The Economic Lot Scheduling Problem in Flow Lines with Sequence-Dependent Setups
The problem of lot sizing, sequencing and scheduling
multiple products in flow line production systems has been studied
by several authors. Almost all of the researches in this area assumed
that setup times and costs are sequence –independent even though
sequence dependent setups are common in practice. In this paper we
present a new mixed integer non linear program (MINLP) and a
heuristic method to solve the problem in sequence dependent case.
Furthermore, a genetic algorithm has been developed which applies
this constructive heuristic to generate initial population. These two
proposed solution methods are compared on randomly generated
problems. Computational results show a clear superiority of our
proposed GA for majority of the test problems.
[1] T. Batch, Selective Pressure in Evolutionary Algorithms. IEEE press1,
NJ, 57-62(1994).
[2] E.A. Bomberger, Dynamic programming approach to a lot size
scheduling problem. Management science. 12:778-784 (1996).
[3] G. Dobson, The ELSP: Achieving feasibility using time-varing lot sizes.
Operations research. 35:764-771 (1987).
[4] W.C. Driscoel, H. Emmoss, Scheduling production on the one machine
with change over costs. AIIE Transactions. 9:388-395 (1977)
[5] S. Fujita, The application of marginal analysis to the ELSP.
AIIETransactrion. 10:354-361 (1978).
[6] G. Gallego, D.X. Show, Complexity of the ELSP with general cyclic
schedules. IEEE Transactions. 29:109-113 (1997).
[7] A.M. Geoffrion, G.W. Graves, Scheduling parallel production lines with
change over costs. Operations Research. 24:595-610 (1976).
[8] O.H. Hong-Choon, I.A. Karimi, Planning production on a single
processor with sequence dependent setups: part1, computer and chemical
enginnering. 5:1021-1030 (2001).
[9] O.H. Hong-Choon, I. Karimi, A planning production on a single
processor with sequence dependent setups: part2, Computer and
chemical enginnering. 25:1031-1043 (2001).
[10] S.A. Irani, U. Gunasena, Single machine setup dependent sequencing
using a setup complexity ranking scheme. Journal of manufacturing
systems. 7:11-23 (1988)
[11] B. Karimi, S.M.T. Fatemi Ghomi, J.M. Wilson, The capacitated lot
sizing problem: a review of models and algorithms. Omega. 31:365-378
(2003)
[12] W.L. Maxwell, The scheduling of economic lot sizes. Navel Research
logistics Quartery.11:89-124 (1964).
[13] J. Ouenniche, The impact of sequencing decisions on multi-item lot
sizing and scheduling in flowshops. International Journal of operational
research. 37: 2253-2270 (1999).
[14] P.W. Poon, J.N. Carter, Genetic algorithm crossover operators for
ordering applications. Computers and Operations Research. 22:135-147
(1995).
[15] J. Roger, A computational approach to the economic lot scheduling
problem. Journal of Management Science. 4: 264-291 (1958).
[16] R. Ruis, C. Maroto, Solving the flowshop scheduling problem with
sequence dependent setup times using advanced metaheuristic. European
Journal of Operational Research. Article in press (2004).
[17] H. Singh, J.B. Foster, Production scheduling with sequence dependent
setup costs. IEE Transaction. 19:43-49 (1987).
[18] G. Taylor, M. Taha, A heuristic model for the sequence-dependent lot
scheduling problem. Production planning and control. Vol8. 3: 213-
225(1997).
[19] S.A. Torabi, S.M.T. Fatemi Ghomi, B. Karimi, A hybrid genetic
algorithm for the finite horizon economic lot and delivery scheduling in
supply chain. European journal of operational research. Article in press
(2005).
[20] S.A. Torabi, B. Karimi, S.M.T. Fatemi Ghomi, The common cycle
economic lot scheduling in flexible job shops: the finite horizon case.
International Journal of Production Economics. 97: 52-65 (2004).
[21] J. Wagner, J. Davis, A search heuristic for the sequence-dependent
economic lot scheduling problem. European Journal of Operational
Research. 141:133-146 (2001).
[1] T. Batch, Selective Pressure in Evolutionary Algorithms. IEEE press1,
NJ, 57-62(1994).
