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Scheduling parallel machines with single vehicle delivery

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Abstract

We investigate the integrated production and distribution scheduling problem in a supply chain. The manufacturer’s production environment is modeled as a parallel machine system. A single capacitated vehicle is employed to deliver products in batches to multiple customers. The scheduling problem can also be viewed as either parallel machines with delivery considerations or a flexible flowshop. Different inventory holding costs, job sizes (volume or storage space required in the transportation unit), and job priorities are taken into account. Efficient mathematical modeling and near-optimal heuristic approaches are presented for minimizing total weighted completion time.

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References

  • Akyol, D.E., Bayhan, G.M.: Minimizing makespan on identical parallel machines using neural networks. Lect. Notes Comput. Sci. 4234, 553–562 (2006)

    Article  Google Scholar 

  • Albers, S., Brucker, P.: The complexity of one-machine batching problems. Discrete. Appl. Math. 47, 87–107 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  • Azizoglu, M., Webster, S.: Scheduling a batch processing machine with incompatible job families. Comput. Ind. Eng. 39, 325–335 (2001)

    Article  Google Scholar 

  • Behnamian, J., Fatemi Ghomi, S.M.T.: Minimizing makespan on a three-machine flowshop batch scheduling problem with transportation using genetic algorithm. Appl. Soft Comput. 12, 768–777 (2012)

    Article  Google Scholar 

  • Bruno, L., Coffman, E.G., Sethi, J.R.: Scheduling independent tasks to reduce mean finishing time. Commun. ACM. 17, 382–387 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  • Cakici, E., Mason, S.J., Fowler, J.W., Geismar, H.N.: Batch scheduling on parallel machines with dynamic job arrivals and incompatible job families. Int. J. Prod. Res. 51, 2462–2477 (2013)

    Article  Google Scholar 

  • Chang, Y.C., Lee, C.Y.: Machine scheduling with job delivery coordination. Eur. J. Oper. Res. 158, 470–487 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, B., Lee, C.: Logistics scheduling with batching and transportation. Eur. J. Oper. Res. 187, 871–876 (2008)

    Article  MathSciNet  Google Scholar 

  • Chen, Z.L., Hall, N.G.: Supply chain scheduling: conflict and cooperation in assembly systems. Oper. Res. 55, 1072–1089 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, Z.L., Vairaktarakis, G.L.: Integrated scheduling of production and distribution operations. Manag. Sci. 51, 614–628 (2005)

    Article  MATH  Google Scholar 

  • Dawande, M., Geismar, H.N., Hall, N.G., Sriskandarajah, C.: Supply chain scheduling: distribution systems. Prod. Oper. Manag. 15, 243–261 (2006)

    Article  Google Scholar 

  • Dobson, G., Nambimadom, R.S.: The batch loading and scheduling problem. Oper. Res. 49, 52–65 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Geismar, H.N., Laporte, G., Lei, L., Sriskandarajah, C.: The integrated production and transportation scheduling problem for a product with a short lifespan. INFORMS J. Comput. 20, 21–33 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Gonga, H., Tanga, L., Duinb, C.W.: A two stage flowshop scheduling problem on a batching machine and a discrete machine with blocking and shared setup times. Comput. Oper. Res. 37, 960–969 (2010)

  • Graham, R.L., Lawler, E.L., Lenstra, J.K.: Optimization and approximation in deterministic machine scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, N.G., Posner, M.E.: Performance prediction and pre-selection for optimization and heuristic solution procedures. Oper. Res. 55, 703–716 (2007)

    Article  MATH  Google Scholar 

  • Hall, N.G., Potts, C.N.: Supply chain scheduling: batching and delivery. Oper. Res. 51, 566–584 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, N.G., Potts, C.N.: The coordination of scheduling and batch deliveries. Ann. Oper. Res. 135, 41–64 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Hoogeveen, H.: Multi-criteria scheduling — invited review. Eur. J. Oper. 167, 592–623 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Hopp, W., Spearman, M.: Factory Physics. McGraw Hill, New York (2000)

