Chapter 12

Assemble-to-Order, Make-to-Order, and Quick Response with Reactive Capacity

The demand-supply mismatch cost• Definition – the demand supply mismatch cost includes the cost of left

over inventory (the “too much” cost) plus the opportunity cost of lost sales (the “too little” cost):

• The maximum profit is the profit without any mismatch costs, i.e., every unit is sold and there are no lost sales:

• The mismatch cost can also be evaluated with

saleslost ExpectedC

inventory over left ExpectedC cost Mismatch

u

o

cpprofit Maximum

Mismatch cost = Maximum profit – Expected profit

When is the mismatch cost high?• Mismatch cost as a percent of the maximum profit

where f(z) = density function of the Normal distribution (In Excel f(z)=normdist(z,0,1,0))

• Hammer 3/2’s mismatch cost as a percentage of the maximum profit is

• The mismatch cost is high when (f(z) / F(z)) and (s / )m are high.

(z)

(z)

%1.143192

1181

7794.0

2966.0

Low critical ratios - high mismatch costsThe mismatch cost is high when (f(z) / F(z)) is high …

… (f(z) / F(z)) is high when the critical ratio is low:

0.0

0.3

0.5

0.8

1.0

1.3

1.5

1.8

2.0

2.3

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85

critical ratio = C u / ( C o + C u )

(z)/

(z)

High demand uncertainty - high mismatch costs• The mismatch cost is high when the coefficient of variation, s/m, is high.• The coefficient of variation is the right measure of demand uncertainty:

– The probability demand is within 20% of the forecast demand depends on the coefficient of variation (COV) and not the standard deviation:Normal demand, = 20, = 10, COV =0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 4 8 12 16 20 24 28 32 36 40

Demand

Pro

babi

lity

31%

20%

Normal demand, = 60

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

10 20 30 40 50 60 70 80 90 100 110

Demand

Pro

babi

lity

95% 31%

= 10COV = 10 / 60 = 0.17

= 30COV = 30 / 60 = 0.5

20%

Unlimited, but expensive reactive capacity

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive 1st order from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Receive 2nd

order from TEC at the end of Apr

Observe Feb and Mar sales and

submit 2nd order to TEC

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive 1st order from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Receive 2nd

order from TEC at the end of Apr

Observe Feb and Mar sales and

submit 2nd order to TEC

• TEC charges a premium of 20% per unit ($132 vs. $110) in the second order.• There are no restrictions imposed on the 2nd order quantity.• O’Neill forecast of total season sales is nearly perfect after observing initial

season sales.• How many units should O’Neill order in October?

Apply Newsvendor logic even with a 2nd order option

• “Too much cost”

• “Too little cost”

• Critical ratio:

• Corresponding z-statistic

• Order quantity

Profit improvement due to the 2nd order option

• With a single ordering opportunity:– Optimal order quantity– Expected profit– Mismatch cost as % of revenue

• The maximum profit is unchanged

• With a second order option:– Optimal order quantity

– Reduction in mismatch cost– Mismatch cost as % of revenue

Limited reactive capacity

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive both orders from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Submit 2nd order to TEC

Observe pre-book orders

from retailers

• Units in the 2nd order are no more expensive than in the 1st order

• But there is limited capacity for a 2nd order

Sample of wetsuits

• 1st order must be at least 10,200 suits so that there is enough capacity for the 2nd order.

• What should we produce in the 1st order?

Sport Model Price Margin Discount

DIVE DIVE COMP 3/2 FULL 1100 660 0.60 120 38% 65%DIVE WMS 7000X 7MM FULL 600 360 0.60 275 38% 65%SURF EPIC 5/3 W/HD 800 296 0.37 225 38% 50%SURF HEAT 3/2 1200 444 0.37 110 38% 50%SURF HEATWAVE 4/3 700 259 0.37 140 38% 50%SURF ZEN-ZIP 4/3 3100 1147 0.37 165 38% 50%TRIATHLON TRIATHLON 4/3 FULL 2600 1690 0.65 210 45% 65%WAKE-BOARD REACTOR 3/2 1500 750 0.50 150 45% 65%WINDSURF CYCLONE 4/3 950 665 0.70 325 45% 65%WINDSURF WMS EVOLUTION 4/3 850 595 0.70 275 45% 65% = expected demand

= standard deviation of demand

Price = wholesale priceMargin = gross margin as a % of priceDiscount = anticipated end of season discount as % of price to sell left over inventory

All of these problems are too lengthy to put on a slide. Check pp. 279-281 for the problem statements for:

12.7 Sarah’s Wedding12.8 Lucky Smokes12.10 TEC