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Silver-Meal Algorithm Cost Analysis

This document summarizes and compares three inventory management algorithms - Silver-Meal, Wagner-Whitin, and least unit cost (LUC) - using sample demand data over 7 months. It provides the order quantity, ending inventory, total costs, and average unit cost for each algorithm to determine the most cost effective approach.

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85 views22 pages

Silver-Meal Algorithm Cost Analysis

This document summarizes and compares three inventory management algorithms - Silver-Meal, Wagner-Whitin, and least unit cost (LUC) - using sample demand data over 7 months. It provides the order quantity, ending inventory, total costs, and average unit cost for each algorithm to determine the most cost effective approach.

Uploaded by

Sơn Trần Bảo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Silver-Meal algorithm (Least period unit cost)

Given
Parameter Value Unit
Unit price ( c ) 4.75
Ordering cost (A) 35
Carrying rate ( r ) 2%
Holding cost per unit (h) 0.095

Demand
Average period cost table 18 31 23 95 29 37
order at t/ 1 2 3 4 5 6
for till month t'
1 120.5 135.3475 128.105 215.66 202.282 200.7892
2 9999 182.25 146.8425 254.3283 227.25 219.762
3 9999 9999 9999 9999 9999 9999
4 9999 9999 9999 486.25 313.3775 269.845
5 9999 9999 9999 9999 9999 9999
6 9999 9999 9999 9999 9999 9999
7 9999 9999 9999 9999 9999 9999
8 9999 9999 9999 9999 9999 9999
9 9999 9999 9999 9999 9999 9999
10 9999 9999 9999 9999 9999 9999
11 9999 9999 9999 9999 9999 9999
12 9999 9999 9999 9999 9999 9999

Month 1 2 3 4 5 6
Demand 18 31 23 95 29 37
Starting inventory 0 0 23 0 185 156
Replenishment 18 54 0 280 0 0
Ending inventory 0 23 0 185 156 119
Total variable cost 2365.5
Total holding cost 64.22
Total ordering cost 140
Total holding + ordering 204.22
50 39 30 88 22 36
7 8 9 10 11 12

210.105 210.24 205.2467 234.046 224.1691 222.8733


226.6767 223.9343 216.2488 246.0967 233.818 231.2164
9999 9999 9999 9999 9999 9999
265.3213 252.271 236.3508 269.4664 250.6744 244.8617
9999 9999 9999 9999 9999 9999
9999 9999 9999 9999 9999 9999
9999 9999 9999 9999 9999 9999
9999 9999 9999 9999 9999 9999
9999 9999 9999 9999 9999 9999
9999 9999 9999 453 279.795 245.81
9999 9999 9999 9999 9999 9999
9999 9999 9999 9999 9999 9999

7 8 9 10 11 12
50 39 30 88 22 36
119 69 30 0 58 36
0 0 0 146 0 0
69 30 0 58 36 0
Given
Parameter Value Unit
Unit price ( c ) 4
Ordering cost (A) 25
Carrying rate ( r ) 5%
Holding cost per unit (h) 0.2

Silver - Meal
Demand
Average period cost table 20 40 110 120 60 30 20
order at t/ 1 2 3 4 5 6 7
for till month t'
1 105 136.5 252.3333 327.25 319.4 291.1667 264.4286
2 9999 185 323.5 391.6667 362.75 319 282.5
3 9999 9999 465 484.5 411 342.75 293.4
4 9999 9999 9999 505 378.5 296.3333 245.25
5 9999 9999 9999 9999 9999 9999 9999
6 9999 9999 9999 9999 9999 9999 9999
7 9999 9999 9999 9999 9999 9999 9999
8 9999 9999 9999 9999 9999 9999 9999
9 9999 9999 9999 9999 9999 9999 9999
10 9999 9999 9999 9999 9999 9999 9999
11 9999 9999 9999 9999 9999 9999 9999
12 9999 9999 9999 9999 9999 9999 9999

Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 0 0 0 140 80 50
Replenishment 20 40 110 260 0 0 0
Ending inventory 0 0 0 140 80 50 30
Total variable cost 3200
Total holding cost 68
Total ordering cost 175
Total holding + ordering 243

