# Walton

Document Sample

```					Walton Bookstore

In August, Walton Bookstore must decide how many of next year's nature calendars to order. Each calendar costs the
bookstore \$7.50 and is sold for \$10. After February 1 all unsold calendars are returned to the publisher for a refund of \$2.50
per calendar. Walton believes that the number of calendars it can sell by February 1 follows the probabilty distribution shown
below. Walton wants to use simulation to determine the number of calendars to order in August in order to maximize
the expected profit from calendar sales.

Calendars
Demanded       Probability
100            0.30
150            0.20
200            0.30
250            0.15
300            0.05
ach calendar costs the
blisher for a refund of \$2.50
probabilty distribution shown
n order to maximize
Simulation of Walton's bookstore

Cost data                                                Demand distribution
Unit cost                     \$7.50                         Probability   Cum Prob       Demand
Unit price                   \$10.00                              0.30         0.00          100
Unit refund                   \$2.50                              0.20         0.30          150
0.30         0.50          200
Calendar                                                         0.15         0.80          250
Order quantity                     200                           0.05         0.95          300

Simulation
Replication           Random #            Demand         Revenue      Ordering Cost Refund
1              0.5740            200      \$2,000.00    \$1,500.00         \$0.00
2              0.0142            100      \$1,000.00    \$1,500.00       \$250.00
3              0.1329            100      \$1,000.00    \$1,500.00       \$250.00
4              0.5879            200      \$2,000.00    \$1,500.00         \$0.00
5              0.3205            150      \$1,500.00    \$1,500.00       \$125.00
6              0.0858            100      \$1,000.00    \$1,500.00       \$250.00
7              0.2545            100      \$1,000.00    \$1,500.00       \$250.00
8              0.5211            200      \$2,000.00    \$1,500.00         \$0.00
9              0.0213            100      \$1,000.00    \$1,500.00       \$250.00
10              0.6517            200      \$2,000.00    \$1,500.00         \$0.00
11              0.4210            150      \$1,500.00    \$1,500.00       \$125.00
12              0.5223            200      \$2,000.00    \$1,500.00         \$0.00
13              0.9258            250      \$2,000.00    \$1,500.00         \$0.00
14              0.5861            200      \$2,000.00    \$1,500.00         \$0.00
15              0.2111            100      \$1,000.00    \$1,500.00       \$250.00
16              0.2075            100      \$1,000.00    \$1,500.00       \$250.00
17              0.8666            250      \$2,000.00    \$1,500.00         \$0.00
18              0.6322            200      \$2,000.00    \$1,500.00         \$0.00
19              0.2039            100      \$1,000.00    \$1,500.00       \$250.00
20              0.9852            300      \$2,000.00    \$1,500.00         \$0.00
21              0.5584            200      \$2,000.00    \$1,500.00         \$0.00
22              0.5293            200      \$2,000.00    \$1,500.00         \$0.00
23              0.3913            150      \$1,500.00    \$1,500.00       \$125.00
24              0.4572            150      \$1,500.00    \$1,500.00       \$125.00
25              0.9951            300      \$2,000.00    \$1,500.00         \$0.00
26              0.5702            200      \$2,000.00    \$1,500.00         \$0.00
27              0.2141            100      \$1,000.00    \$1,500.00       \$250.00
28              0.4082            150      \$1,500.00    \$1,500.00       \$125.00
29              0.3622            150      \$1,500.00    \$1,500.00       \$125.00
30              0.7989            200      \$2,000.00    \$1,500.00         \$0.00
31              0.5672            200      \$2,000.00    \$1,500.00         \$0.00
32              0.1524            100      \$1,000.00    \$1,500.00       \$250.00
33              0.5661            200      \$2,000.00    \$1,500.00         \$0.00
34              0.7809            200      \$2,000.00    \$1,500.00         \$0.00
35              0.1286            100      \$1,000.00    \$1,500.00       \$250.00
36              0.1418            100      \$1,000.00    \$1,500.00       \$250.00
37              0.1600            100      \$1,000.00    \$1,500.00       \$250.00
38              0.3491            150      \$1,500.00    \$1,500.00       \$125.00
39              0.3664            150      \$1,500.00    \$1,500.00       \$125.00
40               0.3038               150     \$1,500.00     \$1,500.00        \$125.00
41               0.9803               300     \$2,000.00     \$1,500.00           \$0.00
42               0.6160               200     \$2,000.00     \$1,500.00           \$0.00
43               0.2229               100     \$1,000.00     \$1,500.00        \$250.00
44               0.5244               200     \$2,000.00     \$1,500.00           \$0.00
45               0.5212               200     \$2,000.00     \$1,500.00           \$0.00
46               0.0014               100     \$1,000.00     \$1,500.00        \$250.00
47               0.6694               200     \$2,000.00     \$1,500.00           \$0.00
48               0.5698               200     \$2,000.00     \$1,500.00           \$0.00
49               0.7649               200     \$2,000.00     \$1,500.00           \$0.00
50               0.1462               100     \$1,000.00     \$1,500.00        \$250.00
Average
Std Dev.
