Simulation of Periodic Review Inventory System in Excel (Improved)
Simulation of Periodic Review Inventory System in Excel (Improved)
Simulation of Periodic Review Inventory System in Excel (Improved)
2012
This PDF file contains its original document file and excel file as attachments
(Use office 2010 for better performance)
Let me know if it helped you! Or if youve made any development in the logic
sobuj@student.sust.edu
For this purpose we have used spreadsheet to analyze the data and the objectives.
3. Model conceptualization:
We have visited the dealer of Supercrete cement. In there we have discussed with them
about the current model. After that we decided which type of data should be collected.
4. Data collection:
We have collected data from their database over last 12 months.
Though the maximum capacity to store is 50,000 bags of cement but they usually keep
18000 bags of cement in off season and 27000 bags of cement in peak season.
Maximum inventory level in off season M = 18000 bags.
Maximum inventory level in peak season M = 27000 bags.
They use fixed time period model to replenish the inventory stock.
The review period T = 3 days.
Lead time is a random variable, but it falls in the range of 1 to 2 days.
The dealer gets demand in random manner which usually falls in the range of 2000 to
3100 bags of cement/per day in off season & 3150 to 5200 bags of cement in peak
season. For simplicity they usually place orders at the end of the day and replenish the
inventory stock at the beginning of the day.
Days
Probability
Cumulative
Probability
2000
2200
2400
2500
2700
2800
2900
3000
3100
Total=
9
12
14
16
19
15
13
12
10
120
0.075
0.100
0.117
0.133
0.158
0.125
0.108
0.100
0.083
0.075
0.175
0.292
0.425
0.583
0.708
0.817
0.917
1.000
075
175
292
425
583
708
817
917
000
14
12
10
Days
8
6
4
2
0
2000
2200
2400
2500
2700
2800
2900
3000
3100 Demand
Days
Probability
Cumulative
Probability
3150
3250
3450
3500
3750
3900
4000
4250
4500
4700
4800
5000
5200
Total=
11
14
17
19
22
25
27
23
21
18
16
15
12
240
0.046
0.058
0.071
0.079
0.092
0.104
0.113
0.096
0.088
0.075
0.067
0.063
0.050
0.046
0.104
0.175
0.254
0.346
0.450
0.563
0.658
0.746
0.821
0.888
0.950
1.000
046
104
175
254
346
450
563
658
746
821
888
950
000
Lead time
(Days)
Times
1
2
Total=
97
23
120
5200
5000
4800
4700
4500
4250
4000
3900
3750
3500
3450
3250
3150
Days
0.81
1.00
01
82
81
00
After generating probability distribution we have put those data in spreadsheet in logical manner.
At first we have performed simulation for the existing inventory system. Then weve performed
simulation for our proposed inventory model.
Simulation of existing model (off season): The beginning inventory was 10,000 bags of cement and 8000 bags of cement order was already placed, the order will reach
the destination after 2 days.
Inventory level =
Cycle
18000
Beginning inventory =
10000
Initial order =
8000
Day
Beginning
Inventory
Random
Digits for
Demand
Demand
Ending
Inventory
Shortage
Quantity
Order
Quantity
Random digit
for lead time
Generated
Lead time
Days until
Order
Arrives
Order
received?
10000
837
3000
7000
No
Ending
inventory
just before
the day order
received
-
7000
069
2000
5000
No
5000
13000
899
3000
10000
8000
78
Received
10000
248
2400
7600
No
7600
15600
413
2500
13100
Received
13100
857
3000
10100
7900
07
No
10100
400
2500
7600
No
7600
15500
838
3000
12500
Received
12500
944
3100
9400
8600
59
No
9400
725
2900
6500
No
6500
15100
219
2400
12700
Received
3
1
2
12700
10000
15300
456
477
830
2700
2700
3000
10000
7300
12300
0
0
0
8000
-
30
-
1
-
1
0
-
No
No
Received
7300
-
12300
042
2000
10300
7700
15
No
10300
053
2000
8300
No
8300
16000
700
2800
13200
Received
13200
468
2700
10500
7500
55
No
10500
154
2200
8300
No
8300
15800
436
2700
13100
Received
13100
001
2000
11100
6900
80
No
11100
332
2500
8600
No
8600
15500
242
2400
13100
Received
13100
552
2700
10400
7600
71
No
10400
740
2900
7500
No
7500
15100
622
2800
12300
Received
12300
098
2200
10100
7900
39
No
10
11
12
13
14
15
16
17
18
19
20
10100
732
2900
7200
No
7200
15100
933
3100
12000
Received
12000
425
2500
9500
8500
