Ko ç University Graduate School of Business MBA Program OPSM 501: Operations Management Week 5: Batching EOQ

Zeynep Aksin [email protected]

High-Inventory Manufacturing 4 months (24 hrs a day, 7 days a week) Order : 1000 units A : 1/2 hr/unit inventory B : 1/10 hr/unit avg.

inventory C : 1 hr/unit B : 1/10 hr/unit 1000 2000 D : 3/4 hr/unit Time (hours)

Low-Inventory Manufacturing 2 months

Move batches of 200 Release materials according to the bottleneck

Order : 1000 units A : 1/2 hr/unit B : 1/10 hr/unit inventory avg.

inventory 1000 2000 C : 1 hr/unit B : 1/10 hr/unit D : 3/4 hr/unit Time (hours)

When do you detect quality problems?

Quality control

A B C B D

Damage done

How do you incorporate engineering changes?

A B C B D

Engineering change one month after start of order

Shorter Lead time - High margins Quoted lead time of the order is 3 months A B C B D overtime No overtime

Due-date performance A B C B D Forecast validity

Batch Flow Operations Carry a Lot of Inventory • SMED (Single minute exchange of die): reduce set-up times

Things that influence flow time   Process control Lotsize – Before I move from one product run to another, how much will I produce • • • Physical constraints Customer order size Managerial decisions  Set-up time/production time

Batching in practice • • • • Common in low volume manufacturing (including a lot of high-tech) Also: transportation, education / training Example: mailing list development Creates an inherent mismatch between demand and supply

Lotsize decision    Three products: P1, P2, P3 Produce 100 units of each Alternatives – 100 P1 100 P2 100P3 – 1P1 1P2 1P3 1P1 1P2 1P3 • 100 times  Set-up time – Cutting tools, cleaning, calibration, loading programs, etc.

Set-up times  Set-up time does not depend on lotsize and is the same for all lotsizes.

 Production time depends on lotsize – Not always (baking, heat treat)  Long set-up times large lotsizes

Example  P1,P2,P3 example – – – Set-up time 60 min.

Production time 10 min/unit Need 3 of each type  Try the alternatives – 1P1, 1P2, 1P3, 1P1, 1P2, 1P3, 1P1, 1P2, 1P3 – 3P1, 3P2, 3P3

Product Space, Efficient frontier

Responsiveness

High Low High per unit costs Smaller batches Reduce set-up times Now Larger batches Low per unit costs Higher frontier

Costs

Process Analysis with Batching • Capacity calculation changes: Capacity given Batch Size=

Batch Size Set-up time + Batch-size*Time per unit

• Note: Capacity increases with batch size: Capacity 0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 1/p Batch Size • Note further: … and so does inventory (and thus flow time) See chapter 5

Example Milling S=120 min p= 2 min/unit B=12? B=300? Recommended B=?

Assembly S=0 p=3 min/unit

Economies of Scale: Inventory Management for a Retailer The South Face retail shop in the SapphireTower has observed a stable monthly demand for its line of Gore-Tex jackets on the order of 100 jackets per month. The retail shop incurs a fixed cost of $2,000 every time it places an order to the Adana warehouse for stock replenishment. The marginal cost of a jacket is $200, and South Face’s cost of capital is approximately 25%.

What order size would you recommend for The South Face?

warehouse retailer

Economies of Scale: Inventory Build-Up Diagram

R

: Annual demand

rate

,

Q

: Number of jackets per replenishment order Inventory

Inventory Profile

: # of jackets in inventory over time.

 Number of orders per year =

R

/

Q.

Q R =

Demand rate  Average number of .

jackets in inventory =

Q

/2 Time

t

Find most economical order quantity: Spreadsheet for The South Face

Number of units per order/batch

Q

50 100 150 200 250 260 270 280 290 300 310 320 330 340 350 400 500 600 700

Number of Batches per

Year: R/Q 4 4 4 3 3 2 2 2 24 12 8 6 4 4 4 5 5 4 4

Annual Setup Cost

48000 24000 16000 12000 9600 9231 8889 8571 8276 8000 7742 7500 7273 7059 6857 6000 4800 4000 3429

Annual Holding Cost

1250 2500 3750 5000 6250 6500 6750 7000 7250 7500 7750 8000 8250 8500 8750 10000 12500 15000 17500

Annual Total Cost

49250 26500 19750 17000 15850 15731 15639 15571 15526 15500 15492 15500 15523 15559 15607 16000 17300 19000 20929

Total Annual Cost Total Annual Cost = Annual Purchasing Cost + Annual Ordering Cost + Annual Holding Cost

R TC = RC + Q S + Q 2 H

  Using calculus, we can take the derivative of the total cost function and set the derivative (slope) equal to zero We can also use economic intuition

R S H Q

: : : : Economies of Scale: Economic Order Quantity

EOQ

Demand per year, Setup or Order Cost ($/setup; $/order), Marginal annual holding cost ($/per unit per year), Order quantity.

Q EOQ

 2

SR H r C h

: : Cost per unit ($/unit), Cost of capital (%/yr), : Physical unit holding cost ($/unit,yr),

H

= (

h

+

r

)

C .

EOQ Total annual costs

H Q/2:

Annual holding cost

S R /Q:

Annual setup cost Batch Size

Q

EOQ Model: if there is a lead time L Q EOQ ROP ROP L = Reorder point L = Lead time (constant) Q = Economic order quantity L Time

Economic Order Quantity (EOQ) Model  Economic Order Quantity (EOQ) Model –

Robust, widely used

–

Insensitive to errors in estimating parameters (40-20-2 Rule):

• 40% error in one of the parameters • 20% error in Q • < 2% of total cost penalty

Learning Objectives:

Batching & Economies of Scale

     Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).

Average inventory for a batch size of

Q

is

Q

/2.

The optimal batch size trades off setup cost and holding cost.

To reduce batch size, one has to

reduce setup cost (time).

Square-root relationship between

Q

and (

R

,

S

): – If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.

– To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.

Announcements    HW 2 is due next time The Goal is due next time Have a nice break!