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Table 3: Problem instances.
H W K
s
R
s
MOQ
Set − 1
1 20 [20,20,20,20] [10,9,8,7] 0
1 20 [20,40,80,150] [10,10,10,10] 0
1 20 [20,40,80,150] [10,9,8,7] 0
1 20 [20,40,80,150] [10,8,7,5] 0
0.5 20 [20,20,20,20] [10,9,8,7] 0
0.5 20 [20,40,80,150] [10,10,10,10] 0
0.5 20 [20,40,80,150] [10,9,8,7] 0
0.5 20 [20,40,80,150] [10,8,7,5] 0
0.1 20 [20,20,20,20] [10,9,8,7] 0
0.1 20 [20,40,80,150] [10,10,10,10] 0
0.1 20 [20,40,80,150] [10,9,8,7] 0
0.1 20 [20,40,80,150] [10,8,7,5] 0
Set − 2
1 30 [20,20,20,20] [10,9,8,7] 0
1 30 [20,20,40,80] [10,10,10,10] 0
1 30 [20,20,40,80] [10,9,8,7] 0
1 30 [20,20,40,80] [10,8,7,5] 0
1 25 [20,20,20,20] [10,9,8,7] 0
1 25 [20,20,40,80] [10,10,10,10] 0
1 25 [20,20,40,80] [10,9,8,7] 0
1 25 [20,20,40,80] [10,8,7,5] 0
1 15 [20,20,20,20] [10,9,8,7] 0
1 15 [20,20,40,80] [10,10,10,10] 0
1 15 [20,20,40,80] [10,9,8,7] 0
1 15 [20,20,40,80] [10,8,7,5] 0
Set − 3
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [0,5,10,15]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [1,6,12,18]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [2,7,14,21]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [3,8,16,24]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [4,9,18,27]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [5,10,20,30]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [6,11,22,33]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [7,12,24,36]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [8,13,26,39]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [9,14,28,42]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [10,15,30,45]
1 20 [40, 40, 40, 40] [10, 9, 8, 7] [11,16,32,48]
Table 4: Comparison of optimal expected costs of common
supplier selection (CS) and dynamic supplier selection (DS)
approaches for input data Set − 1. Backorder cost W = 20,
MOQ = None.
H K
s
R
s
CS DS(Gain %)
1 [20,20,20,20] [10,9,8,7] 1032.0 1032.0(0.0)
1 [20,40,80,150] [10,10,10,10] 1331.8 1331.8(0.0)
1 [20,40,80,150] [10,9,8,7] 1331.8 1330.6(0.1)
1 [20,40,80,150] [10,8,7,5] 1245.3 1242.9(0.2)
0.5 [20,20,20,20] [10,9,8,7] 943.5 943.5(0.0)
0.5 [20,40,80,150] [10,10,10,10] 1244.4 1244.4(0.0)
0.5 [20,40,80,150] [10,9,8,7] 1230.2 1223.2(0.6)
0.5 [20,40,80,150] [10,8,7,5] 1107.4 1090.4(1.5)
0.1 [20,20,20,20] [10,9,8,7] 827.5 827.5(0.0)
0.1 [20,40,80,150] [10,10,10,10] 1130.1 1130.1(0.0)
0.1 [20,40,80,150] [10,9,8,7] 1032.0 1003.5(2.8)
0.1 [20,40,80,150] [10,8,7,5] 825.7 806.0(2.4)
problem has 4 suppliers. Their unit price, fixed or-
der costs are presented in respective result tables. We
also test when minimum order quantity constraint is
also present. The rolling horizon length is set at 20
periods.
Table 5: Comparison of optimal expected costs of common
supplier selection (CS) and dynamic supplier selection (DS)
approaches for input data Set − 2. Inventory holding cost
H = 1, MOQ = None.
W K
s
R
s
CS DS(Gain %)
30 [20,20,20,20] [10,9,8,7] 1049.7 1049.7(0.00)
30 [20,40,80,150] [10,10,10,10] 1352.9 1352.9(0.00)
30 [20,40,80,150] [10,9,8,7] 1352.9 1350.7(0.17)
30 [20,40,80,150] [10,8,7,5] 1265.7 1262.7(0.24)
25 [20,20,20,20] [10,9,8,7] 1041.5 1041.5(0.00)
25 [20,40,80,150] [10,10,10,10] 1343.1 1343.1(0.00)
25 [20,40,80,150] [10,9,8,7] 1343.1 1341.3(0.13)
25 [20,40,80,150] [10,8,7,5] 1257.6 1254.5(0.24)
15 [20,20,20,20] [10,9,8,7] 1018.2 1018.2(0.00)
15 [20,40,80,150] [10,10,10,10] 1314.7 1314.7(0.00)
15 [20,40,80,150] [10,9,8,7] 1314.7 1313.4(0.10)
15 [20,40,80,150] [10,8,7,5] 1228.9 1227.2(0.14)
Table 6: Comparison of optimal expected costs of com-
mon supplier selection (CS) and dynamic supplier selection
(DS) approaches for input data Set − 3. Inventory hold-
ing cost H = 1, backorder cost W = 20, fixed order costs
K
s
= [40, 40, 40, 40], Purchase prices R
s
= [10, 9, 8, 7].
MOQ CS DS Gain (%)
[0, 5, 10, 15] 1152.09 1149.01 0.27
[1, 6, 12, 18] 1156.56 1150.89 0.49
[2, 7, 14, 21] 1163.27 1154.51 0.76
[3, 8, 16, 24] 1172.33 1159.80 1.08
[4, 9, 18, 27] 1194.99 1171.65 1.99
[5, 10, 20, 30] 1209.36 1183.54 2.18
[6, 11, 22, 33] 1222.40 1195.97 2.21
[7, 12, 24, 36] 1264.04 1215.25 4.01
[8, 13, 26, 39] 1288.67 1235.14 4.33
[9, 14, 28, 42] 1304.23 1253.52 4.05
[10, 15, 30, 45] 1310.69 1271.93 3.05
[11, 16, 32, 48] 1317.82 1289.63 2.19
4.2 Results and Discussion
The results are divided into two parts. Tables 4, 5 and
6 present the comparison between the common sup-
plier selection and dynamic supplier selection. When
the suppliers are equivalent in terms of fixed cost or
unit purchase price, both approaches yield equal cost.
Only when suppliers are different in both parameters,
there is a cost difference. The results from Tables 4,
5 show that the cost difference is higher when the
ratio of backorder cost to inventory holding cost is
higher. When the minimum order quantity constraint
is present, even with equal fixed cost for all suppli-
ers, results show a cost different between both ap-
proaches. In each instance, dynamic supplier selec-
tion outperforms common supplier selection. The av-
erage runtime for common supplier selection is 2821
seconds on average.
In the second part, we present the results using our
proposed approximate method in Tables 7, 8 and 9
for the same problem instances. We get major gain in
terms of runtime. The average runtime of our method
is 6 milliseconds. The average error for the problem
ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems
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