Wagner - Whitin
Demand 20 40 110 120 60 30 20
Order at/ For month 1 2 3 4 5 6 7

1 25 33 77 149 197 227 251


2 NA 50 72 120 156 180 200
3 NA NA 58 82 106 124 140
4 NA NA NA 83 95 107 119
5 NA NA NA NA 107 113 121
6 NA NA NA NA NA 120 124
7 NA NA NA NA NA NA 132
8 NA NA NA NA NA NA NA
9 NA NA NA NA NA NA NA
10 NA NA NA NA NA NA NA
11 NA NA NA NA NA NA NA
12 NA NA NA NA NA NA NA

Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 40 0 120 0 50 20
Replenishment 60 0 230 0 110 0 0
Ending inventory 40 0 120 0 50 20 0
Total variable cost 3200
Total holding cost 70
Total ordering cost 150
Total holding + ordering 220

LUC
Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 150 110 0 60 0 50
Replenishment 170 0 0 180 0 80 0
Ending inventory 150 110 0 60 0 50 30
Total variable cost 3200
Total holding cost 104
Total ordering cost 150
Total holding + ordering 254
Demand
Average unit cost table 20 40 110 120 60 30 20
order at t/ 1 2 3 4 5 6 7
for till month t'
1 5.25 4.55 4.452941 4.513793 4.562857 4.597368 4.6275
2 9999 9999 9999 9999 9999 9999 9999
3 9999 9999 9999 9999 9999 9999 9999
4 9999 9999 9999 4.208333 4.205556 4.233333 4.265217
5 9999 9999 9999 9999 9999 9999 9999
6 9999 9999 9999 9999 9999 4.833333 4.58
7 9999 9999 9999 9999 9999 9999 9999
8 9999 9999 9999 9999 9999 9999 9999
9 9999 9999 9999 9999 9999 9999 9999
10 9999 9999 9999 9999 9999 9999 9999
11 9999 9999 9999 9999 9999 9999 9999
12 9999 9999 9999 9999 9999 9999 9999

Fixed order quantity (FOQ) EOQ 129.0994

Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 150 110 0 0 80 50
Replenishment 170 0 0 120 140 0 0
Ending inventory 150 110 0 0 80 50 30
Total variable cost 3200
Total holding cost 84
Total ordering cost 175
Total holding + ordering 259

PPB
Ordering cost (A) 25

Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 40 0 120 0 80 50
Replenishment 60 0 230 0 140 0 0
Ending inventory 40 0 120 0 80 50 30
Total variable cost 3200
Total holding cost 96
Total ordering cost 125
Total holding + ordering 221

Carrying cost 1 2 3 4 5 6 7
1 0.0 8.0 52.0 124.0 172.0 202.0 226.0
2 0.0 0.0 22.0 70.0 106.0 130.0 150.0
3 0.0 0.0 0.0 24.0 48.0 66.0 82.0
4 0.0 0.0 0.0 0.0 12.0 24.0 36.0
5 0.0 0.0 0.0 0.0 0.0 6.0 14.0
6 0.0 0.0 0.0 0.0 0.0 0.0 4.0
7 0.0 0.0 0.0 0.0 0.0 0.0 0.0
8 0.0 0.0 0.0 0.0 0.0 0.0 0.0
9 0.0 0.0 0.0 0.0 0.0 0.0 0.0
10 0.0 0.0 0.0 0.0 0.0 0.0 0.0
11 0.0 0.0 0.0 0.0 0.0 0.0 0.0
12 0.0 0.0 0.0 0.0 0.0 0.0 0.0

POQ
Raw Round
Period Order quantity (POQ) 1.936492 2
Month 1 2 3 4 5 6 7
Demand 20 40 110 120 60 30 20
Starting inventory 0 40 0 120 0 30 0
Replenishment 60 0 230 0 90 0 50
Ending inventory 40 0 120 0 30 0 30
Total variable cost 3200
Total holding cost 76
Total ordering cost 150
Total holding + ordering 226
30 80 120 130 40
8 9 10 11 12

