**Answers are provided in Question 1 and 2, see below for more details**

Western Pharmaceuticals

Once George has initiated the supply chain design project, his next task was to investigate the firm's inventory management capability relative to the refined supply chain. The integration of the Western and Atlantic Medical distribution systems required a refinement of the firm's inventory management system.

Although the firm wanted to have a comprehensive inventory analysis, the information available was limited due to the merger and a simultaneous move to an Enterprise Resource Planning system. In fact, in terms of quickly available data, there was only a limited sample from the Atlantic Medical Sales and Inventory records.

For a sample of 100 stock keeping units (SKUs), the data base includes the average and standard deviation of weekly sales, average order cycle time (OCT), replenishment order quantity (OQ), and the average inventory. Based on history, the current standard deviation in the replenishment cycle time is 1 week. The sales, order quantities, and inventory are recorded in cases. The historical information is provided for each of the three existing distribution centers.

Question 1:

What should the case fill rate be for each product given the current uncertainty levels and order quantities?

I have provided the answers BELOW but I need to understand HOW it was calculated. What is or are the formulas to get those two answers below?

The answer is 96.31 percent fill rate by value and 96.10 percent fill rate in terms of units.

Question 2:

What are the safety stock and average inventory levels for each product necessary to achieve 95 percent case fill rate for reach product?

I have provided the answer BELOW but I need to understand HOW it was calculated. What is or are the formulas to get the answer below?

The answer is $7.5 million to achieve a 95 percent fill rate, while the existing situation only yields a 96 percent with twice the inventory.

\fNB Dmd Mach Did Standard Total Mech Inv NB Std Mech Std OCT AtI OQ NB OQ Mech OQ Product Total Demand (Weekly) (Weekly) Inventory 464.3 16.045 10,473 188.9 100.5 727 929 P 042 363.3 1731.3 368.3 646.1 13.629 5.639 6,190 1,922 1,434 4,772 5,008 295.2 391.3 2.213 2423.8 669.7 P 045 60.9 96.5 41.253 698 47.9 56.3 252.3 75.7 99.2 2,383 163.6 80 852 P 047 1108.1 1,829 3,921 3,848 P 048 10.204 17,508 3,805 930.1 1.201.3 3385.2 1183.7 752.8 20,301 13,107 2,771 385 P 050 1249.0 192.7 2.847 4,137 239.7 1710.2 723.5 2,252 499.4 1,447 1381.1 10.915 17,964 3,144 12,478 3,598 70.8 14,607 7,905 4,985 18.713 2,910 169.1 57.1 198.4 219 P 054 204.8 475.3 24.755 3.636 97.1 216.2 951 2.117 226. 154.2 913 879 P 056 1105.9 209.8 P 057 1464.8 9,503 2,681 88.7 1,310 P 058 14,973 4,652 340.6 2.132 120.8 164.9 13.303 3,270 2,275 307.2 415.3 359.0 P 060 163.1 64.3 5,849 1,144 2,771 1,548 481.4 B,250 302 3,191 786 963 130.6 286.2 18.032 1.048 129.0 56.8 261 403.4 3.662 86.4 44.5 99.8 15.951 8,023 3,038 746.7 2.411 2,798 P 064 3581.2 1205.6 P 065 22,867 6,588 12,247 7,447 9,906 39.7 473 221 572.1 225.5 826 02.7 52.6 73.5 38.5 P 067 289.5 108.7 52.3 128.5 45.832 622 1,281 620 322.4 1,173 4,422 1,618 175.6 668 P 068 334 310 P 069 70.6 155.0 P 070 306.5 99.8 62.0 2,202 36.8 ANNNN 399 248 579 P 071 185.4 55.4 234 31.5 24.9 179.1 20.885 1.244 923 527 398 716 334.6 758 827 1021.5 228.9 413.5 10.805 10.694 P 074 753.4 320.9 1,675 3,632 316.8 P 075 1041.9 10,118 1,261 5,208 354.4 NNN 180.2 12.319 9,653 89.2 236.9 679 764 P 076 901.9 4,734 6,197 3,788 573.3 538.1 2,362 2,732 P 077 3079.0 320 1040.3 261.7 1,613 737 7,110 14.9 21.910 234.0 272 P 079 83.1 68.0 3,765 2,146 5,680 3,012 718.6 262.2 721.1 1,887 P 080 2355.2 397.8 305.3 606.0 8,827 2,322 4,912 1,858 210.4 98.7 P 082 373.2 371.2 42.900 2,944Product Total Demand ATL Did NB Dmd Mech Did Standard Total Atl Inven NB Inven Mech Inv Atl Std NB Std Mech Std OCT AtI OQ NB OQ Mech OQ (Weekly) (Weekly) (Weekly) (Weekly) Cost Inventory (Average) (Average) (Average) P 083 3370.0 1183.8 688.0 8.818 13,169 3,494 3,459 6,217 2,795 261,4 531.4 N 2,368 1,376 2,996 P 084 3743.8 1540.0 697.0 1506.8 11.967 10,517 1,954 2,021 645.4 248.0 N 1,394 3,014 P 085 1994.8 925.4 309.4 760.0 48.255 4,288 2.046 344 1.598 626.9 204.2 1.851 1,520 P 086 830.7 285.1 166.5 379.2 12.409 8,792 2,700 1,721 4,372 2,160 128.3 76.4 361.9 570 333 758 P 087 855.6 384.0 146.3 9.018 11,466 4,371 2,140 4,956 3,497 290.6 132.8 272.8 1,536 585 1,301 P 088 13.7 5.8 3.2 4.7 39.836 2,486 437 60 350 22.4 17.0 23 19 P 089 554.4 277.1 102.0 175.3 38.030 2,677 1,297 561 1,037 112.8 32.5 68.9 N 554 204 351 P 090 1670.7 690.4 358.9 621.3 5.057 19,915 8,364 7,546 6,691 560.4 229.8 396.3 A 2,762 1,436 2,485 P 091 555.8 135.7 87.9 332.2 43.741 2.365 953 1,411 763 250.6 139.5 397.8 N 271 176 664 P 092 137.1 41.6 34.4 32.133 3,176 598 920 1,558 558 27.0 23.2 166 137 P 093 2038.4 746.0 359.5 932.9 8.822 11,519 3,761 2,793 4,965 3,009 749.9 319.3 876.3 1,492 719 1,866 P 094 1936.0 764.5 359.8 811.7 11.658 8,993 2,593 2,195 4,204 2,074 364.9 174.0 357.8 1,529 720 1,623 P 095 745.7 242.7 424.9 18.356 6,127 1,535 928 1,228 216.1 160.3 474.0 N N 485 156 P 096 1 109.2 380.8 573.3 17.112 7,115 1,948 1,045 4,122 1,559 299.0 682.9 N 762 310 1,147 P 097 416.6 136.4 188.8 16.024 6,191 1,731 2,202 2,258 1,385 216.9 131.0 242.0 546 365 755 P 098 398.4 54.2 147.9 6.031 15,391 4.819 2,024 8,548 3,855 231.6 67.0 208.3 785 217 592 P 099 130.3 48.9 31.9 49.4 32.133 856 1,942 42.8 26.8 36.5 196 198 P 100 289.9 116.0 33.381 3,335 1,532 1,033 142.8 52.7 105.3 2 580 232