoryD = Demand/Yearp = Production or Delivery Rateu = Usage Rate

EOQ with Incremental Replenishment

Total Cost = Carrying Cost + Setup Cost

(Imax/2) H + (D/Qo) S

Economic run quantity Qo = 2DS/H * p/(p-u)

Cycle time (time between runs)

Qo /u

Run time (production phase)

Qo /p

Maximum Inventory Level Imax = (Qo /p)(p-u)

Average Inventory Level Iaverage = Imax /2

Assumptions

Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually, production

periodically Production rate is constant Lead time doesn’t vary No quantity discounts

EOQ Replenishment Example

A toy manufacturer uses 48,000 rubber wheels per year for its product. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the:

Optimal run sizeMinimum total annual cost for carrying and setupCycle time for the optimal run sizeRun time

D = 48,000 wheels per yearS = $45 H = $1 per wheel per yearp = 800 wheels per dayu = 48,000 wheels per 240 days, or 200 wheels per day

Qo = 2DS/H * p/(p-u) =

Imax = (Qo /p)(p-u) =

TCmin = (Imax/2) H + (D/Qo) S =

Cycle time = Qo /u =

Run time = Qo /p =

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