Assessing the Cost Impact of Multiple Transportation Modes to Enhance Sustainability in an Integrated, Two Stage, Automotive Supply Chain
Abstract
:1. Introduction
2. Literature Review
3. Methodology
3.1. Integer Linear Programming Model
I | set of machines, indexed by i |
J | set of cranes, indexed by j |
P | set of part types, indexed by p |
W | set of distribution centers, indexed by w |
T | set of time periods, indexed by t |
R | set of transportation modes, indexed by r |
Dt, p, w | demand by distribution center w of part type p in time period t (parts) |
unit production time (cycle time) of part type p (mins) | |
F | length of time period (mins) |
Si, p, p’ | changeover time from part type to part type on machine i (mins) |
Ep | maximum quantity of parts per unit load of part type p (parts/unit load) |
K | plant finished part warehouse capacity (unit loads) |
G | vehicle capacity (unit loads) |
Hp | unit inventory holding cost of part type p ($/part/period) |
Lr, w | cost of one trip from plant to distribution center w via transportation mode r ($/trip) |
Mi | cost of downtime on machine i ($/min) |
Np | cost of outsourcing of part type p ($/part) |
Ai, p | equals one if machine i is compatible with part type p, 0 otherwise |
Bj, i | equals one if crane j can serve setup on machine i, 0 otherwise |
Cp, p’ | equals one if setup from part type to part type requires a crane, 0 otherwise |
duration (time periods) of trip to distribution center w via transportation mode r | |
lead time multiple |
quantity of part type p transported to distribution center w in time period t via transportation mode r | ||
number of trips to distribution center w via transportation mode r in time period t | ||
quantity of finished part inventory of part type p in time period t | ||
quantity of part type p processed on machine i in time period t | ||
quantity of outsourcing of part type p demanded by distribution center w in time period t | ||
equals one if machine i processes part type p in time period t, 0 otherwise | ||
equals one if machine i changes over from part type to part type in time period t, 0 otherwise | ||
equals one if crane j serves setup on machine i in time period t, 0 otherwise | ||
(1) | ||
subject to | ||
tT, rR, wW | (2) | |
t = 1..-1, pP, r = 1, wW | (3) | |
t = ..|T|, pP, wW | (4) | |
tT | (5) | |
t = 1, pP | (6) | |
tT, pP, t | (7) | |
t = 1, iI, pP | (8) | |
tT, iI, pP, t | (9) | |
tT, iI, pP, P, t | (10) | |
tT, iI, pP | (11) | |
tT, iI | (12) | |
tT, iI, t | (13) | |
tT, jJ, iI, t | (14) | |
tT, jJ, t | (15) | |
tT, iI, t | (16) | |
and integer | , pP, wW, tT | (17) |
, , | iI,
jJ,
pP, p’P, tT | (18) |
3.2. Hybrid Simulated Annealing Algorithm
3.3. Experimentation Strategy
4. Results and Discussion
5. Conclusions and Future Research
Author Contributions
Conflicts of Interest
References
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Instance Set | Part Type (Machine) Mix | Number of Part Types (|P|) | Number of Machines (|I|) | Number of Cranes (|J|) | Number of Time Periods (|T|) | Number of DCs (|W|) |
---|---|---|---|---|---|---|
1 (large) | 2 | 25 | 10 | 5 | 16 | 3 |
2 (small) | 1 | 5 | 5 | 5 | 16 | 3 |
3 (medium) | 0 | 25 | 5 | 3 | 16 | 1 |
Part Type (Machine) Mix | Small (%) | Medium (%) | Large (%) |
---|---|---|---|
Mi× 0 | 60 | 20 | 20 |
Mi× 1 | 20 | 60 | 20 |
Mi×2 | 20 | 20 | 60 |
Parameters | Values |
---|---|
Si,p,p’ | 15, 30, 40, 45, 55 |
Small: DU [10, 45], Medium: DU [46, 80], Large: DU [81, 120] | |
Np | Small: DU [10, 40], Medium: DU [41, 70], Large: DU [71, 100] |
Hp | Small: DU [1, 4], Medium: DU [5, 7], Large: DU [8, 10] |
Ep | Small: DU [201, 5000], Medium: DU [51, 200], Large: DU [10, 50] |
Mi | Small: DU [10, 40], Medium: DU [41, 70], Large: DU [71, 100] |
K | 7|I| |
G | 10 |
Lw | DC1: 100, DC2: 300, DC3: 500 |
F | 6 |
S (mins) | Tool Change | Color Change |
---|---|---|
Small machine | 40 | 15 |
Medium machine | 45 | 30 |
Large machine | 55 | 45 |
Parameter | Assumptions |
---|---|
Dt, p, w |
|
Ai, p |
|
Bj, i |
|
Cp, p’ |
|
Cost Multiples | Time Multiples | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
0.1 | 562.5 | 468.3 | 427.6 | 415.1 | 418.0 | 431.9 | 450.9 |
0.3 | 566.5 | 470.8 | 428.7 | 417.8 | 419.9 | 434.8 | 460.1 |
0.5 | 572.1 | 474.3 | 431.2 | 419.8 | 421.3 | 434.9 | 461.7 |
0.7 | 575.2 | 475.7 | 433.8 | 422.8 | 422.8 | 438.4 | 463.5 |
0.9 | 579.4 | 478.3 | 440.6 | 428.1 | 423.9 | 448.1 | 465.3 |
Cost Multiples | Time Multiples | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
0.1 | 81.1 | 61.3 | 54.9 | 54.2 | 59.1 | 63.4 | 70.2 |
0.3 | 84.0 | 64.3 | 56.3 | 56.5 | 61.5 | 66.0 | 70.3 |
0.5 | 86.9 | 65.9 | 58.4 | 60.3 | 62.6 | 66.8 | 70.4 |
0.7 | 89.8 | 69.7 | 58.9 | 61.5 | 66.3 | 68.7 | 71.1 |
0.9 | 92.7 | 72.5 | 62.5 | 62.6 | 68.3 | 70.5 | 71.4 |
Cost Multiples | Time Multiples | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
0.1 | 296.4 | 254.9 | 234.4 | 227.3 | 226.6 | 231.9 | 239.8 |
0.3 | 296.7 | 255.2 | 234.7 | 227.5 | 226.9 | 232.1 | 240.0 |
0.5 | 297.1 | 255.5 | 235.0 | 227.8 | 227.1 | 232.4 | 240.2 |
0.7 | 297.4 | 255.8 | 235.3 | 228.1 | 227.4 | 232.8 | 240.4 |
0.9 | 297.7 | 256.1 | 235.5 | 228.3 | 227.6 | 232.8 | 240.6 |
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Masoud, S.A.; Mason, S.J. Assessing the Cost Impact of Multiple Transportation Modes to Enhance Sustainability in an Integrated, Two Stage, Automotive Supply Chain. Informatics 2017, 4, 34. https://doi.org/10.3390/informatics4040034
Masoud SA, Mason SJ. Assessing the Cost Impact of Multiple Transportation Modes to Enhance Sustainability in an Integrated, Two Stage, Automotive Supply Chain. Informatics. 2017; 4(4):34. https://doi.org/10.3390/informatics4040034
Chicago/Turabian StyleMasoud, Sherif A., and Scott J. Mason. 2017. "Assessing the Cost Impact of Multiple Transportation Modes to Enhance Sustainability in an Integrated, Two Stage, Automotive Supply Chain" Informatics 4, no. 4: 34. https://doi.org/10.3390/informatics4040034