77
No
9500
926
3100
6400
No
6400
14900
689
2800
12100
Received
12100
062
2000
10100
7900
04
No
1
2
10100
16000
037
594
2000
2800
8100
13200
0
0
0
-
No
Received
8100
-
13200
200
2400
10800
7200
28
No
10800
625
2800
8000
No
8000
15200
127
2200
13000
Received
13000
038
2000
11000
7000
91
No
11000
211
2400
8600
No
8600
071
2000
6600
No
6600
13600
062
2000
11600
6400
46
Received
11600
513
2700
8900
No
8900
15300
865
3000
12300
Received
12300
834
3000
9300
8700
27
No
9300
911
3000
6300
No
6300
15000
515
2700
12300
Received
12300
854
3000
9300
8700
95
No
9300
501
2700
6600
No
6600
988
3100
3500
No
3500
12200
469
2700
9500
8500
99
Received
9500
705
2800
6700
No
6700
071
2000
4700
No
4700
13200
948
3100
10100
7900
71
Received
10100
357
2500
7600
No
7600
15500
461
2700
12800
Received
12800
725
2900
9900
8100
04
No
9900
896
3000
6900
No
6900
15000
230
2400
12600
Received
12600
560
2700
9900
8100
98
No
9900
622
2800
7100
No
21
22
23
24
25
26
27
28
29
30
31
32
7100
388
2500
4600
No
4600
12700
776
2900
9800
8200
63
Received
9800
063
2000
7800
No
7800
16000
103
2200
13800
Received
13800
440
2700
11100
6900
44
No
11100
596
2800
8300
No
8300
15200
327
2500
12700
Received
12700
567
2700
10000
8000
55
No
10000
128
2200
7800
No
7800
15800
608
2800
13000
Received
13000
950
3100
9900
8100
18
No
9900
589
2800
7100
No
7100
15200
785
2900
12300
Received
12300
071
2000
10300
7700
35
No
10300
295
2500
7800
No
7800
15500
571
2700
12800
Received
12800
822
3000
9800
8200
15
No
9800
165
2200
7600
No
7600
15800
761
2900
12900
Received
12900
311
2500
10400
7600
75
No
10400
567
2700
7700
No
7700
15300
527
2700
12600
Received
12600
942
3100
9500
8500
86
No
9500
989
3100
6400
No
6400
597
2800
3600
No
3600
12100
340
2500
9600
8400
51
Received
9600
172
2200
7400
No
7400
15800
837
3000
12800
Received
12800
821
3000
9800
8200
96
No
9800
121
2200
7600
No
7600
580
2700
4900
No
4900
13100
899
3000
10100
7900
42
Received
10100
487
2700
7400
No
7400
15300
343
2500
12800
Received
33
34
35
36
37
38
39
40
41
42
43
12800
319
2500
10300
7700
59
No
10300
387
2500
7800
No
7800
15500
684
2800
12700
Received
12700
690
2800
9900
8100
82
No
9900
934
3100
6800
No
6800
739
2900
3900
No
3900
12000
384
2500
9500
8500
65
Received
9500
073
2000
7500
No
7500
16000
206
2400
13600
Received
13600
298
2500
11100
6900
23
No
11100
291
2400
8700
No
8700
15600
878
3000
12600
Received
12600
956
3100
9500
8500
59
No
9500
996
3100
6400
No
6400
14900
345
2500
12400
Received
12400
309
2500
9900
8100
96
No
9900
652
2800
7100
No
7100
144
2200
4900
No
4900
13000
262
2400
10600
7400
66
Received
10600
189
2400
8200
No
8200
15600
690
2800
12800
Received
12800
904
3000
9800
8200
47
No
9800
120
2200
7600
No
7600
15800
133
2200
13600
Received
13600
267
2400
11200
6800
11
No
11200
388
2500
8700
No
8700
15500
340
2500
13000
Received
13000
627
2800
10200
7800
50
No
10200
122
2200
8000
No
8000
15800
277
2400
13400
Received
13400
289
2400
11000
7000
22
No
11000
951
3100
7900
No
7900
14900
956
3100
11800
Received
11800
963
3100
8700
9300
87
No
44
45
46
47
48
49
50
51
52
Average
ending
inventory
8700
332
2500
6200
No
6200
745
2900
3300
No
3300
12600
423
2500
10100
7900
35
Received
10100
895
3000
7100
No
7100
15000
711
2900
12100
Received
12100
753
2900
9200
8800
95
No
9200
035
2000
7200
No
7200
827
3000
4200
No
4200
13000
222
2400
10600
7400
47
Received
10600
890
3000
7600
No
7600
15000
439
2700
12300
Received
12300
966
3100
9200
8800
56
No
9200
936
3100
6100
No
6100
14900
788
2900
12000
Received
12000
812
2900
9100
8900
08
No
9100
729
2900
6200
No
6200
15100
342
2500
12600
Received
12600
727
2900
9700
8300
17
No
9700
948
3100
6600
No
6600
14900
241
2400
12500
Received
12500
356
2500
10000
8000
21
No
10000
960
3100
6900
No
6900
14900
339
2500
12400
Received
12400
292
2500
9900
8100
49
No
9900
707
2800
7100
No
7100
15200
228
2400
12800
Received
12800
620
2800
10000
8000
09
No
10052
Avg. order
7948
Shortage=
Avg. daily
demand
Demand=
2649
9478
1.19
333.79
14942
11107
683.45
6877
61.79%
= 683.45
SS= NORMSINV (0.99999999) Standard deviation of demand during T+L period
= 5.61 683.45 = 3483.15 units.