251.625 273.4444 315.7 357.9091 348.75


264.4286 285.375 328.3333 370.9 359
269.5 290.4286 335.125 378.7778 364.1
225 254.1667 307 356.375 341.6667
9999 9999 9999 9999 9999
9999 9999 9999 9999 9999
9999 9999 9999 9999 9999
9999 9999 9999 9999 9999
9999 345 424.5 473.6667 401.25
9999 9999 505 525.5 409
9999 9999 9999 545 356.5
9999 9999 9999 9999 9999

8 9 10 11 12
30 80 120 130 40
30 0 0 0 40
0 80 120 170 0
0 0 0 40 0

30 80 120 130 40
8 9 10 11 12

293 421 637 897 985


236 348 540 774 854
170 266 434 642 714
143 223 1061 549 613
139 203 323 479 535
136 184 280 410 458
138 170 242 346 386
144 160 208 286 318
NA 161 185 237 261
NA NA 185 211 227
NA NA NA 210 218
NA NA NA NA 235

8 9 10 11 12
30 80 120 130 40
0 80 0 0 40
110 0 120 170 0
80 0 0 40 0

8 9 10 11 12
30 80 120 130 40
30 0 120 0 0
0 200 0 130 40
0 120 0 0 0

30 80 120 130 40
8 9 10 11 12

4.681395 4.82549 5.011111 5.180263 5.23125


9999 9999 9999 9999 9999
9999 9999 9999 9999 9999
4.326923 4.485294 4.671739 4.832203 4.880952
9999 9999 9999 9999 9999
4.5125 4.55625 4.660714 4.768293 4.806667
9999 9999 9999 9999 9999
9999 9999 9999 9999 9999
9999 4.3125 4.245 4.306061 4.337838
9999 9999 9999 9999 9999
9999 9999 9999 4.192308 4.194118
9999 9999 9999 9999 4.625

8 9 10 11 12
30 80 120 130 40
30 0 0 0 0
0 80 120 130 40
0 0 0 0 0

8 9 10 11 12
30 80 120 130 40
30 0 120 0 40
0 200 0 170 0
0 120 0 40 0

8 9 10 11 12
268.0 396.0 612.0 872.0 960.0
186.0 298.0 490.0 724.0 804.0
112.0 208.0 376.0 584.0 656.0
60.0 140.0 284.0 466.0 530.0
32.0 96.0 216.0 372.0 428.0
16.0 64.0 160.0 290.0 338.0
6.0 38.0 110.0 214.0 254.0
0.0 16.0 64.0 142.0 174.0
0.0 0.0 24.0 76.0 100.0
0.0 0.0 0.0 26.0 42.0
0.0 0.0 0.0 0.0 8.0
0.0 0.0 0.0 0.0 0.0

8 9 10 11 12
30 80 120 130 40
30 0 120 0 40
0 200 0 170 0
0 120 0 40 0
Given
Parameter Value Unit
Unit price ( c ) 65
Ordering cost (A) 50
Carrying rate ( r ) 2%
Holding cost per unit (h) 1.05

Silver Meal
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 350 150 150 0 0 1350
Replenishment 700 0 0 0 500 1950 0
Ending inventory 350 150 150 0 0 1350 900
Total variable cost 204750
Total holding cost 4567.5
Total ordering cost 150
Total holding + ordering 4717.5

Demand
Average period cost table 350 200 0 150 500 600 450
order at t/ 1 2 3 4 5 6 7
for till month t'
1 22800 18005 12003.33 11558.13 16166.5 20497.08 22152.5
2 99999 99999 99999 99999 99999 99999 99999
3 99999 99999 99999 99999 99999 99999 99999
4 99999 99999 99999 99999 99999 99999 99999
5 99999 99999 99999 99999 32550 36090 34125
6 99999 99999 99999 99999 99999 39050 34386.25
7 99999 99999 99999 99999 99999 99999 99999
8 99999 99999 99999 99999 99999 99999 99999
9 99999 99999 99999 99999 99999 99999 99999
10 99999 99999 99999 99999 99999 99999 99999
11 99999 99999 99999 99999 99999 99999 99999
12 99999 99999 99999 99999 99999 99999 99999

