Imperfect Reworking Process Consideration in Integrated Inventory Model under Permissible Delay in Payments
Table 1
Optimal solutions for various values of permissible delay period
.
(day)
Profit ($/yr)
(day)
Vendor
Buyer
Joint
0
10
β
p2 =
8.6191
L2 =
65.9521
3951.9107
714.0734
7140.7344
6542.7743
15639.3831
22182.1574
5
10
0.2313
p2 =
8.6097
L2 =
65.8780
3958.3844
714.4393
7144.3930
6546.5177
15648.1525
22194.6702
10
10
0.5903
p2 =
8.6007
L2 =
65.7660
3964.5993
714.3443
7143.4434
6549.8114
15658.0354
22207.8468
15
10
1.0290
p2 =
8.5920
L2 =
65.6157
3970.6225
713.7949
7137.9488
6552.7706
15668.9163
22221.6869
20
10
1.5361
p2 =
8.5837
L2 =
65.4278
3976.3830
712.7838
7127.8381
6555.2744
15680.9170
22236.1914
25
10
2.1074
p2 =
8.5758
L2 =
65.2024
3981.8788
711.3094
7113.0936
6557.3194
15694.0429
22251.3623
30
10
2.7421
p2 =
8.5683
L2 =
64.9392
3987.1080
709.3688
7093.6881
6558.9020
15708.3011
22267.2031
40
10
4.2066
p2 =
8.5545
L2 =
64.2988
3996.7599
704.0736
7040.7364
6560.6634
15740.2516
22300.9150
41
10
4.3680
p2 =
8.5532
L2 =
64.2263
3997.6711
703.4398
7034.3977
6560.7450
15743.6916
22304.4366
42
10
4.5321
p2 =
8.5519
L2 =
64.1521
3998.5827
702.7877
7027.8768
6560.8266
15747.1593
22307.9859
43
10
4.6991
p2 =
8.5506
L2 =
64.0763
3999.4946
702.1173
7021.1732
6560.9080
15750.6547
22311.5627
44
10
4.8689
p2 =
8.5494
L2 =
63.9994
4000.3367
701.4221
7014.2213
6560.8706(b)
15754.2967
22315.1673
45
10
5.0417
p2 =
8.5482
L2 =
63.9208
4001.1791
700.7085
7007.0854
6560.8330
15757.9668
22318.7998
50
10
5.9502
p2 =
8.5424
L2 =
63.5041
4005.2548
696.8497
6968.4967
6560.4028
15776.9794
22337.3822
60
11
8.4755
p2 =
8.5341
L2 =
60.2724
4011.0993
662.3522
7285.8737
6556.3448
15820.4483
22376.7931
70
11
11.0359
p1 =
8.5309
L1 =
60.2343
4013.3564
662.3060(a)
7285.3655
6545.3169
15872.9112
22418.2281
80
11
14.0380
p1 =
8.5280
L1 =
60.2221
4015.4037
662.5092
7287.6008
6533.9086
15925.7575
22459.6661
90
11
17.5552
p1 =
8.5250
L1 =
60.2094
4017.5234
662.7195
7289.9147
6522.6064
15978.4997
22501.1061
(a) When 0 < m β€ 70, the optimal order quantity is negatively
correlated to the length of the permissible delay period m. (b) When m <
44, the vendorβs expected total annual profit is positively correlated to the
length of the permissible delay period m but as m β₯ 44, it is reverse.