Suppose that ONeil is experiencing a volatile economic period and the management is much less optimistic about the growth of the sales in the upcoming season. Note that the average sales in the past season was only 824 units per product (standard deviation was 964). They would like to develop a more robust data-driven policy at least as a baseline instead of relying on personal experiences. That is, what if the demand pattern in the upcoming spring season remains the same as that of the last spring, how should they place order (assuming the retail price, sourcing cost and salvage value per unit are $190, $110 and $90, respectively)? Please use the sales data in the past season to conduct prospective analysis and perspective analysis, respectively. (refer to the excel picture for the data)

1. Use the sales data in the past season to estimate an approximate demand distribution (assuming that the demand is normally distributed). Next use the estimated normal demand distribution to derive an optimal ordering solution to maximizing the expected profit of each product (e.g., Hammer 3/2) using the analytical formula. Then use the sales data again to assess the performance of the proposed prospective solution.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Price & 190 & & Overage cost & $20 & & Forecast (per SKU) & 3200 & & Prospective Analysis & & & & Retrospective Analysi & & \\ \hline Cost & 110 & & Underage cost & $80 & & Mean demand & 3193 & & & & & & & & \\ \hline Salvage value & 90 & & Critical Ratio & 0.8000 & & Standard deviation & 1183 & & Order & 4188 & & & Opt quantity & $ & 4,360 \\ \hline & & & z-value & 0.8416212 & & NV solution (=mean +z std) & 4188 & & Avg Profit & $223,104 & & & Max Profit & $ & 223,294 \\ \hline & & & (std normal table) & 0.85 & & (std normal table) & 4198 & & & & & & & & \\ \hline & & & & & & & & & & & & & & & \\ \hline & & & & & & Actual demand scaled by predicted growth rate (new & (Truncated by order) & & & & & & & & \\ \hline Product description & Forecast & Actual sales & A/F Ratio & Rank & Percentile & Predicted "actual" demand by sku & Predicted sales & Predited LI & Predited Profit & & & & & $ & 223,104 \\ \hline Zen-Zip 2MM Full & 470 & 116 & 0.25 & 1 & 3.0% & 790 & 790 & 3398 & (4,760) & & step size & 20 & 4000 & $ & 222,152 \\ \hline Zen 3/2 & 3190 & 1190 & 0.37 & 2 & 6.1% & 1194 & 1194 & 2994 & 35,640 & & & & 4020 & $ & 222,297 \\ \hline Zen 4/3 & 430 & 239 & 0.56 & 3 & 9.1% & 1779 & 1779 & 2409 & 94,140 & & & & 4040 & $ & 222,442 \\ \hline WMS Elite 3/2 & 650 & 364 & 0.56 & 4 & 12.1% & 1792 & 1792 & 2396 & 95,440 & & & & 4060 & $ & 222,588 \\ \hline WMS Hammer 3/2 Full & 6490 & 3673 & 0.57 & 5 & 15.2% & 1811 & 1811 & 2377 & 97,340 & & & & 4080 & $ & 222,685 \\ \hline JR Hammer 3/2 & 1220 & 721 & 0.59 & 6 & 18.2% & 1891 & 1891 & 2297 & 105,340 & & & & 4100 & $ & 222,770 \\ \hline Heatwave 4/3 & 430 & 274 & 0.64 & 7 & 21.2% & 2039 & 2039 & 2149 & 120,140 & & & & 4120 & $ & 222,855 \\ \hline Zen 2MMS/S Full & 680 & 453 & 0.67 & 8 & 24.2% & 