Wagner-Whitin
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 0 0 0 0 0 0
Replenishment 350 200 0 150 500 600 450
Ending inventory 0 0 0 0 0 0 0
Total variable cost 204750
Total holding cost 0
Total ordering cost 500
Total holding + ordering 500
Demand 350 200 0 150 500 600 450
Order at/ For month 1 2 3 4 5 6 7

1 50 260 260 732.5 2832.5 5982.5 8817.5


2 NA 100 100 415 1990 4510 6872.5
3 NA NA 150 307.5 1357.5 3247.5 5137.5
4 NA NA NA 150 675 1935 3352.5
5 NA NA NA NA 200 830 1775
6 NA NA NA NA NA 250 722.5
7 NA NA NA NA NA NA 300
8 NA NA NA NA NA NA NA
9 NA NA NA NA NA NA NA
10 NA NA NA NA NA NA NA
11 NA NA NA NA NA NA NA
12 NA NA NA NA NA NA NA

LUC
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 0 0 0 0 0 0
Replenishment 350 200 0 150 500 600 450
Ending inventory 0 0 0 0 0 0 0
Total variable cost 204750
Total holding cost 0
Total ordering cost 500
Total holding + ordering 500
Demand
Average unit cost table 350 200 0 150 500 600 450
order at t/ 1 2 3 4 5 6 7
for till month t'
1 65.14286 65.47273 65.47273 66.04643 67.36042 68.32361 68.91889
2 99999 65.25 65.25 66.04286 67.28235 68.07586 68.59079
3 99999 99999 99999 99999 99999 99999 99999
4 99999 99999 99999 65.33333 65.88462 66.468 66.91324
5 99999 99999 99999 99999 65.1 65.61818 66.04839
6 99999 99999 99999 99999 99999 65.08333 65.49762
7 99999 99999 99999 99999 99999 99999 65.11111
8 99999 99999 99999 99999 99999 99999 99999
9 99999 99999 99999 99999 99999 99999 99999
10 99999 99999 99999 99999 99999 99999 99999
11 99999 99999 99999 99999 99999 99999 99999
12 99999 99999 99999 99999 99999 99999 99999

FOQ
Economic Order quantity
(EOQ) 158.1139
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 0 0 150 0 0 0
Replenishment 350 200 150 0 500 600 450
Ending inventory 0 0 150 0 0 0 0
Total variable cost 204750
Total holding cost 315
Total ordering cost 500
Total holding + ordering 815

PPB
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 0 0 0 0 0 0
Replenishment 350 200 0 150 500 600 450
Ending inventory 0 0 0 0 0 0 0
Total variable cost 204750
Total holding cost 0
Total ordering cost 500
Total holding + ordering 500

Carrying cost 1 2 3 4 5 6 7
1 0.0 210.0 210.0 682.5 2782.5 5932.5 8767.5
2 0.0 0.0 0.0 315.0 1890.0 4410.0 6772.5
3 0.0 0.0 0.0 157.5 1207.5 3097.5 4987.5
4 0.0 0.0 0.0 0.0 525.0 1785.0 3202.5
5 0.0 0.0 0.0 0.0 0.0 630.0 1575.0
6 0.0 0.0 0.0 0.0 0.0 0.0 472.5
7 0.0 0.0 0.0 0.0 0.0 0.0 0.0
8 0.0 0.0 0.0 0.0 0.0 0.0 0.0
9 0.0 0.0 0.0 0.0 0.0 0.0 0.0
10 0.0 0.0 0.0 0.0 0.0 0.0 0.0
11 0.0 0.0 0.0 0.0 0.0 0.0 0.0
12 0.0 0.0 0.0 0.0 0.0 0.0 0.0

