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# **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.

Product
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

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