PRE-RELEASE VERSION

Ludo (B)

Newsvendor Calculations

Source: http://www.cdc.gov/ulcer/consumer.htm

01/2009-5548
This case was written by Nils Rudi, Associate Professor of Technology and Operations Management. It is intended to
be used as a basis for class discussion rather than to illustrate either effective or ineffective handling of an
administrative situation.
Copyright © 2009 INSEAD

This pre-release version may be used for teaching purposes but it has not yet received an official case number by the European
Case Clearing House.
 PRE-RELEASE VERSION

People in general have difficulties making decisions under uncertainty. This is also observed
in how newsvendor-type decisions are made in reality. Hence scientific methods are called for
in order to trade off the underage costs, overage costs and effect of uncertainty in the right
proportions. In addition, a scientific decision method will help avoid decision biases, which
tend to be rather strong in the newsvendor model. Here, we outline how to make newsvendor
calculations, and provide an example of how these are carried out.

We go through a 10-step process of making the fundamental calculations for newsvendor

analysis. In doing so, we use the following example:

The Brazilian students of your MBA promotion are organizing a ‘Brazilian Week’. As part of
this initiative, during this week they will sell a yellow and green T-shirt with “Brazilian
Week” and the year printed on it. They will pay c = €7 per T-shirt and sell it for r = €10 per
T-shirt. (To make life easier, they have decided to offer the T-shirt in only one size). The
MBA rugby team is a large consumer of T-shirts during practice (and don’t care much about
how they look) and have agreed to buy each leftover T-shirt for €2, which results in salvage
value s = €2 per T-shirt. Based on experience from past national weeks, the Brazilian
students estimate demand for T-shirts to be normally distributed with mean μ = 300 and
standard deviation σ = 100 .

10-step Process for Fundamental Newsvendor Calculations

Step 1: Calculate unit underage and unit overage costs

Using the formulas from the Ludo (A) case, we find the unit underage cost to be:

cu = r − c = €10 − €7 = €3,

and the unit overage cost to be:

co = c − s = €7 − €2 = €5.

Step 2: Calculate the newsvendor fractile

Using the formula from the Ludo (A) case, we find the newsvendor fractile to be:

cu €3
= = 0.375.
cu + co €3 + €5

∗
Step 3: Find z , the unit normal z -factor corresponding to the newsvendor
fractile

Using Table 1 in this note, we find the z -value which is closest to 0.375. This is z ∗ = −0.32 .
NOTE: To find z ∗ in Table 1, you will search inside (i.e., within the rows and columns of)
Table 1 for 0.375 and find outside (i.e., using the horizontal and vertical column headings) in
Table 1 the corresponding z ∗ value -0.32.

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Step 4: Find the optimal order quantity using z ∗ based on the formula
Q∗ = μ + σ ⋅ z ∗

Q∗ = μ + σ ⋅ z ∗ = 300 + 100 ⋅ (−0.32) = 268 .

This means that it is optimal to order 32 T-shirts below the mean demand. The reason for
ordering less than the mean demand is that the unit underage cost cu is less than the unit
overage cost co .

Step 5: Find the unit normal loss function L corresponding to z ∗

Using Table 2, we find the L -value which corresponds to the closest z -value z ∗ = −0.32 .
This is L = 0.57920 .

NOTE: To find L in Table 2, you will search outside (i.e., using the horizontal and vertical
column headings) in Table 2 for -0.32 and find inside (i.e., within the rows and columns of)
Table 2 the corresponding L value 0.57920.

Step 6: Calculate the expected number of unmet demands (underage) U

using the formula U = σ ⋅ L

U = σ ⋅ L = 100 ∗ 0.57920 ≈ 57.9 .

This means that when ordering Q∗ = 268 , we expect that about 58 persons who would like to
buy a T-shirt are not able to do so because of the stock-out of T-shirts.

Step 7: Calculate the expected number of sold units S using the formula
S = μ −U .

The intuition for this formula is as follows: We expect demand to be μ , and out of these
demands we expect that U are not met. So the difference between expected demand and
expected unmet demand becomes expected sales:

S = μ −U = 300 − 57.9 = 242.1 .

So when ordering Q∗ = 268 units, we expect that 242.1 of them will actually be sold.

Step 8: Calculate the number of leftover units (overage) O using the formula
O = Q∗ − S .

The intuition for this formula is as follows: The expected number of units left over is the
difference between the quantity that we buy Q∗ and the quantity sold S :

O = Q∗ − S = 268 − 242.1 = 25.9 .

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∗
So when ordering Q = 268 units, we expect that 25.9 of them will not be sold to regular
demand but will instead have to be salvaged.

