P3 (25 points). Modify the news vendor problem in Section 2.7.1 to use independent demands for each trial value of q, and note the difference in the behavior of the output, particularly in the mean plot on the left. (Hint: carefully read the model in lecture 3-Newsvendor.xls posted on Canvas) Simulation with arena I Simulation with arena INPUT DATA Wholesale price c = $0.55 Retail price = $1.00 Scrap prices = $0.03 Demand parameter x = 135.70 Demand parameter o = 27.10 70 121 8 9 10 11 12 13 14 15 16 17 18 60 50 40 Mean Daily Profit ($) 8 140 30 153 9 100 Q 120 Q = 140 qe 160 o 180 1 1661 100 0 45.00 120 Day Demand Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit 0 54.00 140 0 63.00 160 2 1231 100 0 72.00 166 14 67.42 0 45.00 120 0 54.00 123 17 46.51 123 3 1241 37 36.11 123 57 25.71 100 0 45.00 120 0 54.00 124 16 47.48 124 36 37,08 124 4 160 100 56 26.68 0 45.00 120 0 54.00 140 0 63.00 160 5 160 0 72.00 143 100 20 61.60 0 45.00 120 0 54.00 140 0 63.00 143 17 55.51 143 37 45.11 6 1391 100 0 45.00 120 0 54.00 139 1 62.03 139 139 21 51.63 7 1241 100 41 41.231 120 0 45.00 0 54.00 124 16 47.48 124 8 36 37.08 124 1211 100 56 26.68 0 45.00 120 0 54.00 121 19 44.57 9 121 167 39 34.17 100 59 23.77 120 0 45.00 0 54.00 140 0 63.00 10 160 0 72.00 167 1061 100 106 13 68.39 0 45.00 14 40.42 106 34 30.02 106 1641 54 19.62 11 106 100 120 0 45.00 74 9.22 0 54.00 140 0 63.00 160 12 164 148 0 72.00 16 65,48 100 0 45.00 120 0 54.00 140 0 63.001 148 12 60.36 13 148 174 100 0 45.00 32 49.96 120 0 54.00 0 63.00 160 14 174 87 87 0 72.00 6.75.18 13 32.39 87 33 21.991 87 53 11.59 87 73 1.19) 87 15 93 -9.21 153 100 0 45.00 120 0 54.001 140 0 63.00 16 153 231 100 7 65.21 0 45.00 120 27 54.81 0 54.00 140 0 63.00 160 0 72.00 17 180 0 81.00 137 100 0 45.00 120 0 54.00 137 3 60.09 137 23 49.69 137 18 144 43 39 291 100 0 45.00 120 0 54.00 140 0 63.00 144 144 16 56.48 92 19 92 8 37.24 92 36 46.08 28 26.84 92 48 16.44 92 68 6.04 92 20 100 88 -4.36 0.45.00 120 0 54.00 140 0 63.001 155 21 5 67.15 100 25 56.75 0 45.00 120 0 54.00 140 157 0 63.00 3 69.09 22 157 172 23 58.691 100 0 45.000 0 54.00 140 160 0 63.00 23 172 175 100 120 0 72.00 0 45.00 8 73.241 0 54.00 140 0 63.00 0 72.00 24 175 160 100 158 120 5 76.15 0 45.00 0 54.00 140 0 63.00 158 25 158 131 2 70.06 22 59.66 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 26 167 49 33.471 100 0 45.00 120 0 54.00 140 0 63.00 160 27 0 72.00 167 103 100 13 68.391 103 0 45.00 17 37.51 103 37 27.11 103 28 103 155 57 16.71 77 6.31 100 0 45.00 120 0 54.00 140 0 63.001 155 155 5 67.151 29 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.291 97 63 10.89 97 83 0.491 30 112 100 0 45.00 112 8 46.241 112 28 35 84 112 48 25.441 112 68 15.04 E(ProfilDay) 44.22 E(ProfilDay) 50.02 E(ProhiDay) 52.52 E(Profit Day) 50.95E(Profit Day) 43.30 + 1.001 33.33 $6.02 8.60 9.73 155 10 80 100 120 140 160 180 200 9 (papers) 157 155 120 22 23 24 25 26 27 28 29 30 31 02 33 100 35 Sheet1 24 25 26 27 28 29 30 H K L N O R S 158 100 0 45.00 120 0 54.00 140 0163.000 158 2170.06 158 22 59.661 131 100 0 45.00 120 0 54.00 131 9 54 