Integrated Production-Inventory Supply Chain Model
Read this article. An integrated production-inventory model is constructed to address supplier, manufacturer, and retailer uncertainties. According to the author, what are the three types of uncertainties in supply chain management?
Numerical example
Crisp environment
The input data of different parameters for Case 1 and Case 2 are shown in Table 1, and the expected optimum value of the total profit is given in Table 2.
Table 1 Input data of different parameters for Case 1 and Case 2
Parameters | c s | c m | c r | c r 1 | h s | h m | T s | p m | n | r | ρ | id s | id m | id r | I e | A s | A m | A r | m | i p | D C | D R |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Case 1 | 7 | 14 | 25 | 35 | 0.15 | 0.8 | 10 | 16 | 4 | 4 | 0.4 | 1 | 2 | 3 | 1 | 25 | 40 | 45 | 20 | 16 | 55 | 100 |
Case 2 | 10 | 12 | 26 | 25 | 0.17 | 0.9 | 12 | 25 | 17 | 5 | 0.3 | 1.5 | 2.5 | 3.5 | 1 | 30 | 28 | 52 | 24 | 45 | 120 | 130 |
Table 2 Optimum results for objective functions and other parameters
Parameter | Case 1 | Case 2 |
---|---|---|
ATP∗ | 1,039.45 | 1,108.93 |
70.49 |
79.23 |
|
T | 2.85 | 1.59 |
APS∗ | 246.51 | 253.56 |
APM∗ | 468.25 | 463.18 |
APR∗ | 321.43 | 390.47 |
Sensitivity analysis
The major contribution of the supply chain is mainly in the inclusion of the manufacturer. We consider product reworking of defective items which are reworked just after regular production, with a different holding cost for good and defective items in the three-layer supply chain. An integrated production-inventory model is presented for the supplier, manufacturer, and retailer supply chain under conditionally permissible delay in payments which has developed in both crisp and uncertain environments (Table 3).Table 3 Optimum value changes due to parametric changes
Uncertain environment
Input
data of different crisp parameters for Case 1 and Case 2 are given in
Table 1; the remaining uncertain parameters are depicted in Table 4.
Optimal values of objective and decision variables are given in Table 5
and graphically represented in Figure 5.
Table 4 Input data of different zigzag parameters for Case 1 and Case 2
Parameters in uncertain environments | ||||
---|---|---|---|---|
Case 1 | L(0.8,1.2,1.4) | L(1.5,2.0,2.5) | L(1.4,2,2.3) | L(0.04,0.06,0.08) |
Case 2 | L(1.4,1.8,2.4) | L(2,2.3,2.9) | L(1.4,2.1,2.5) | L(0.06,0.08,0.1) |
Parameter | Case 1 | Case 2 |
---|---|---|
ATP∗ | 1,056.43 |
1,520.43 |
69.76 |
78.31 |
|
T | 1.75 | 1.76 |
APS∗ | 248.71 | 276.76 |
APM∗ | 463.43 | 467.35 |
APR∗ | 324.43 | 393.73 |
Figure 5 Average profit versus supply rate of suppliers in Case 1 and Case 2.
![](https://learn.saylor.org/pluginfile.php/5619158/mod_book/chapter/50086/02.jpeg)