Step 9: Calculate expected opportunity cost G using the formula

G = cu ⋅U + co ⋅O

The formula for the expected opportunity cost is the unit underage cost cu , times the expected
underage U plus the unit overage cost co , times the expected overage O :

G = cu ⋅U + co ⋅O = €3 ⋅ 57.9 + €5 ⋅ 25.9 = €303.2 .

Step 10: Calculate expected profit π using the formula π = ( r − c ) ⋅ E [ D] − G

The formula of the expected profit is the expected profit if one had perfect demand
information before placing the order less the expected opportunity cost.

π = ( r − c ) ⋅ E [ D ] − G = ( €10 − €7 ) ⋅ 300 − €303.2 = €596.8 .

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Table 1: Normal Probability Table

z 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09
-2.9 0.00187 0.00181 0.00175 0.00169 0.00164 0.00159 0.00154 0.00149 0.00144 0.00139
-2.8 0.00256 0.00248 0.00240 0.00233 0.00226 0.00219 0.00212 0.00205 0.00199 0.00193
-2.7 0.00347 0.00336 0.00326 0.00317 0.00307 0.00298 0.00289 0.00280 0.00272 0.00264
-2.6 0.00466 0.00453 0.00440 0.00427 0.00415 0.00402 0.00391 0.00379 0.00368 0.00357
-2.5 0.00621 0.00604 0.00587 0.00570 0.00554 0.00539 0.00523 0.00508 0.00494 0.00480
-2.4 0.00820 0.00798 0.00776 0.00755 0.00734 0.00714 0.00695 0.00676 0.00657 0.00639
-2.3 0.01072 0.01044 0.01017 0.00990 0.00964 0.00939 0.00914 0.00889 0.00866 0.00842
-2.2 0.01390 0.01355 0.01321 0.01287 0.01255 0.01222 0.01191 0.01160 0.01130 0.01101
-2.1 0.01786 0.01743 0.01700 0.01659 0.01618 0.01578 0.01539 0.01500 0.01463 0.01426
-2.0 0.02275 0.02222 0.02169 0.02118 0.02068 0.02018 0.01970 0.01923 0.01876 0.01831
-1.9 0.02872 0.02807 0.02743 0.02680 0.02619 0.02559 0.02500 0.02442 0.02385 0.02330
-1.8 0.03593 0.03515 0.03438 0.03362 0.03288 0.03216 0.03144 0.03074 0.03005 0.02938
-1.7 0.04457 0.04363 0.04272 0.04182 0.04093 0.04006 0.03920 0.03836 0.03754 0.03673
-1.6 0.05480 0.05370 0.05262 0.05155 0.05050 0.04947 0.04846 0.04746 0.04648 0.04551
-1.5 0.06681 0.06552 0.06426 0.06301 0.06178 0.06057 0.05938 0.05821 0.05705 0.05592
-1.4 0.08076 0.07927 0.07780 0.07636 0.07493 0.07353 0.07215 0.07078 0.06944 0.06811
-1.3 0.09680 0.09510 0.09342 0.09176 0.09012 0.08851 0.08691 0.08534 0.08379 0.08226
-1.2 0.11507 0.11314 0.11123 0.10935 0.10749 0.10565 0.10383 0.10204 0.10027 0.09853
-1.1 0.13567 0.13350 0.13136 0.12924 0.12714 0.12507 0.12302 0.12100 0.11900 0.11702
-1.0 0.15866 0.15625 0.15386 0.15151 0.14917 0.14686 0.14457 0.14231 0.14007 0.13786
-0.9 0.18406 0.18141 0.17879 0.17619 0.17361 0.17106 0.16853 0.16602 0.16354 0.16109
-0.8 0.21186 0.20897 0.20611 0.20327 0.20045 0.19766 0.19489 0.19215 0.18943 0.18673
-0.7 0.24196 0.23885 0.23576 0.23270 0.22965 0.22663 0.22363 0.22065 0.21770 0.21476
-0.6 0.27425 0.27093 0.26763 0.26435 0.26109 0.25785 0.25463 0.25143 0.24825 0.24510
-0.5 0.30854 0.30503 0.30153 0.29806 0.29460 0.29116 0.28774 0.28434 0.28096 0.27760
-0.4 0.34458 0.34090 0.33724 0.33360 0.32997 0.32636 0.32276 0.31918 0.31561 0.31207
-0.3 0.38209 0.37828 0.37448 0.37070 0.36693 0.36317 0.35942 0.35569 0.35197 0.34827
-0.2 0.42074 0.41683 0.41294 0.40905 0.40517 0.40129 0.39743 0.39358 0.38974 0.38591
-0.1 0.46017 0.45620 0.45224 0.44828 0.44433 0.44038 0.43644 0.43251 0.42858 0.42465
0.0 0.50000 0.49601 0.49202 0.48803 0.48405 0.48006 0.47608 0.47210 0.46812 0.46414
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.52790 0.53188 0.53586
0.1 0.53983 0.54380 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535
0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409
0.3 0.61791 0.62172 0.62552 0.62930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173
0.4 0.65542 0.65910 0.66276 0.66640 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793
0.5 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.71226 0.71566 0.71904 0.72240
0.6 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.75490
0.7 0.75804 0.76115 0.76424 0.76730 0.77035 0.77337 0.77637 0.77935 0.78230 0.78524
0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327
0.9 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891
1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214
1.1 0.86433 0.86650 0.86864 0.87076 0.87286 0.87493 0.87698 0.87900 0.88100 0.88298
1.2 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147
1.3 0.90320 0.90490 0.90658 0.90824 0.90988 0.91149 0.91309 0.91466 0.91621 0.91774
1.4 0.91924 0.92073 0.92220 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189
1.5 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408
1.6 0.94520 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.95254 0.95352 0.95449
1.7 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.96080 0.96164 0.96246 0.96327
1.8 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062
1.9 0.97128 0.97193 0.97257 0.97320 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670
2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.98030 0.98077 0.98124 0.98169
2.1 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98461 0.98500 0.98537 0.98574
2.2 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899
2.3 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158
2.4 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361
2.5 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.99492 0.99506 0.99520
2.6 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643
2.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.99720 0.99728 0.99736
2.8 0.99744 0.99752 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807
2.9 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861