27 131 29 43.87 131 49 33.47 167 100 0 45.00 120 0 54.00 140 0163.00 160 0 72.00 167 13 68.39 103 100 0 45.00 103 17 37.51 103 37 27.11 103 57 16.71 103 77 6.31 155 100 0 45.00 120 0 54.00 140 0163.00 155 5 67.15 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.29 97 63 10.89 97 83 0.49 112 100 0 45.00 112 8 46.24 112 28 35.84 112 48 25.44 112 68 15.04 E(ProfitDay) 44 22 E(Profit/Day) 50.02 E(Profit/Day) 52.52 E(ProfitDay) 50.95 E(Profit/Day) 43.30 1.00 3.33 6.02 8.60 9.73 Prob(Loss) 0.00 Prob(Loss) 0.00 Prob(LOSS)10.00 Prob(Loss) 0.00 Prob(Loss)007 Cum. Freq 0 Cum. Freq. 0 0 0 0 Histogram Data Bin Tops -40 -20 0 20 40 60 80 100 Cum. Freq. 0 0 0 0 0 0 0 0 2 2 30 28 30 0 30 0 Cum. Freq. 0 0 0 0 0 0 0 4 4 30 26 30 0 30 0 NOO OOOOOO 88NOOO on ololo 5 10 15 30 30 Cum, Freq. 0 0 0 2 2 6 4 12 6 21 9 29 8 30 5 5 5 15 0 4 5 19 0 SONIDO DO CD E F H K 1. N P R S T 1 Newsvendor Problem - 30 Days INPUT DATA Wholesale price c = $0.55 Retail prices $1.00 Scrap price 8 = $0.03 Demand parameter x = 135.70 Demand parameter = 27.10 100 123 0 100 124 100 100 70 100 8 9 10 11 12 13 14 15 16 60 50 Mean Daily Profit (S) 40 30 120 0100 120 140 9 160 0 180 Day Demand Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit 1 166 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 166 14 67.42 2 123 0 45.00 120 0 54.00 17 46.51 123 37 36.11 123 57 25.71 3 124 0 45.00 120 0 54.00 124 16 47.48 124 36 37.08 56 26.68 4 160 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 160 20 61.601 5 143 100 0 45.00 120 0 54.00 140 0 63.00 143 17 55.51 143 37 45.11 6 139 0 45.00 120 0 54.00 139 162.03 139 21 51.631 139 41 41.231 7 124 100 0 45.00 120 0 54.00 124 16 47.48 124 36 37.08 124 56 26.68 8 121 0 45.00 120 0 54.00 121 19 44.57 121 3934.17 121 59 23.77 9 167 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 167 13 68.391 10 106 100 0 45.00 106 14 40.42 106 34 30.02 106 54 19.62 106 74 9.22 11 164 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 164 16 65.481 12 148 100 0 45001 120 0 54.00 140 0 63.001 148 12 60.36 148 32 49.96 13 174 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 174 6 75.18 14 87 87 13 32.391 87 33 21.99 87 53 11.591 87 73 1.19 87 93 -9.21 15 153 100 0 45.00 120 0 54.00 140 0 63.00 153 7 65.21 153 27 54.811 16 231 100 0 45.00 0 54.00 140 0 63.00 160 0 72.00 180 0 81.00 17 137 100 0 45.00 120 0 54.00 137 3 60.09 137 23 49.69 137 43 39.29 18 144 100 0 45.00 120 0 54.00 140 0 63.00 144 16 56.48 144 36 46.081 19 92 92 8 37.241 92 28 26.84 92 48 16.44 92 68 6.04 92 88 -4.36 20 155 100 0 45.00 120 0 54.00 140 0 63.00 155 5 67.15 155 25 56.75 21 157 100 0 45.00 120 0 54.00 140 0 63.00 157 3 69.09 157 23 58.69 22 172 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 172 8 73.24 23 1751 100 0 45.001 0 54.00 140 0 63.00 160 0 72.00 175 24 5 76.15 158 100 0 45.00 120 0 54.00 140 0 63.00 158 2 70.06 158 22 59.66 25 131 100 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 49 33.471 26 167 100 0 45.00 120 0 54.00 0 63.00 160 0 72.00 167 13 68.39 27 103 100 0 45.00 103 17 37.51 37 27.11 103 57 16.71 103 28 155 77 