2132 & 2132 & 2056 & 129,440 & & & & 4140 & $ & 222,939 \\ \hline Epic 5/3 W/HD & 120 & 83 & 0.69 & 9 & 27.3% & 2213 & 2213 & 1975 & 137,540 & & & & 4160 & $ & 223,024 \\ \hline Epic 4/3 & 1020 & 732 & 0.72 & 10 & 30.3% & 2296 & 2296 & 1892 & 145,840 & & & & 4180 & $ & 223,094 \\ \hline WMS Epic 2MM Full & 390 & 311 & 0.80 & 11 & 33.3% & 2552 & 2552 & 1636 & 171,440 & & & & 4200 & $ & 223,118 \\ \hline Zen FL 3/2 & 450 & 365 & 0.81 & 12 & 36.4% & 2596 & 2596 & 1592 & 175,840 & & & & 4220 & $ & 223,142 \\ \hline EPIC 2MM S/S Full & 740 & 607 & 0.82 & 13 & 39.4% & 2625 & 2625 & 1563 & 178,740 & & & & 4240 & $ & 223,167 \\ \hline ZEN-Zip 4/3 & 3810 & 3289 & 0.86 & 14 & 42.4% & 2762 & 2762 & 1426 & 192,440 & & & & 4260 & $ & 223,191 \\ \hline WMS Zen-Zip 4/3 & 170 & 163 & 0.96 & 15 & 45.5% & 3068 & 3068 & 1120 & 223,040 & & & & 4280 & $ & 223,215 \\ \hline JR Epic 3/2 & 180 & 175 & 0.97 & 16 & 48.5% & 3111 & 3111 & 1077 & 227,340 & & & & 4300 & $ & 223,239 \\ \hline Heat 4/3 & 460 & 450 & 0.98 & 17 & 51.5% & 3130 & 3130 & 1058 & 229,240 & & & & 4320 & $ & 223,264 \\ \hline JR Zen 3/2 & 140 & 143 & 1.02 & 18 & 54.5% & 3269 & 3269 & 919 & 243,140 & & & & 4340 & $ & 223,288 \\ \hline WMS Zen 3/2 & 180 & 195 & 1.08 & 19 & 57.6% & 3467 & 3467 & 721 & 262,940 & & & & 4360 & $ & 223,294 \\ \hline WMS Epic 5/3 W/HD & 320 & 369 & 1.15 & 20 & 60.6% & 3690 & 3690 & 498 & 285,240 & & & & 4380 & $ & 223,258 \\ \hline Zen-Zip 5/4/3 W/Hood & 270 & 317 & 1.17 & 21 & 63.6% & 3757 & 3757 & 431 & 291,940 & & & & 4400 & $ & 223,221 \\ \hline Zen-Zip 3/2 & 660 & 788 & 1.19 & 22 & 66.7% & 3821 & 3821 & 367 & 298,340 & & & & 4420 & $ & 223,185 \\ \hline Hammer S/S Full & 1490 & 1832 & 1.23 & 23 & 69.7% & 3934 & 3934 & 254 & 309,640 & & & & 4440 & $ & 223,148 \\ \hline Heatwave 3/2 & 170 & 212 & 1.25 & 24 & 72.7% & 3991 & 3991 & 197 & 315,340 & & & & 4460 & $ & 223,112 \\ \hline Heat 3/2 & 500 & 635 & 1.27 & 25 & 75.8% & 4064 & 4064 & 124 & 322,640 & & & & 4480 & $ & 223,076 \\ \hline Hammer 3/2 & 1300 & 1696 & 1.30 & 26 & 78.8% & 4175 & 4175 & 13 & 333,740 & & & & 4500 & $ & 223,039 \\ \hline WMS Epic 3/2 & 610 & 830 & 1.36 & 27 & 81.8% & 4354 & 4188 & 0 & 335,040 & & & & 4520 & $ & 223,003 \\ \hline EVO4/3 & 440 & 623 & 1.42 & 28 & 84.8% & 4531 & 4188 & 0 & 335,040 & & & & 4540 & $ & 222,939 \\ \hline WMS Epic 4/3 & 1060 & 1552 & 1.46 & 29 & 87.9% & 4685 & 4188 & 0 & 335,040 & & & & 4560 & $ & 222,842 \\ \hline JR Epic 4/3 & 380 & 571 & 1.50 & 30 & 90.9% & 4808 & 4188 & 0 & 335,040 & & & & 4580 & $ & 222,745 \\ \hline EVO3/2 & 380 & 587 & 1.54 & 31 & 93.9% & 4943 & 4188 & 0 & 335,040 & & & & 4600 & $ & 222,648 \\ \hline JR Zen FL 3/2 & 90 & 140 & 1.56 & 32 & 97.0% & 4978 & 4188 & 0 & 335,040 & & & & 4620 & $ & 222,552 \\ \hline Epic 3/2 & 2190 & 3504 & 1.60 & 33 & 100.0% & 5120 & 4188 & 0 & 335,040 & & & & 4640 & $ & 222,455 \\ \hline Average & 942 & 824 & 0.9978 & & & & & & & & & & 4660 & $ & 222,358 \\ \hline Standard devai & 1303 & & 0.3695 & & & & & & & & & & 30 & $ & 222.261 \\ \hline \end{tabular}