A Joint Scheduling of Production and Distribution Operations in a Flow Shop Manufacturing System

Document Type : Article

Authors

1 Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran

2 Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran.

Abstract

In traditional scheduling problems and in many real-world applications the production operations are scheduled regardless of distribution decisions. Indeed, the completion time of a job in such problems is traditionally defined as the time when the production sequences of a job are finished. However, in many practical environments completed orders are delivered to customers immediately after production stages without any further inventory storage. Therefore, in this paper, we investigate an integrated scheduling model of production and distribution problems simultaneously. It is assumed that products are proceed through a permutation flow shop scheduling manufacturing system and delivered to customers via available vehicles. The objective in our integrated model is to minimize maximum returning time (MRT), which is the time that last vehicle delivers last order to relevant customer and returns to production center. The problem formulated mathematically, and then an improved imperialist competitive algorithm (I-ICA) is proposed for solving it. Furthermore, sufficient numbers of test problems are generated for computational study. Various parameters of the algorithm are analyzed to calibrate the algorithm by means of the Taguchi method. At the end, the effectiveness of the proposed model and suggested algorithm is evaluated through a computational study where obtained results show the appropriate performance of integrated model and solving approach with regard to the other algorithms.

Keywords

Main Subjects


References

1. Chang, Y.C. and Lee, C.Y. Machine scheduling with job delivery coordination", European Journal of Operational Research, 158, pp. 470-487 (2004).
2. Potts, C.N. Analysis of a heuristic for one machine sequencing with release dates and delivery times", Operations Research, 28, pp. 1436-1441 (1980).
3. Hall, L.A. and Shmoys, B. Jackson's rule for singlemachine
scheduling: Making a good heuristic better",
Mathematics of Operations Research, 17, pp. 22-35
(1992).
4. Matsuo, H. The weighted total tardiness problem
with xed shipping times and overtime utilization",
Operations Research, 36, pp. 293-307 (1988).
5. Herrmann, J.W. and Lee, C.Y. On scheduling to minimize
earliness-tardiness and batch delivery costs with
a common due date", European Journal of Operational
Research, 70, pp. 272-288 (1993).
6. Yuan, J. A note on the complexity of singlemachine
scheduling with a common due date, earlinesstardiness,
and batch delivery costs", European Journal
of Operational Research, 94, pp. 203-205 (1996).
7. Chen, Z.L. Scheduling and common due date assignment
with earliness-tardiness penalties and batch
delivery costs", European Journal of Operational Research,
93, pp. 49-60 (1996).
8. Cheng, T.C.E., Gordon, V.S., and Kovalyov, M.Y.
Single machine scheduling with batch deliveries",
European Journal of Operational Research, 94, pp.
277-283 (1996).
9. Yang, X. Scheduling with generalized batch delivery
dates and earliness penalties", IIE Transactions, 32,
pp. 735-741 (2000).
10. Hall, N.G., Lesaoana, M.A., and Potts, C.N. Scheduling
with xed delivery dates", Operations Research,
49, pp. 134-144 (2001).
11. Hall, N.G. and Potts, C.N. Supply chain scheduling:
Batching and delivery", Working Paper, Department
of Management Sciences, The Ohio State University,
Columbus, OH (2000).
12. Lee, C.Y. and Chen, Z.L. Machine scheduling with
transportation considerations", Journal of Scheduling,
4, pp. 3-24 (2001).
13. Hall, N.G. and Potts, C.N. Supply chain scheduling:
batching and delivery", Operations Research, 51, pp.
566-584 (2003).
14. Garcia, J.M., Lozano, S., and Canca, D. Coordinated
scheduling of production and delivery from multiple
plants", Robotics and Computer-Integrated Manufacturing,
20, pp. 191-198 (2004).
15. Li, C.L., Vairaktarakis, G., and Lee, C.Y. Machine
scheduling with deliveries to multiple customer locations",
European Journal of Operational Research,
164, pp. 39-51 (2005).
16. He, Y., Zhong, W., and Gu, H. Improved algorithms
for two single machine scheduling problems", Theoretical
Computer Science, 363, pp. 257-265 (2006).
17. Zhong, W.Y., Dosa, G., and Tan, Z.Y. On the
machine scheduling problem with job delivery coordination",
European Journal of Operational Research,
182, pp. 1057-1072 (2007).
18. Su, C.Sh., Pan, J.C.H., and Hsu, T.S. A new heuristic
algorithm for the machine scheduling problem with job
delivery coordination", Theoretical Computer Science,
410, pp. 2581-2591 (2009).
19. Li, C.L. and Vairaktarakis, G.L. Coordinating production
and distribution of jobs with bundling operations",
IIE Transactions, 39, pp. 203-215 (2007).
20. Wang, X.L. and Cheng, T.C.E. Machine scheduling
with an availability constraint and job delivery coordination",
Naval Research Logistics, 54, pp. 11-20
(2007).
21. Chen, B. and Lee, C.Y. Logistics scheduling with
batching and transportation", European Journal of
Operational Research, 189, pp. 871-876 (2008).
22. Lu, L., Yuang, J., and Zhang, L. Single machine
scheduling with release dates and job delivery to minimize
the makespan", Theoretical Computer Science,
393, pp. 102-108 (2008).
23. Liu, P. and Lu, X. An improved approximation
algorithm for single machine scheduling with job delivery",
Theoretical Computer Science, 412, pp. 270-274
(2011).
24. Woeginger, G.J. Heuristics for parallel machine
scheduling with delivery times", Acta Informatica, 31,
pp. 503-512 (1994).
S. Mohammadi et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 911{930 929
25. Wang, G. and Cheng, T.C.E. Parallel machine
scheduling with batch delivery costs", International
Journal of Production Economics, 68, pp. 177-183
(2000).
26. Hall, N.G. and Potts, C.N. The coordination of
scheduling and batch deliveries", Annals of Operations
Research, 135, pp. 41-64 (2005).
27. Chen, Z.L. and Vairaktarakis, G.L. Integrated
scheduling of production and distribution operations",
Management Science, 51, pp. 614-628 (2005).
28. Ullrich, C.A. Integrated machine scheduling and vehicle
routing with time windows", European Journal of
Operational Research, 227, pp. 152-165 (2013).
29. Wan, L. and Zhang, A. Coordinated scheduling on
parallel machines with batch delivery", International
Journal of Production Economics, 150, pp. 199-203
(2014).
30. Lee, I.S. A coordinated scheduling of production-anddelivery
under dynamic delivery cost environments",
Computers & Industrial Engineering, 81, pp. 22-25
(2015).
31. Lu, L., Zhang, L., and Wan, L. Integrated production
and delivery scheduling on a serial batch machine
to minimize the makespan", Theoretical Computer
Science, 572, pp. 50-57 (2015).
32. Yuan, J., Soukhal, A., Chen, Y., and Lu, L. A
note on the complexity of
ow shop scheduling with
transportation constraints", European Journal of Operational
Research, 178, pp. 918-925 (2007).
33. Pan, J.C.H.,Wu, C.L., Huang, H.C., and Su, C.S. Coordinating
scheduling with batch deliveries in a twomachine