6.31 100 0 45.00 120 0 54.00 140 0 63.00 5 67.15 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.29 97 63 10.89 97 112 83 0.49 100 0.45.00 112 8 46.24 112 28 35 84 112 48 25.44 112 68 15.04 E(Profit Day) 44 22 E(Profit Day 50.02 E(ProfitDay) 52.52 E(ProfilDay) 50.95 E(Profit Day) 43.30 1.00 13.33 6.02 8.60 9.73 20 20 10 80 100 120 140 160 180 200 9 (papers) 120 24 25 26 27 28 29 30 140 103 31 155 32 33 34 35 B G o S 22 23 24 25 26 27 131 E F . K L R 1721 100 0 45.00 120 054.00 140 0163.00 160 072.00 172 8 73.24 175 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 175 5 76.15 158 100 0 45.00 120 0 54.00 140 0 63.00 158 2 70.06 158 22 59.66 100 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 49 33.47 167 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 167 13 68.39 103 100 0 45.00 103 17 37.51 103 37 27.11 103 57 16.71 103 776.31 155 100 0 45.00 120 0 54.00 140 0 63.00 155 5 67.151 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21:29 63 10.891 97 83 0.49 112 100 0 45.00 112 8 46.24 112 28 35.84 112 48 25.44 112 68 15.04 E(Profit/Day) 44 22 E(ProfitDay) 50.02 EProfitDay) 52.52 E(Profit/Day) 50.95 E(Profit/Day) 4330 + 1.00 + 3.33 + 6.021 + 8.60 9.731 Prob(Loss) 0.00 Prob(Loss) 0.00 Prob(LOS) 0.00 Prob(Loss) 0.00 Prob(LOSS) 0.07 28 97 29 30 Cum. Freq. Cum. Freq. Cum. Freq Histogram Data Bin Tops -40 -20 0 20 40 60 80 100 Cum. Freq 0 0 0 0 0 0 2 2 30 28 30 0 30 0 DO NOOO 0 0 0 4 30 30 30 0 0 0 4 26 88 ONOOO ODANOOO OONS Un nou coole 5 10 15 30 30 Cum Freq 0 0 2 21 6 41 12 6 21 9 29 8 30 11 P3 (25 points). Modify the news vendor problem in Section 2.7.1 to use independent demands for each trial value of q, and note the difference in the behavior of the output, particularly in the mean plot on the left. (Hint: carefully read the model in lecture 3-Newsvendor.xls posted on Canvas) Simulation with arena I Simulation with arena INPUT DATA Wholesale price c = $0.55 Retail price = $1.00 Scrap prices = $0.03 Demand parameter x = 135.70 Demand parameter o = 27.10 70 121 8 9 10 11 12 13 14 15 16 17 18 60 50 40 Mean Daily Profit ($) 8 140 30 153 9 100 Q 120 Q = 140 qe 160 o 180 1 1661 100 0 45.00 120 Day Demand Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit 0 54.00 140 0 63.00 160 2 1231 100 0 72.00 166 14 67.42 0 45.00 120 0 54.00 123 17 46.51 123 3 1241 37 36.11 123 57 25.71 100 0 45.00 120 0 54.00 124 16 47.48 124 36 37,08 124 4 160 100 56 26.68 0 45.00 120 0 54.00 140 0 63.00 160 5 160 0 72.00 143 100 20 61.60 0 45.00 120 0 54.00 140 0 63.00 143 17 55.51 143 37 45.11 6 1391 100 0 45.00 120 0 54.00 139 1 62.03 139 139 21 51.63 7 1241 100 41 41.231 120 0 45.00 0 54.00 124 16 47.48 124 8 36 37.08 124 1211 100 56 26.68 0 45.00 120 0 54.00 121 19 44.57 9 121 167 39 34.17 100 59 23.77 120 0 45.00 0 54.00 140 0 63.00 10 160 0 72.00 167 1061 100 106 13 68.39 0 45.00 14 40.42 106 34 30.02 106 1641 54 19.62 11 106 100 120 0 45.00 74 9.22 0 54.00 140 0 63.00 160 12 164 148 0 72.00 16 65,48 100 0 45.00 120 0 54.00 140 0 63.001 148 12 60.36 13 148 174 100 0 45.00 32 49.96 120 0 54.00 0 63.00 160 14 174 87 87 