POQ
Raw Round
Period Order quantity (POQ 0.602339 1
Month 1 2 3 4 5 6 7
Demand 350 200 0 150 500 600 450
Starting inventory 0 0 0 0 0 0 0
Replenishment 350 200 0 150 500 600 450
Ending inventory 0 0 0 0 0 0 0
Total variable cost 204750
Total holding cost 0
Total ordering cost 500
Total holding + ordering 500
8 9 10 11 12
350 200 0 150 200
900 550 350 350 200
0 0 0 0 0
550 350 350 200 0

350 200 0 150 200


8 9 10 11 12

22548.75 21674.44 19507 18763.18 18475.42


99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
31556.88 28013.5 23344.58 21537.5 20654.06
30752.5 26471.88 21177.5 19404.17 18669.29
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999
99999 99999 99999 99999 99999

8 9 10 11 12
350 200 0 150 200
0 0 0 0 0
350 200 0 150 200
0 0 0 0 0
350 200 0 150 200
8 9 10 11 12

11390 13070 13070 14645 16955


9077.5 10547.5 10547.5 11965 14065
6975 8235 8235 9495 11385
4822.5 5872.5 7235 6975 8655
2877.5 3717.5 3717.5 4662.5 6132.5
1457.5 2087.5 2087.5 2875 4135
667.5 1087.5 1087.5 1717.5 2767.5
350 560 560 1032.5 1872.5
NA 400 400 715 1345
NA NA 450 607.5 1027.5
NA NA NA 450 660
NA NA NA NA 500

8 9 10 11 12
350 200 0 150 200
0 0 0 0 0
350 200 0 150 200
0 0 0 0 0

350 200 0 150 200


8 9 10 11 12

69.38077 69.66786 69.66786 69.96441 70.38254


69.01222 69.28469 69.28469 69.58269 70.00536
99999 99999 99999 99999 99999
67.30366 67.56556 67.56556 67.86458 68.29038
66.43553 66.69881 66.69881 67.00556 67.44184
65.89821 66.17969 66.17969 66.52857 67.01795
65.52188 65.8375 65.8375 66.27609 66.86481
65.14286 65.47273 65.47273 66.04643 66.74722
99999 65.25 65.25 66.04286 66.80909
99999 99999 99999 99999 99999
99999 99999 99999 65.33333 65.74286
99999 99999 99999 99999 65.25
8 9 10 11 12
350 200 0 150 200
0 0 0 150 0
350 200 150 0 200
0 0 150 0 0

8 9 10 11 12
350 200 0 150 200
0 0 0 0 0
350 200 0 150 200
0 0 0 0 0

8 9 10 11 12
11340.0 13020.0 13020.0 14595.0 16905.0
8977.5 10447.5 10447.5 11865.0 13965.0
6825.0 8085.0 8085.0 9345.0 11235.0
4672.5 5722.5 5722.5 6825.0 8505.0
2677.5 3517.5 3517.5 4462.5 5932.5
1207.5 1837.5 1837.5 2625.0 3885.0
367.5 787.5 787.5 1417.5 2467.5
0.0 210.0 210.0 682.5 1522.5
0.0 0.0 0.0 315.0 945.0
0.0 0.0 0.0 157.5 577.5
0.0 0.0 0.0 0.0 210.0
0.0 0.0 0.0 0.0 0.0

8 9 10 11 12
350 200 0 150 200
0 0 0 0 0
350 200 0 150 200
0 0 0 0 0
Week 1 2 3 4 5
Demand 21 33 29 15 9

Unit variable cost (c ) 0.7 $/unit


Holding cost (h ) 0.0056 $/unit/week
Ordering cost (A ) 300 $/order

c
(order at/until t-1) 1 2 3 4 5 6
1 314.7 337.9848 358.6096 369.3616 375.8632
2 323.1 343.5624 354.2304 360.6816
3 320.3 330.884 337.2848
4 310.5 316.8504
5 306.3

z 1 2 3 4 5 6
1 314.7 337.9848 358.6096 369.3616 375.8632
2 637.8 658.2624 668.9304 675.3816
3 658.2848 668.8688 675.2696
4 669.1096 675.46
5 675.6616
z* 0 314.7 337.9848 358.6096 369.3616 375.8632
p* 1 1 1 1 1 3

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