Recipe for finding optimal order quantity Q∗ :

Step What How Example

Step 1. Calculate underage and cu = r − c cu = €10 − €7 = €3
overage costs
co = c − s co = €7 − €2 = €5
cu + co = €3+ €5 = 0.375
Step 2. Calculate newsvendor cu cu €3
cu + co
fractile
Step 3. Find z ∗ corresponding to Look up in table above z ∗ = −0.32
newsvendor fractile
Step 4. Find Q∗ using z ∗ Q∗ = μ + σ ⋅ z ∗ Q∗ = 300 + 100 ⋅ (−0.32) = 268

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Table 2: Normal Loss Table

z 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09
-2.9 2.90054 2.91052 2.92051 2.93049 2.94047 2.95046 2.96044 2.97042 2.98041 2.99040
-2.8 2.80076 2.81074 2.82071 2.83069 2.84066 2.85064 2.86062 2.87060 2.88058 2.89056
-2.7 2.70106 2.71103 2.72099 2.73096 2.74093 2.75090 2.76087 2.77084 2.78081 2.79079
-2.6 2.60146 2.61142 2.62137 2.63133 2.64129 2.65125 2.66121 2.67117 2.68113 2.69110
-2.5 2.50200 2.51194 2.52188 2.53183 2.54177 2.55171 2.56166 2.57161 2.58156 2.59151
-2.4 2.40272 2.41264 2.42256 2.43248 2.44241 2.45234 2.46227 2.47220 2.48213 2.49207
-2.3 2.30366 2.31356 2.32345 2.33335 2.34325 2.35316 2.36307 2.37298 2.38289 2.39280
-2.2 2.20489 2.21475 2.22462 2.23449 2.24436 2.25423 2.26411 2.27400 2.28388 2.29377
-2.1 2.10647 2.11629 2.12612 2.13595 2.14579 2.15563 2.16547 2.17532 2.18517 2.19503
-2.0 2.00849 2.01827 2.02805 2.03783 2.04762 2.05742 2.06722 2.07702 2.08683 2.09665
-1.9 1.91105 1.92077 1.93049 1.94022 1.94996 1.95970 1.96945 1.97920 1.98896 1.99872
-1.8 1.81428 1.82392 1.83357 1.84323 1.85290 1.86257 1.87226 1.88195 1.89164 1.90134
-1.7 1.71829 1.72785 1.73742 1.74699 1.75658 1.76617 1.77578 1.78539 1.79501 1.80464
-1.6 1.62324 1.63270 1.64217 1.65165 1.66114 1.67064 1.68015 1.68967 1.69920 1.70874
-1.5 1.52931 1.53865 1.54800 1.55736 1.56674 1.57612 1.58552 1.59494 1.60436 1.61380
-1.4 1.43667 1.44587 1.45508 1.46431 1.47356 1.48281 1.49208 1.50137 1.51067 1.51998
-1.3 1.34553 1.35457 1.36363 1.37270 1.38179 1.39090 1.40002 1.40916 1.41831 1.42748
-1.2 1.25610 1.26496 1.27384 1.28274 1.29165 1.30059 1.30954 1.31851 1.32750 1.33650
-1.1 1.16862 1.17727 1.18595 1.19465 1.20336 1.21210 1.22086 1.22964 1.23844 1.24726
-1.0 1.08332 1.09174 1.10019 1.10866 1.11716 1.12568 1.13422 1.14279 1.15138 1.15999
-0.9 1.00043 1.00860 1.01680 1.02503 1.03328 1.04156 1.04986 1.05819 1.06654 1.07491
-0.8 0.92021 0.92810 0.93603 0.94398 0.95196 0.95997 0.96801 0.97607 0.98417 0.99229
-0.7 0.84288 0.85048 0.85810 0.86576 0.87345 0.88117 0.88892 0.89669 0.90450 0.91234
-0.6 0.76867 0.77595 0.78325 0.79059 0.79797 0.80537 0.81281 0.82028 0.82778 0.83531
-0.5 0.69780 0.70473 0.71170 0.71870 0.72573 0.73281 0.73991 0.74705 0.75422 0.76143
-0.4 0.63044 0.63701 0.64362 0.65027 0.65695 0.66367 0.67042 0.67721 0.68404 0.69090
-0.3 0.56676 0.57296 0.57920 0.58547 0.59178 0.59813 0.60452 0.61094 0.61740 0.62390