0 72.00 6.75.18 13 32.39 87 33 21.991 87 53 11.59 87 73 1.19) 87 15 93 -9.21 153 100 0 45.00 120 0 54.001 140 0 63.00 16 153 231 100 7 65.21 0 45.00 120 27 54.81 0 54.00 140 0 63.00 160 0 72.00 17 180 0 81.00 137 100 0 45.00 120 0 54.00 137 3 60.09 137 23 49.69 137 18 144 43 39 291 100 0 45.00 120 0 54.00 140 0 63.00 144 144 16 56.48 92 19 92 8 37.24 92 36 46.08 28 26.84 92 48 16.44 92 68 6.04 92 20 100 88 -4.36 0.45.00 120 0 54.00 140 0 63.001 155 21 5 67.15 100 25 56.75 0 45.00 120 0 54.00 140 157 0 63.00 3 69.09 22 157 172 23 58.691 100 0 45.000 0 54.00 140 160 0 63.00 23 172 175 100 120 0 72.00 0 45.00 8 73.241 0 54.00 140 0 63.00 0 72.00 24 175 160 100 158 120 5 76.15 0 45.00 0 54.00 140 0 63.00 158 25 158 131 2 70.06 22 59.66 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 26 167 49 33.471 100 0 45.00 120 0 54.00 140 0 63.00 160 27 0 72.00 167 103 100 13 68.391 103 0 45.00 17 37.51 103 37 27.11 103 28 103 155 57 16.71 77 6.31 100 0 45.00 120 0 54.00 140 0 63.001 155 155 5 67.151 29 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.291 97 63 10.89 97 83 0.491 30 112 100 0 45.00 112 8 46.241 112 28 35 84 112 48 25.441 112 68 15.04 E(ProfilDay) 44.22 E(ProfilDay) 50.02 E(ProhiDay) 52.52 E(Profit Day) 50.95E(Profit Day) 43.30 + 1.001 33.33 $6.02 8.60 9.73 155 10 80 100 120 140 160 180 200 9 (papers) 157 155 120 22 23 24 25 26 27 28 29 30 31 02 33 100 35 Sheet1 24 25 26 27 28 29 30 H K L N O R S 158 100 0 45.00 120 0 54.00 140 0163.000 158 2170.06 158 22 59.661 131 100 0 45.00 120 0 54.00 131 9 54 27 131 29 43.87 131 49 33.47 167 100 0 45.00 120 0 54.00 140 0163.00 160 0 72.00 167 13 68.39 103 100 0 45.00 103 17 37.51 103 37 27.11 103 57 16.71 103 77 6.31 155 100 0 45.00 120 0 54.00 140 0163.00 155 5 67.15 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.29 97 63 10.89 97 83 0.49 112 100 0 45.00 112 8 46.24 112 28 35.84 112 48 25.44 112 68 15.04 E(ProfitDay) 44 22 E(Profit/Day) 50.02 E(Profit/Day) 52.52 E(ProfitDay) 50.95 E(Profit/Day) 43.30 1.00 3.33 6.02 8.60 9.73 Prob(Loss) 0.00 Prob(Loss) 0.00 Prob(LOSS)10.00 Prob(Loss) 0.00 Prob(Loss)007 Cum. Freq 0 Cum. Freq. 0 0 0 0 Histogram Data Bin Tops -40 -20 0 20 40 60 80 100 Cum. Freq. 0 0 0 0 0 0 0 0 2 2 30 28 30 0 30 0 Cum. Freq. 0 0 0 0 0 0 0 4 4 30 26 30 0 30 0 NOO OOOOOO 88NOOO on ololo 5 10 15 30 30 Cum, Freq. 0 0 0 2 2 6 4 12 6 21 9 29 8 30 5 5 5 15 0 4 5 19 0 SONIDO DO CD E F H K 1. N P R S T 1 Newsvendor Problem - 30 Days INPUT DATA Wholesale price c = $0.55 Retail prices $1.00 Scrap price 8 = $0.03 Demand parameter x = 135.70 Demand parameter = 27.10 100 123 0 100 124 100 100 70 100 8 9 10 11 12 13 14 15 16 60 50 Mean Daily Profit (S) 40 30 120 0100 120 140 9 160 0 180 Day Demand Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit Sold Scrap Profit 1 166 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 166 14 67.42 2 123 0 45.00 120 0 54.00 17 46.51 123 37 36.11 123 57 25.71 3 124 0 45.00 120 0 54.00 124 16 47.48 124 36 37.08 56 26.68 4 160 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 160 20 61.601 5 143 100 0 45.00 120 0 54.00 