So the Inventory level should be = DT+L + SS = 14941.15 15000 units
Proposed new Inventory level is 15000 units with the same demand pattern and lead
time.
The proposed models simulation is shown below,
Simulation of proposed model (off season): The beginning inventory was 10,000 bags of cement and 5000 bags of cement order was already placed, the order will
reach the destination after 2 days.
Inventory level =
Cycle
15000
Beginning inventory =
10000
Initial order =
5000
Day
Beginning
Inventory
Random
Digits for
Demand
Demand
Ending
Inventory
Shortage
Quantity
Order
Quantity
Random digit
for lead time
Generated
Lead time
Days until
Order
Arrives
Order
received?
Ending inventory
just before the
day order
received
10000
629
2800
7200
No
7200
734
2900
4300
No
4300
9300
698
2800
6500
8500
16
Received
6500
712
2900
3600
No
3600
12100
548
2700
9400
Received
9400
827
3000
6400
8600
24
No
6400
321
2500
3900
No
3900
12500
104
2200
10300
Received
10300
719
2900
7400
7600
79
No
7400
423
2500
4900
No
4900
12500
433
2700
9800
Received
9800
406
2500
7300
7700
01
No
7300
471
2700
4600
No
4600
12300
530
2700
9600
Received
9600
770
2900
6700
8300
07
No
6700
013
2000
4700
No
4700
13000
920
3100
9900
Received
9900
791
2900
7000
8000
23
No
7000
933
3100
3900
No
3900
11900
080
2200
9700
Received
9700
762
2900
6800
8200
83
No
6800
980
3100
3700
No
3700
643
2800
900
No
900
9100
269
2400
6700
8300
13
Received
6700
769
2900
3800
No
3800
12100
186
2400
9700
Received
10
11
12
13
14
15
16
17
18
19
20
9700
328
2500
7200
7800
84
No
7200
788
2900
4300
No
4300
342
2500
1800
No
1800
9600
858
3000
6600
8400
94
Received
6600
249
2400
4200
No
4200
663
2800
1400
No
1400
9800
490
2700
7100
7900
73
Received
7100
253
2400
4700
No
4700
12600
155
2200
10400
Received
10400
427
2700
7700
7300
97
No
7700
748
2900
4800
No
4800
539
2700
2100
No
2100
9400
575
2700
6700
8300
25
Received
6700
810
2900
3800
No
3800
12100
594
2800
9300
Received
9300
246
2400
6900
8100
15
No
6900
204
2400
4500
No
4500
12600
063
2000
10600
Received
10600
663
2800
7800
7200
42
No
7800
994
3100
4700
No
4700
11900
720
2900
9000
Received
9000
803
2900
6100
8900
30
No
6100
195
2400
3700
No
3700
12600
537
2700
9900
Received
9900
634
2800
7100
7900
05
No
7100
437
2700
4400
No
4400
12300
969
3100
9200
Received
9200
819
3000
6200
8800
78
No
6200
936
3100
3100
No
3100
11900
312
2500
9400
Received
9400
036
2000
7400
7600
60
No
7400
262
2400
5000
No
5000
12600
067
2000
10600
Received
21
22
23
24
25
26
27
28
29
30
31
10600
749
2900
7700
7300
89
No
7700
966
3100
4600
No
4600
491
2700
1900
No
1900
9200
588
2800
6400
8600
72
Received
6400
838
3000
3400
No
3400
12000
498
2700
9300
Received
9300
023
2000
7300
7700
97
No
7300
949
3100
4200
No
4200
088
2200
2000
No
2000
9700
833
3000
6700
8300
12
Received
6700
797
2900
3800
No
3800
12100
283
2400
9700
Received
9700
061
2000
7700
7300
19
No
7700
824
3000
4700
No
4700
12000
976
3100
8900
Received
8900
059
2000
6900
8100
40
No
6900
476
2700
4200
No
4200
12300
600
2800
9500
Received
9500
878
3000
6500
8500
46
No
6500
213
2400
4100
No
4100
12600
425
2500
10100
Received
10100
655
2800
7300
7700
09
No
7300
178
2400
4900
No
4900
12600
899
3000
9600
Received
9600
035
2000
7600
7400
97
No
7600
520
2700
4900
No
4900
257
2400
2500
No
2500
9900
709
2900
7000
8000
61
Received
7000
786
2900
4100
No
4100
12100
863
3000
9100
Received
9100
110
2200
6900
8100
14
No
6900
564
2700
4200
No
4200
12300
107