-0.2 0.50689 0.51271 0.51856 0.52445 0.53038 0.53634 0.54235 0.54840 0.55448 0.56060
-0.1 0.45094 0.45635 0.46181 0.46731 0.47285 0.47842 0.48404 0.48969 0.49539 0.50112
0.0 0.39894 0.40396 0.40902 0.41412 0.41926 0.42444 0.42966 0.43492 0.44022 0.44556
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.39894 0.39396 0.38902 0.38412 0.37926 0.37444 0.36966 0.36492 0.36022 0.35556
0.1 0.35094 0.34635 0.34181 0.33731 0.33285 0.32842 0.32404 0.31969 0.31539 0.31112
0.2 0.30689 0.30271 0.29856 0.29445 0.29038 0.28634 0.28235 0.27840 0.27448 0.27060
0.3 0.26676 0.26296 0.25920 0.25547 0.25178 0.24813 0.24452 0.24094 0.23740 0.23390
0.4 0.23044 0.22701 0.22362 0.22027 0.21695 0.21367 0.21042 0.20721 0.20404 0.20090
0.5 0.19780 0.19473 0.19170 0.18870 0.18573 0.18281 0.17991 0.17705 0.17422 0.17143
0.6 0.16867 0.16595 0.16325 0.16059 0.15797 0.15537 0.15281 0.15028 0.14778 0.14531
0.7 0.14288 0.14048 0.13810 0.13576 0.13345 0.13117 0.12892 0.12669 0.12450 0.12234
0.8 0.12021 0.11810 0.11603 0.11398 0.11196 0.10997 0.10801 0.10607 0.10417 0.10229
0.9 0.10043 0.09860 0.09680 0.09503 0.09328 0.09156 0.08986 0.08819 0.08654 0.08491
1.0 0.08332 0.08174 0.08019 0.07866 0.07716 0.07568 0.07422 0.07279 0.07138 0.06999
1.1 0.06862 0.06727 0.06595 0.06465 0.06336 0.06210 0.06086 0.05964 0.05844 0.05726
1.2 0.05610 0.05496 0.05384 0.05274 0.05165 0.05059 0.04954 0.04851 0.04750 0.04650
1.3 0.04553 0.04457 0.04363 0.04270 0.04179 0.04090 0.04002 0.03916 0.03831 0.03748
1.4 0.03667 0.03587 0.03508 0.03431 0.03356 0.03281 0.03208 0.03137 0.03067 0.02998
1.5 0.02931 0.02865 0.02800 0.02736 0.02674 0.02612 0.02552 0.02494 0.02436 0.02380
1.6 0.02324 0.02270 0.02217 0.02165 0.02114 0.02064 0.02015 0.01967 0.01920 0.01874
1.7 0.01829 0.01785 0.01742 0.01699 0.01658 0.01617 0.01578 0.01539 0.01501 0.01464
1.8 0.01428 0.01392 0.01357 0.01323 0.01290 0.01257 0.01226 0.01195 0.01164 0.01134
1.9 0.01105 0.01077 0.01049 0.01022 0.00996 0.00970 0.00945 0.00920 0.00896 0.00872
2.0 0.00849 0.00827 0.00805 0.00783 0.00762 0.00742 0.00722 0.00702 0.00683 0.00665
2.1 0.00647 0.00629 0.00612 0.00595 0.00579 0.00563 0.00547 0.00532 0.00517 0.00503
2.2 0.00489 0.00475 0.00462 0.00449 0.00436 0.00423 0.00411 0.00400 0.00388 0.00377
2.3 0.00366 0.00356 0.00345 0.00335 0.00325 0.00316 0.00307 0.00298 0.00289 0.00280
2.4 0.00272 0.00264 0.00256 0.00248 0.00241 0.00234 0.00227 0.00220 0.00213 0.00207
2.5 0.00200 0.00194 0.00188 0.00183 0.00177 0.00171 0.00166 0.00161 0.00156 0.00151
2.6 0.00146 0.00142 0.00137 0.00133 0.00129 0.00125 0.00121 0.00117 0.00113 0.00110
2.7 0.00106 0.00103 0.00099 0.00096 0.00093 0.00090 0.00087 0.00084 0.00081 0.00079
2.8 0.00076 0.00074 0.00071 0.00069 0.00066 0.00064 0.00062 0.00060 0.00058 0.00056
2.9 0.00054 0.00052 0.00051 0.00049 0.00047 0.00046 0.00044 0.00042 0.00041 0.00040