Min
Max
95% confidence interval for mean profit
Lower limit
Upper limit

Data table for average profit as a function of the order quantity

Order quantity Avg Profit        Std Dev.     Min           Max
\$192.50        \$333.24     (\$250.00)     \$500.00
100           \$250.00          \$0.00        \$0.00      \$250.00
125           \$252.50         \$87.93       \$87.93      \$312.50
150           \$255.00        \$175.85        \$0.00      \$375.00
175           \$223.75        \$249.40     (\$125.00)     \$437.50
200           \$192.50        \$333.24     (\$250.00)     \$500.00
225             \$86.25       \$355.35     (\$375.00)     \$562.50
250            (\$20.00)      \$384.64     (\$500.00)     \$625.00
275          (\$133.75)       \$406.08     (\$625.00)     \$687.50
300          (\$247.50)       \$431.16     (\$750.00)     \$750.00

Average Profit vs. Order Quantity

\$300.00
\$200.00
Avg Profit

\$100.00
\$0.00
100    125     150   175     200   225   250   275   300
(\$100.00)
(\$200.00)
(\$300.00)
Order Quantity
Profit
\$500.00
(\$250.00)
(\$250.00)
\$500.00
\$125.00
(\$250.00)
(\$250.00)
\$500.00
(\$250.00)
\$500.00
\$125.00
\$500.00
\$500.00
\$500.00
(\$250.00)
(\$250.00)
\$500.00
\$500.00
(\$250.00)
\$500.00
\$500.00
\$500.00
\$125.00
\$125.00
\$500.00
\$500.00
(\$250.00)
\$125.00
\$125.00
\$500.00
\$500.00
(\$250.00)
\$500.00
\$500.00
(\$250.00)
(\$250.00)
(\$250.00)
\$125.00
\$125.00
\$125.00
\$500.00
\$500.00
(\$250.00)
\$500.00
\$500.00
(\$250.00)
\$500.00
\$500.00
\$500.00
(\$250.00)
\$192.50
\$333.24
(\$250.00)
\$500.00
% confidence interval for mean profit
\$98.25
\$286.75
Simulation of Walton's bookstore

Cost data                          Demand distribution
Unit cost           \$7.50           Probability Cum Prob    Demand
Unit price         \$10.00                0.30       0.00       100
Unit refund         \$2.50                0.20       0.30       150
0.30       0.50       200
Calendar                                 0.15       0.80       250
Order quantity        200                0.05       0.95       300

Simulation
Replication      Random # Demand   Revenue   Cost          Refund    Profit
Simulation of Walton's bookstore

Cost data                              Demand distribution
Unit cost               \$7.50           Probability Cum Prob    Demand
Unit price             \$10.00                0.30        0.00      100
Unit refund             \$2.50                0.20        0.30      150
0.30        0.50      200
Calendar                                     0.15        0.80      250
Order quantity            200                0.05        0.95      300

Simulation
Replication          Random # Demand Revenue     Cost      Refund   Profit
1      0.8400     250 \$2,000.00 \$1,500.00     \$0.00 \$500.00

Data Table for replications
Replication      Profit
\$500.00
1         125
2        -250
3         125
4         500
5         500
6         500
7         500
8         500
9         500
10          125
11         -250
12         -250
13          500
14          125
15         -250
16          500
17          500
18         -250
19          500
20          500
21          500
22         -250
23          500
24         -250
25         -250
26          125
27          500
28          500
29          500
30          500
31         -250
32          125
33          125
34          500
35         125
36        -250
37         125
38         500
39        -250
40        -250
41         500
42         125
43         500
44        -250
45         125
46         500
47        -250
48        -250
49         125
50         500
Average           \$191.18
Stdev             \$324.38
Min              (\$250.00)
Max               \$500.00

95% confidence interval
Lower limit        \$99.43
Upper limit      \$282.92
Simulation of Walton's bookstore

Cost data                               Demand distribution
Unit cost               \$7.50            Probability Cum Prob   Demand
Unit price             \$10.00                 0.30       0.00      100
Unit refund             \$2.50                 0.20       0.30      150
0.30       0.50      200
Calendar                                      0.15       0.80      250
Order quantity            200                 0.05       0.95      300

Simulation
Replication          Random # Demand Revenue Cost          Refund   Profit
1      0.9201     250 \$2,000.00 \$1,500.00     \$0.00 \$500.00

Data Table with various order quantities
Replication                             Order quantity
\$500.00          100        150          200       250      300
1        250            0        125      -125        0
2        250            0        500      -500     -750   300
3        250        375         -250       250        0
250
4        250        375         -250      -500        0
5        250        375         -250      -500     -375   200
6        250        375          500      -500        0   150
7        250            0        500       625      750   100
8        250        375          125       625        0
9        250            0        500      -125     -375    50
10         250            0        500      -125        0     0
11         250            0       -250       625        0    -50   100   150
12         250        375          500      -500      750
-100
13         250        375          500       250      375
14         250            0       -250      -500     -375   -150
15         250            0        500       250        0   -200
16         250        375         -250       625     -375
17         250        375         -250      -500     -750
18         250        375          500       250     -750
19         250        375          500       625     -375
20         250        375          125      -500      375
21         250        375          500      -500      750
22         250        375          500       250     -750
23         250            0       -250       625     -750
24         250        375          500       250     -750
25         250        375          500       625        0
26         250            0        500       250     -375
27         250        375         -250      -500     -375
28         250        375         -250      -500     -375
29         250        375         -250       250     -375
30         250        375          500       250     -750
31         250        375          500      -500        0
32         250        375          500      -500        0
33         250        375          500       250        0
34         250        375         -250      -500        0
35   250   375    -250    -500   -750
36   250     0     500    -500   -750
37   250   375    -250    -500      0
38   250   375     500    -500      0
39   250     0     500     250      0
40   250   375     125    -500    375
41   250     0     500     625   -750
42   250   375     125    -500   -375
43   250   375     500     250   -375
44   250   375     500     250      0
45   250     0    -250    -125   -750
46   250     0     500    -500      0
47   250   375    -250     250      0
48   250   375     125     250    375
49   250     0    -250    -125    375
50   250   375     125     250    750
Average        250   255   192.5   -42.5   -150
Series1

200   250   300

```
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