2200
10100
Received
32
33
34
35
36
37
38
39
40
41
42
10100
846
3000
7100
7900
02
No
7100
250
2400
4700
No
4700
12600
458
2700
9900
Received
9900
184
2400
7500
7500
90
No
7500
531
2700
4800
No
4800
726
2900
1900
No
1900
9400
045
2000
7400
7600
00
Received
7400
043
2000
5400
No
5400
545
2700
2700
No
2700
10300
274
2400
7900
7100
68
Received
7900
417
2500
5400
No
5400
12500
098
2200
10300
Received
10300
085
2200
8100
6900
81
No
8100
125
2200
5900
No
5900
737
2900
3000
No
3000
9900
443
2700
7200
7800
71
Received
7200
929
3100
4100
No
4100
11900
933
3100
8800
Received
8800
800
2900
5900
9100
31
No
5900
237
2400
3500
No
3500
12600
623
2800
9800
Received
9800
607
2800
7000
8000
72
No
7000
143
2200
4800
No
4800
12800
171
2200
10600
Received
10600
662
2800
7800
7200
94
No
7800
247
2400
5400
No
5400
975
3100
2300
No
2300
9500
955
3100
6400
8600
05
Received
6400
431
2700
3700
No
3700
12300
245
2400
9900
Received
9900
020
2000
7900
7100
65
No
7900
688
2800
5100
No
5100
12200
414
2500
9700
Received
43
44
45
46
47
48
49
50
51
52
53
9700
669
2800
6900
8100
28
No
6900
112
2200
4700
No
4700
12800
159
2200
10600
Received
10600
024
2000
8600
6400
81
No
8600
705
2800
5800
No
5800
986
3100
2700
No
2700
9100
962
3100
6000
9000
72
Received
6000
786
2900
3100
No
3100
12100
362
2500
9600
Received
9600
128
2200
7400
7600
51
No
7400
706
2800
4600
No
4600
12200
616
2800
9400
Received
9400
815
2900
6500
8500
67
No
6500
374
2500
4000
No
4000
12500
970
3100
9400
Received
9400
293
2500
6900
8100
43
No
6900
602
2800
4100
No
4100
12200
088
2200
10000
Received
10000
162
2200
7800
7200
50
No
7800
990
3100
4700
No
4700
11900
367
2500
9400
Received
9400
661
2800
6600
8400
51
No
6600
071
2000
4600
No
4600
13000
061
2000
11000
Received
11000
138
2200
8800
6200
70
No
8800
363
2500
6300
No
6300
12500
057
2000
10500
Received
10500
447
2700
7800
7200
08
No
7800
328
2500
5300
No
5300
12500
431
2700
9800
Received
9800
845
3000
6800
8200
61
No
6800
383
2500
4300
No
4300
12500
710
2900
9600
Received
54
55
56
57
58
59
60
61
62
63
64
9600
015
2000
7600
7400
54
No
7600
829
3000
4600
No
4600
12000
492
2700
9300
Received
9300
709
2900
6400
8600
57
No
6400
760
2900
3500
No
3500
12100
799
2900
9200
Received
9200
599
2800
6400
8600
99
No
6400
428
2700
3700
No
3700
377
2500
1200
No
1200
9800
271
2400
7400
7600
24
Received
7400
092
2200
5200
No
5200
12800
078
2200
10600
Received
10600
010
2000
8600
6400
30
No
8600
875
3000
5600
No
5600
12000
020
2000
10000
Received
10000
649
2800
7200
7800
15
No
7200
725
2900
4300
No
4300
12100
321
2500
9600
Received
9600
039
2000
7600
7400
18
No
7600
866
3000
4600
No
4600
12000
749
2900
9100
Received
9100
354
2500
6600
8400
09
No
6600
297
2500
4100
No
4100
12500
464
2700
9800
Received
9800
658
2800
7000
8000
54
No
7000
827
3000
4000
No
4000
12000
675
2800
9200
Received
9200
388
2500
6700
8300
25
No
6700
844
3000
3700
No
3700
12000
583
2700
9300
Received
9300
166
2200
7100
7900
16
No
7100
129
2200
4900
No
4900
12800
184
2400
10400
Received
65
66
67
68
69
70
71
72
Average
ending
inventory
10400
493
2700
7700
7300
51
No
7700
840
3000
4700
No
4700
12000
158
2200
9800
Received
9800
894
3000
6800
8200
68
No
6800
496
2700
4100
No
4100
12300
983
3100
9200
Received
9200
258
2400
6800
8200
01
No
6800
805
2900
3900
No
3900
12100
748
2900
9200
Received
9200
622
2800
6400
8600
42
No
6400
155
2200
4200
No
4200
12800
376
2500
10300
Received
10300
966
3100
7200
7800
47
No
7200
513
2700