ow shop", International Journal of Advanced
Manufacturing Technology, 40, pp. 607-616 (2009).
34. Soukhal, A., Oulamara, A., and Martineau, P. Complexity
of
ow shop scheduling problems with transportation
constraints", European Journal of Operational
Research, 161, pp. 32-41 (2005).
35. Atashpaz, G.E. and Lucas, C. Imperialist competitive
algorithm: an algorithm for optimization inspired by
imperialistic competition", IEEE Congress, pp. 4661-
4667 (2007).
36. Seidgar, H., Kiani, M., Abedi, M., and Fazlollahtabar,
H. An ecient imperialist competitive algorithm for
scheduling in the two-stage assembly
ow shop problem",
International Journal of Production Research,
52, pp. 1240-1256 (2014).
37. Rabiee, M., Zandieh, M., and Jafarian, A. Scheduling
of a no-wait two-machine
ow shop with sequencedependent
setup times and probable rework using
robust meta-heuristics", International Journal of Production
Research, 50, pp. 7428-7446 (2012).
38. Behnamian, J. and Zandieh. M. A discrete colonial
competitive algorithm for hybrid
owshop scheduling
to minimize earliness and quadratic tardiness penalties",
Expert Systems with Applications, 38, pp. 14490-
14498 (2011).
39. Shokrollahpour, E., Zandieh, M., and Dorri, B. A
novel imperialist competitive algorithm for bi-criteria
scheduling of the assembly
owshop problem", International
Journal of Production Research, 49, pp. 3087-
3103 (2011).
40. Attar, S.F., Mohammadi, M., and Tavakkoli-
Moghaddam, R. A novel imperialist competitive algorithm
to solve
exible
ow shop scheduling problem
in order to minimize maximum completion time",
International Journal of Computer Applications, 28,
pp. 27-32 (2011).
41. Karimi, N., Zandieh, M., and Naja , A.A. Group
scheduling in
exible
ow shops: a hybridised
approach of imperialist competitive algorithm and
electromagnetic-like mechanism", International Journal
of Production Research, 49, pp. 4965-4977 (2011).
42. Javadian, N., Rezaeian, J., Khorshidian, H., and
Rahmani, K. Single machine preemptive scheduling
by hybridized meta-heuristic approach", IEEE, pp.
750-753 (2011).
43. Carlier, J. Ordonnancements a contraintes disjonctives",
Recherche Perationelle/Operations Research,
12, pp. 333-351 (1978).
44. Reeves, C.R. A genetic algorithm for
ow shop
sequencing", Computers & Operations Research, 22,
pp. 5-11 (1995).
45. Taillard, E. Benchmarks for basic scheduling problems",
European Journal of Operational Research, 64,
pp. 278-285 (1993).
46. Montgomery, D.C., Design and Analysis of Experiments,
5th ed., Wiley, New York (2000).
47. Naderi, B., Zandieh, M., and Fatemi-Ghomi, S.M.T.
Scheduling job shop problems with sequence dependent
setup times", International Journal of Production
Research, 47, pp. 5959-5976 (2009).
48. Taguchi, G. Introduction to quality engineering",
White Plains, Asian Productivity Organization/
UNIPUB (2000).
49. Qian, B., Wang, L., Hu, R., Wang, W.L., Huang, D.X.,
and Wang, X. A hybrid di erential evolution method
for permutation
ow-shop scheduling", International
Journal of Advanced Manufacturing Technology, 38,
pp. 757-777 (2008).
50. Nawaz, M., Enscore, J.E., and Ham, I. A heuristic algorithm
for the m-machine, n-job
owshop sequencing
problem", OMEGA, 11, pp. 91-95 (1983).
51. Mokhtari, H., Kamal-Abadi, I.N., and Cheraghalikhani,
A. A multi-objective
ow shop scheduling
with resource-dependent processing times: trade-o
between makespan and cost of resources", International
Journal of Production Research, 49(19), pp.
5851-5875 (2010).
52. Campbell, H.G., Dudek, R.A., and Smith, M.L. A
heuristic algorithm for the n job, m machine sequencing
problem", Management Science, 16(10), pp. 630-
637 (1970).