[2] E.A. Bomberger, Dynamic programming approach to a lot size
scheduling problem. Management science. 12:778-784 (1996).
[3] G. Dobson, The ELSP: Achieving feasibility using time-varing lot sizes.
Operations research. 35:764-771 (1987).
[4] W.C. Driscoel, H. Emmoss, Scheduling production on the one machine
with change over costs. AIIE Transactions. 9:388-395 (1977)
[5] S. Fujita, The application of marginal analysis to the ELSP.
AIIETransactrion. 10:354-361 (1978).
[6] G. Gallego, D.X. Show, Complexity of the ELSP with general cyclic
schedules. IEEE Transactions. 29:109-113 (1997).
[7] A.M. Geoffrion, G.W. Graves, Scheduling parallel production lines with
change over costs. Operations Research. 24:595-610 (1976).
[8] O.H. Hong-Choon, I.A. Karimi, Planning production on a single
processor with sequence dependent setups: part1, computer and chemical
enginnering. 5:1021-1030 (2001).
[9] O.H. Hong-Choon, I. Karimi, A planning production on a single
processor with sequence dependent setups: part2, Computer and
chemical enginnering. 25:1031-1043 (2001).
[10] S.A. Irani, U. Gunasena, Single machine setup dependent sequencing
using a setup complexity ranking scheme. Journal of manufacturing
systems. 7:11-23 (1988)
[11] B. Karimi, S.M.T. Fatemi Ghomi, J.M. Wilson, The capacitated lot
sizing problem: a review of models and algorithms. Omega. 31:365-378
(2003)
[12] W.L. Maxwell, The scheduling of economic lot sizes. Navel Research
logistics Quartery.11:89-124 (1964).
[13] J. Ouenniche, The impact of sequencing decisions on multi-item lot
sizing and scheduling in flowshops. International Journal of operational
research. 37: 2253-2270 (1999).
[14] P.W. Poon, J.N. Carter, Genetic algorithm crossover operators for
ordering applications. Computers and Operations Research. 22:135-147
(1995).
[15] J. Roger, A computational approach to the economic lot scheduling
problem. Journal of Management Science. 4: 264-291 (1958).
[16] R. Ruis, C. Maroto, Solving the flowshop scheduling problem with
sequence dependent setup times using advanced metaheuristic. European
Journal of Operational Research. Article in press (2004).
[17] H. Singh, J.B. Foster, Production scheduling with sequence dependent
setup costs. IEE Transaction. 19:43-49 (1987).
[18] G. Taylor, M. Taha, A heuristic model for the sequence-dependent lot
scheduling problem. Production planning and control. Vol8. 3: 213-
225(1997).
[19] S.A. Torabi, S.M.T. Fatemi Ghomi, B. Karimi, A hybrid genetic
algorithm for the finite horizon economic lot and delivery scheduling in
supply chain. European journal of operational research. Article in press
(2005).
[20] S.A. Torabi, B. Karimi, S.M.T. Fatemi Ghomi, The common cycle
economic lot scheduling in flexible job shops: the finite horizon case.
International Journal of Production Economics. 97: 52-65 (2004).
[21] J. Wagner, J. Davis, A search heuristic for the sequence-dependent
economic lot scheduling problem. European Journal of Operational
Research. 141:133-146 (2001).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:63465", author = "M. Heydari and S. A. Torabi", title = "The Economic Lot Scheduling Problem in Flow Lines with Sequence-Dependent Setups", abstract = "The problem of lot sizing, sequencing and scheduling
multiple products in flow line production systems has been studied
by several authors. Almost all of the researches in this area assumed
that setup times and costs are sequence –independent even though
sequence dependent setups are common in practice. In this paper we
present a new mixed integer non linear program (MINLP) and a
heuristic method to solve the problem in sequence dependent case.
Furthermore, a genetic algorithm has been developed which applies
this constructive heuristic to generate initial population. These two
proposed solution methods are compared on randomly generated
problems. Computational results show a clear superiority of our
proposed GA for majority of the test problems.", keywords = "Economic lot scheduling problem, finite horizon,
genetic algorithm, mixed zero-one nonlinear programming,
sequence-dependent.", volume = "2", number = "11", pages = "1267-8", }