4500
No
4500
12300
013
2000
10300
Received
10300
594
2800
7500
7500
40
No
7500
122
2200
5300
No
5300
12800
184
2400
10400
Received
10400
516
2700
7700
7300
01
No
7700
441
2700
5000
No
5000
12300
537
2700
9600
Received
9600
589
2800
6800
8200
00
No
6800
640
2800
4000
No
4000
064
2000
2000
No
2000
10200
285
2400
7800
7200
27
Received
7128
Avg. order
7872
Shortage=
Avg. daily
demand
Demand=
2624
6599
3925
73.83%
1.19
Simulation of existing model (Peak season): The beginning inventory was 16000 bags of cement and 10500 bags of cement order was already placed, the order will
reach the destination after 2 days.
Inventory level =
Cycle
26500
Beginning inventory =
16000
Initial order =
10500
Day
Beginning
Inventory
Random Digits
for Demand
Demand
Ending
Inventory
Shortage
Quantity
Order
Quantity
Random digit
for lead time
Generated
Lead time
Days until
Order
Arrives
Order
received?
16000
779
4700
11300
No
Ending
inventory just
before the day
order received
-
11300
010
3150
8150
No
8150
18650
488
4000
14650
11850
20
Received
14650
799
4700
9950
No
9950
21800
621
4250
17550
Received
17550
517
4000
13550
12950
63
No
13550
478
4000
9550
No
9550
22500
875
4800
17700
Received
17700
186
3500
14200
12300
73
No
14200
398
3900
10300
No
10300
22600
574
4250
18350
Received
3
1
2
18350
14900
22500
154
540
126
3450
4000
3450
14900
10900
19050
0
0
0
11600
-
46
-
1
-
1
0
-
No
No
Received
10900
-
19050
359
3900
15150
11350
06
No
15150
185
3500
11650
No
11650
23000
350
3900
19100
Received
19100
896
5000
14100
12400
92
No
14100
568
4250
9850
No
9850
804
4700
5150
No
5150
17550
537
4000
13550
12950
14
Received
13550
201
3500
10050
No
10050
23000
217
3500
19500
Received
3
1
19500
16000
225
325
3500
3750
16000
12250
0
0
10500
-
80
-
1
-
1
0
No
No
12250
22750
066
3250
19500
Received
19500
607
4250
15250
11250
22
No
10
11
12
13
14
15
16
17
18
19
20
15250
000
5200
10050
No
10050
21300
012
3150
18150
Received
18150
616
4250
13900
12600
66
No
13900
945
5000
8900
No
8900
21500
571
4250
17250
Received
17250
502
4000
13250
13250
29
No
1
2
13250
21300
971
788
5200
4700
8050
16600
0
0
0
-
No
Received
8050
-
16600
114
3450
13150
13350
83
No
13150
570
4250
8900
No
8900
213
3500
5400
No
5400
18750
113
3450
15300
11200
85
Received
15300
335
3750
11550
No
11550
324
3750
7800
No
7800
19000
722
4500
14500
12000
87
Received
14500
563
4250
10250
No
10250
149
3450
6800
No
6800
18800
099
3250
15550
10950
06
Received
15550
139
3450
12100
No
12100
23050
284
3750
19300
Received
19300
029
3150
16150
10350
55
No
16150
154
3450
12700
No
12700
23050
746
4700
18350
Received
18350
464
4000
14350
12150
55
No
14350
690
4500
9850
No
9850
22000
033
3150
18850
Received
18850
557
4000
14850
11650
91
No
14850
900
5000
9850
No
9850
945
5000
4850
No
4850
16500
443
3900
12600
13900
01
Received
12600
628
4250
8350
No
8350
22250
848
4800
17450
Received
17450
714
4500
12950
13550
13
No
12950
672
4500
8450
No
8450
21
22
23
24
25
26
27
28
29
30
31
22000
188
3500
18500
Received
18500
434
3900
14600
11900
05
No
14600
208
3500
11100
No
11100
23000
447
3900
19100
Received
19100
546
4000
15100
11400
82
No
15100
397
3900
11200
No
11200
540
4000
7200
No
7200
18600
477
4000
14600
11900
69
Received
14600
222
3500
11100
No
11100
23000
308
3750
19250
Received
19250
708
4500
14750
11750
47
No
14750
173
3450
11300
No
11300
23050
910
5000
18050
Received
18050
785
4700
13350
13150
29
No
13350
896
5000
8350
No
8350
21500
094
3250
18250