Recipe for finding expected profit when ordering optimal order quantity π ⎛⎜⎝ Q : ∗⎞
⎟
⎠

Step What How Example

Step 5. Find L ⎛ z ∗ ⎞ using z ∗
⎜ ⎟
Look up in table above L = 0.57920
⎝ ⎠
Step 6. Calculate expected underage U =σ ⋅L U = 100 ∗ 0.57920 ≈ 57.9
Step 7. Calculate expected sales S = μ −U S = 300 − 57.9 = 242.1
Step 8. Calculate expected overage O = Q∗ − S O = 268 − 242.1 = 25.9
Step 9. Calculate expected opportunity cost G = c ⋅U + c ⋅O
u o
G = €3 ⋅ 57.9 + €5 ⋅ 25.9 = €303.2
Step 10. Calculate expected profit π = ( r − c ) ⋅ E [ D] − G π = ( €10 − €7 ) ⋅ 300 − €303.2 = €596.8

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∗
Appendix 1: Can I Find z and L Directly in Excel?

You can use Excel to do steps 3 and 5, and hence eliminate the need to use the tables to make
newsvendor calculations.

Step 3: z ∗ is found by writing the following expression in an Excel cell:

= normsinv(cu / (cu + co )) .

So for the example, writing the following in an Excel cell:

= normsinv(0.375)

will result in the z ∗ -value -0.31864.

Step 5: The expression to use in Excel to find the L -value corresponding to a z -value is a bit
more complex:

= z ∗ normsdist( z ) + normdist( z, 0,1, false) − z.

(Note that the first “normsdist” is written with one more ‘s’ than the second “normdist”). For
the example, writing the following in an Excel cell:

= −0.31864 ∗ normsdist(−0.31864) + normdist(−0.31864, 0,1, false) − (−0.31864)

will result in the L -value 0.578345.

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Appendix 2
How do I Make Newsvendor Calculations when I use a Non-optimal Order Quantity?

If you use a non-optimal value of Q , you must calculate the corresponding z -value by the formula
Q−μ
z= σ , and then use these two values for Q and z in steps 5 to 10. For example, if you decided to
order Q = 400 T-shirts in the example above, the corresponding z -value is found to be:
Q−μ
z= σ = 400 − 300
100 = 1 . We can then do steps 5 to 10 as follows:
Step 5: The L value corresponding to z = 1 is found to be L = 0.08332 using Table 2.
Step 6: U = σ L = 100 ∗ 0.08332 ≈ 8.3
Step 7: S = μ −U = 300 − 8.3 = 291.7
Step 8: O = Q − S = 400 − 291.7 = 108.3

Step 9: G = cu ⋅U + co ⋅O = €3 ⋅ 8.3 + €5 ⋅108.3 = €566.4

Step 10: π = ( r − c ) ⋅ E [ D ] − G = ( €10 − €7 ) ⋅ 300 − €566.4 = €333.6

So when ordering Q = 400 instead of the optimal order quantity Q∗ = 268 , expected profit becomes
π = €333.6 rather than π = €596.8 , or a decrease in expected profit of about 44%.

Copyright © 2009 INSEAD 7 01/2009-5548