140 0 63.00 143 17 55.51 143 37 45.11 6 139 0 45.00 120 0 54.00 139 162.03 139 21 51.631 139 41 41.231 7 124 100 0 45.00 120 0 54.00 124 16 47.48 124 36 37.08 124 56 26.68 8 121 0 45.00 120 0 54.00 121 19 44.57 121 3934.17 121 59 23.77 9 167 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 167 13 68.391 10 106 100 0 45.00 106 14 40.42 106 34 30.02 106 54 19.62 106 74 9.22 11 164 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 164 16 65.481 12 148 100 0 45001 120 0 54.00 140 0 63.001 148 12 60.36 148 32 49.96 13 174 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 174 6 75.18 14 87 87 13 32.391 87 33 21.99 87 53 11.591 87 73 1.19 87 93 -9.21 15 153 100 0 45.00 120 0 54.00 140 0 63.00 153 7 65.21 153 27 54.811 16 231 100 0 45.00 0 54.00 140 0 63.00 160 0 72.00 180 0 81.00 17 137 100 0 45.00 120 0 54.00 137 3 60.09 137 23 49.69 137 43 39.29 18 144 100 0 45.00 120 0 54.00 140 0 63.00 144 16 56.48 144 36 46.081 19 92 92 8 37.241 92 28 26.84 92 48 16.44 92 68 6.04 92 88 -4.36 20 155 100 0 45.00 120 0 54.00 140 0 63.00 155 5 67.15 155 25 56.75 21 157 100 0 45.00 120 0 54.00 140 0 63.00 157 3 69.09 157 23 58.69 22 172 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 172 8 73.24 23 1751 100 0 45.001 0 54.00 140 0 63.00 160 0 72.00 175 24 5 76.15 158 100 0 45.00 120 0 54.00 140 0 63.00 158 2 70.06 158 22 59.66 25 131 100 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 49 33.471 26 167 100 0 45.00 120 0 54.00 0 63.00 160 0 72.00 167 13 68.39 27 103 100 0 45.00 103 17 37.51 37 27.11 103 57 16.71 103 28 155 77 6.31 100 0 45.00 120 0 54.00 140 0 63.00 5 67.15 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21.29 97 63 10.89 97 112 83 0.49 100 0.45.00 112 8 46.24 112 28 35 84 112 48 25.44 112 68 15.04 E(Profit Day) 44 22 E(Profit Day 50.02 E(ProfitDay) 52.52 E(ProfilDay) 50.95 E(Profit Day) 43.30 1.00 13.33 6.02 8.60 9.73 20 20 10 80 100 120 140 160 180 200 9 (papers) 120 24 25 26 27 28 29 30 140 103 31 155 32 33 34 35 B G o S 22 23 24 25 26 27 131 E F . K L R 1721 100 0 45.00 120 054.00 140 0163.00 160 072.00 172 8 73.24 175 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 175 5 76.15 158 100 0 45.00 120 0 54.00 140 0 63.00 158 2 70.06 158 22 59.66 100 0 45.00 120 0 54.00 131 9 54.27 131 29 43.87 131 49 33.47 167 100 0 45.00 120 0 54.00 140 0 63.00 160 0 72.00 167 13 68.39 103 100 0 45.00 103 17 37.51 103 37 27.11 103 57 16.71 103 776.31 155 100 0 45.00 120 0 54.00 140 0 63.00 155 5 67.151 155 25 56.75 97 97 3 42.09 97 23 31.69 97 43 21:29 63 10.891 97 83 0.49 112 100 0 45.00 112 8 46.24 112 28 35.84 112 48 25.44 112 68 15.04 E(Profit/Day) 44 22 E(ProfitDay) 50.02 EProfitDay) 52.52 E(Profit/Day) 50.95 E(Profit/Day) 4330 + 1.00 + 3.33 + 6.021 + 8.60 9.731 Prob(Loss) 0.00 Prob(Loss) 0.00 Prob(LOS) 0.00 Prob(Loss) 0.00 Prob(LOSS) 0.07 28 97 29 30 Cum. Freq. Cum. Freq. Cum. Freq Histogram Data Bin Tops -40 -20 0 20 40 60 80 100 Cum. Freq 0 0 0 0 0 0 2 2 30 28 30 0 30 0 DO NOOO 0 0 0 4 30 30 30 0 0 0 4 26 88 ONOOO ODANOOO OONS Un nou coole 5 10 15 30 30 Cum Freq 0 0 2 21 6 41 12 6 21 9 29 8 30 11