Received
18250
114
3450
14800
11700
19
No
14800
039
3150
11650
No
11650
23350
800
4700
18650
Received
18650
163
3450
15200
11300
92
No
15200
939
5000
10200
No
10200
594
4250
5950
No
5950
17250
838
4800
12450
14050
70
Received
12450
189
3500
8950
No
8950
23000
765
4700
18300
Received
18300
062
3250
15050
11450
50
No
15050
348
3900
11150
No
11150
22600
115
3450
19150
Received
19150
918
5000
14150
12350
83
No
14150
529
4000
10150
No
10150
823
4800
5350
No
5350
17700
288
3750
13950
12550
70
Received
13950
077
3250
10700
No
10700
32
33
34
35
36
37
38
39
40
41
42
43
23250
020
3150
20100
Received
20100
723
4500
15600
10900
78
No
15600
686
4500
11100
No
11100
22000
944
5000
17000
Received
17000
197
3500
13500
13000
35
No
13500
818
4700
8800
No
8800
21800
902
5000
16800
Received
16800
401
3900
12900
13600
75
No
12900
685
4500
8400
No
8400
22000
193
3500
18500
Received
18500
940
5000
13500
13000
44
No
13500
233
3500
10000
No
10000
23000
951
5200
17800
Received
17800
109
3450
14350
12150
33
No
14350
115
3450
10900
No
10900
23050
491
4000
19050
Received
19050
175
3450
15600
10900
84
No
15600
947
5000
10600
No
10600
425
3900
6700
No
6700
17600
024
3150
14450
12050
49
Received
14450
195
3500
10950
No
10950
23000
829
4800
18200
Received
18200
504
4000
14200
12300
18
No
14200
918
5000
9200
No
9200
21500
642
4250
17250
Received
17250
087
3250
14000
12500
49
No
14000
542
4000
10000
No
10000
22500
018
3150
19350
Received
19350
595
4250
15100
11400
79
No
15100
051
3250
11850
No
11850
23250
133
3450
19800
Received
19800
626
4250
15550
10950
42
No
15550
219
3500
12050
No
12050
23000
665
4500
18500
Received
44
45
46
47
48
49
50
51
52
Average
ending
inventory
18500
780
4700
13800
12700
47
No
13800
093
3250
10550
No
10550
23250
269
3750
19500
Received
19500
549
4000
15500
11000
78
No
15500
210
3500
12000
No
12000
23000
647
4250
18750
Received
18750
447
3900
14850
11650
17
No
14850
579
4250
10600
No
10600
22250
436
3900
18350
Received
18350
538
4000
14350
12150
30
No
14350
508
4000
10350
No
10350
22500
807
4700
17800
Received
17800
486
4000
13800
12700
34
No
13800
148
3450
10350
No
10350
23050
754
4700
18350
Received
18350
907
5000
13350
13150
50
No
13350
242
3500
9850
No
9850
23000
121
3450
19550
Received
19550
951
5200
14350
12150
88
No
14350
426
3900
10450
No
10450
115
3450
7000
No
7000
19150
029
3150
16000
10500
12
Received
16000
235
3500
12500
No
12500
23000
855
4800
18200
Received
18200
502
4000
14200
12300
55
No
14200
992
5200
9000
No
9000
21300
903
5000
16300
Received
16300
978
5200
11100
15400
25
No
14345
Avg. order
12155
Shortage=
Avg. daily
demand
Demand=
4052
16986
13536
1.19
1248.68
64%
9542
= 1248.68
SS= NORMSINV (0.99999999) Standard deviation of demand during T+L period
= 5.61 1248.68 = 7005.1 units.
So the Inventory level should be = DT+L + SS = 23991.1 24000 units
Proposed new Inventory level is 24000 units with the same demand pattern and lead
time.
The proposed models simulation is shown below,
Simulation of proposed model (Peak season): The beginning inventory is 16000 bags of cement and 8000 bags of cement order was already placed, the order will
reach the destination after 2 days.
Inventory level =
Cycle
24000
Beginning inventory =
16000
Initial order =
8000
Day
Beginning
Inventory
Random Digits
for Demand
Demand
Ending
Inventory
Shortage
Quantity
Order
Quantity
Random digit
for lead time
Generated
Lead time
Days until
Order Arrives
Order
received?
16000
730
4500
11500
No
Ending inventory
just before the
day order
received
-
11500
474
4000
7500
No
7500
18000
525
4000
14000
10000
49
Received
14000
266
3750
10250
No
10250
20250
086
3250
17000
Received
17000
620
4250
12750
11250
96
No
12750
986
5200
7550
No
7550
070
3250
4300
No
4300
15550
267
3750
11800
12200
86
Received
11800
903
5000
6800
No
6800
526
4000
2800
No
2800
15000
159
3450
11550
12450
64
Received
11550
886
4800
6750
No
6750
19200
438
3900
15300
Received
15300
869
4800
10500
13500
24
No
10500
860
4800
5700
No
5700
19200
517
4000
15200
Received
15200
862
4800
10400
13600
39
No
10400
328
3750
6650
No
6650
20250
752
4700
15550
Received
15550
215
3500
12050
11950
90
No
12050
749
4700
7350
No
7350
214
3500
3850
No
3850
15800
456
4000
11800
12200
02
Received
11800
498
4000
7800
No
7800
20000
662
4500
15500
Received
15500
050
3250
12250
11750
27
No
10
11
12
13
14
15
16
17
18
19
20
12250
338
3750
8500
No
8500
20250
380
3900
16350
Received
16350
096
3250
13100
10900
62
No
13100
919
5000
8100
No
8100
19000
249
3500
15500
Received
15500
868
4800
10700
13300
73
No
10700
641
4250
6450
No
6450
19750
402
3900
15850
Received
15850
737
4500
11350
12650
89
No
11350
893
5000
6350
No
6350
085
3250
3100
No
3100
15750
025
3150
12600
11400
98
Received
12600
278
3750
8850
No
8850
395
3900
4950
No
4950
16350
686
4500
11850
12150
81
Received
11850
275
3750
8100
No
8100
164
3450
4650
No
4650
16800
361
3900
12900
11100
30
Received
12900
628
4250
8650
No
8650
19750
720
4500
15250
Received
15250
358
3900
11350
12650
23
No
11350
362
3900
7450
No
7450
20100
408
3900
16200
Received
16200
069
3250
12950
11050
07
No
12950
287
3750
9200
No
9200
20250
867
4800
15450
Received
15450
644
4250
11200
12800
61
No
11200
400
3900
7300
No
7300
20100
292
3750
16350
Received
16350
910
5000
11350
12650
48
No
11350
256
3750
7600
No
7600
20250
099
3250
17000
Received
17000
840
4800
12200
11800
23
No
21
22
23
24
25
26
27
28
29
30
31
12200
480
4000
8200
No
8200
20000
572
4250
15750
Received
15750
736
4500
11250
12750
89
No
11250
545
4000
7250
No
7250
555
4000
3250
No
3250
16000
209
3500
12500
11500
98
Received
12500
424
3900
8600
No
8600
185
3500
5100
No
5100
16600
738
4500
12100
11900
92
Received
12100
686
4500
7600
No
7600
829
4800
2800
No
2800
14700
059
3250
11450
12550
72
Received
11450
393
3900
7550
No
7550
20100
117
3450
16650
Received
16650
769
4700
11950
12050
24
No
11950
331
3750
8200
No
8200
20250
269
3750
16500
Received
16500
269
3750
12750
11250
91
No
12750
515
4000
8750
No
8750
758
4700
4050
No
4050
15300
522
4000
11300
12700
63
Received
11300
025
3150
8150
No
8150
20850
264
3750
17100
Received
17100
988
5200
11900
12100
96
No
11900
190
3500
8400
No
8400
465
4000
4400
No
4400
16500
203
3500
13000
11000
20
Received
13000
935
5000
8000
No
8000
19000
324
3750
15250
Received
15250
969
5200
10050
13950
60
No
10050
270
3750
6300
No
6300
20250
128
3450
16800
Received
16800
933
5000
11800
12200
80
No
32
33
34
35
36
37
38
39
40
41
42
11800
340
3750
8050
No
8050
20250
061
3250
17000
Received
17000
553
4000
13000
11000
90
No
13000
980
5200
7800
No
7800
457
4000
3800
No
3800
14800
897
5000
9800
14200
99
Received
9800
351
3900
5900
No
5900
916
5000
900
No
900
15100
735
4500
10600
13400
42
Received
10600
247
3500
7100
No
7100
20500
091
3250
17250
Received
17250
987
5200
12050
11950
25
No
12050
428
3900
8150
No
8150
20100
254
3500
16600
Received
16600
718
4500
12100
11900
28
No
12100
200
3500
8600
No
8600
20500
768
4700
15800
Received
15800
681
4500
11300
12700
84
No
11300
898
5000
6300
No
6300
532
4000
2300
No
2300
15000
059
3250
11750
12250
50
Received
11750
990
5200
6550
No
6550
18800
032
3150
15650
Received
15650
315
3750
11900
12100
18
No
11900
181
3500
8400
No
8400
20500
344
3750
16750
Received
16750
321
3750
13000
11000
54
No
13000
961
5200
7800
No
7800
18800
807
4700
14100
Received
14100
145
3450
10650
13350
89
No
10650
413
3900
6750
No
6750
295
3750
3000
No
3000
16350
540
4000
12350
11650
12
Received
43
44
45
46
47
48
49
50
51
52
53
12350
393
3900
8450
No
8450
20100
593
4250
15850
Received
15850
178
3500
12350
11650
48
No
12350
835
4800
7550
No
7550
19200
487
4000
15200
Received
15200
420
3900
11300
12700
07
No
11300
248
3500
7800
No
7800
20500
001
3150
17350
Received
17350
912
5000
12350
11650
25
No
12350
750
4700
7650
No
7650
19300
139
3450
15850
Received
15850
150
3450
12400
11600
00
No
12400
726
4500
7900
No
7900
835
4800
3100
No
3100
14700
652
4250
10450
13550
82
Received
10450
128
3450
7000
No
7000
410
3900
3100
No
3100
16650
079
3250
13400
10600
43
Received
13400
860
4800
8600
No
8600
19200
154
3450
15750
Received
15750
909
5000
10750
13250
73
No
10750
991
5200
5550
No
5550
18800
398
3900
14900
Received
14900
531
4000
10900
13100
30
No
10900
849
4800
6100
No
6100
19200
355
3900
15300
Received
15300
734
4500
10800
13200
12
No
10800
500
4000
6800
No
6800
20000
308
3750
16250
Received
16250
024
3150
13100
10900
82
No
13100
253
3500
9600
No
9600
315
3750
5850
No
5850
16750
501
4000
12750
11250
50
Received
54
55
56
57
58
59
60
61
62
63
64
12750
615
4250
8500
No
8500
19750
701
4500
15250
Received
15250
487
4000
11250
12750
41
No
11250
717
4500
6750
No
6750
19500
340
3750
15750
Received
15750
969
5200
10550
13450
31
No
10550
581
4250
6300
No
6300
19750
787
4700
15050
Received
15050
625
4250
10800
13200
43
No
10800
690
4500
6300
No
6300
19500
688
4500
15000
Received
15000
288
3750
11250
12750
56
No
11250
997
5200
6050
No
6050
18800
842
4800
14000
Received
14000
502
4000
10000
14000
48
No
10000
730
4500
5500
No
5500
19500
289
3750
15750
Received
15750
394
3900
11850
12150
28
No
11850
028
3150
8700
No
8700
20850
626
4250
16600
Received
16600
730
4500
12100
11900
21
No
12100
202
3500
8600
No
8600
20500
084
3250
17250
Received
17250
414
3900
13350
10650
53
No
13350
270
3750
9600
No
9600
20250
880
4800
15450
Received
15450
128
3450
12000
12000
25
No
12000
222
3500
8500
No
8500
20500
979
5200
15300
Received
15300
105
3450
11850
12150
74
No
11850
236
3500
8350
No
8350
20500
005
3150
17350
Received
17350
428
3900
13450
10550
83
No
65
66
67
68
69
70
71
72
Average
ending
inventory
13450
909
5000
8450
No
8450
232
3500
4950
No
4950
15500
817
4700
10800
13200
17
Received
10800
679
4500
6300
No
6300
19500
501
4000
15500
Received
15500
283
3750
11750
12250
04
No
11750
978
5200
6550
No
6550
18800
644
4250
14550
Received
14550
257
3750
10800
13200
19
No
10800
737
4500
6300
No
6300
19500
130
3450
16050
Received
16050
758
4700
11350
12650
21
No
11350
330
3750
7600
No
7600
20250
338
3750
16500
Received
16500
608
4250
12250
11750
52
No
12250
870
4800
7450
No
7450
19200
410
3900
15300
Received
15300
240
3500
11800
12200
85
No
11800
862
4800
7000
No
7000
316
3750
3250
No
3250
15450
693
4500
10950
13050
99
Received
10950
749
4700
6250
No
6250
213
3500
2750
No
2750
15800
386
3900
11900
12100
82
Received
11775
Avg. order
12225
Avg. daily
demand
Demand=
4087
10526
1.35
6403
Performance of
proposed model =
Shortage=
73.32%