    Google Scholar 

  • Ji, M., He, Y., Cheng, T.C.E.: Batch delivery scheduling with batch delivery cost on a single machine. Eur. J. Oper. Res. 176, 745–755 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Kyparisis, G.J., Koulamas, C.: A note on weighted completion time minimization in a flexible flow shop. Oper. Res. Lett. 29, 5–11 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Koh, S.G., Koo, P.H., Kim, D.C., Hur, W.S.: Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families. Int. J. Prod. Econ. 98, 81–96 (2005)

    Article  Google Scholar 

  • Lee, C.Y., Chen, Z.L.: Machine scheduling with transportation considerations. J. sched. 4, 3–24 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Lei, D., Wang, T.: An effective neighborhood search algorithm for scheduling a flowshop of batch processing machines. Comput. Ind. Eng. 61, 739–743 (2011)

    Article  Google Scholar 

  • Lenstra, J.K., Rinnooy Kan, A.H.G., Brucker, P.: Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362 (1977)

    Article  MathSciNet  Google Scholar 

  • Li, C.L., Vairaktarakis, G.L., Lee, C.Y.: Machine scheduling with deliveries to multiple customer locations. Eur. J. Oper. Res. 164, 39–51 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Mazdeh, M.M., Sarhadi, M., Hindi, K.S.: A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs. Eur. J. Oper. Res. 183, 74–86 (2007)

    Article  MATH  Google Scholar 

  • Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1998)

    Google Scholar 

  • Naderi, B., Khalili, M., Taghavifard, M.T., Roshanaei, V.: A variable neighborhood search for hybrid flexible flowshops with setup times minimizing total completion time. J. Appl. Sci. 8, 2843–2850 (2008)

    Article  Google Scholar 

  • Potts, C.N., Kovalyov, M.Y.: Scheduling with batching: A review. Eur. J. Oper. Res. 120, 228–249 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Qi, X.: A logistics scheduling model: inventory cost reduction by batching. Naval Res. Logist. 52, 312–320 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Selvarajah, E., Zhang, R.: Supply chain scheduling at the manufacturer to minimize inventory holding and delivery costs. Int. J. Prod. Econ. 147(Part A), 17–124 (2014)

    Google Scholar 

  • Simchi-Levi, D., Kaminski, P., Simchi-Levi, E.: Designing and Managing the Supply Chain. McGraw Hill, New York (2003)

    Google Scholar 

  • Tang, L., Liu, P.: Flowshop scheduling problems with transportation or deterioration between the batching and single machines. Comput. Ind. Eng. 56, 1289–1295 (2009)

    Article  Google Scholar 

  • Uzsoy, R.: Scheduling a single batch processing machine with non-identical job sizes. Int. J. Prod. Res. 32, 1615–1635 (1994)

    Article  MATH  Google Scholar 

  • Uzsoy, R.: Scheduling batch processing machines with incompatible job families. Int. J. Prod. Res. 33, 2685–2708 (1995)

    Article  MATH  Google Scholar 

  • Van Buer, M.G., Woodruff, D.L., Olson, R.T.: Solving the medium newspaper production/distribution problem. Eur. J. Oper. Res. 115, 237–253 (1999)

  • Wang, G., Cheng, T.C.E.: Parallel machine scheduling with batch delivery costs. Int. J. Prod. Econ. 68, 177–183 (2000)

    Article  Google Scholar 

  • Wolsey, L.A.: Integer Programming. Wiley, New York (1998)

    MATH  Google Scholar 

  • Zhong, W., Dosa, G., Tan, Z.: On the machine scheduling problem with job delivery coordination. Eur. J. Oper. Res. 182, 1057–1072 (2007)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. IBM, Istanbul, Turkey

    Eray Cakici

  2. Department of Industrial Engineering, Clemson University, Clemson, SC, USA

    Scott J. Mason

  3. Department of Information and Operations Management, Mays Business School, Texas A&M University, College Station, TX, USA

    H. Neil Geismar

  4. Department of Supply Chain Management, Arizona State University, Phoenix, AZ, USA

    John W. Fowler

Authors
  1. Eray Cakici
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  2. Scott J. Mason
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  3. H. Neil Geismar
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  4. John W. Fowler
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Corresponding author

Correspondence to Eray Cakici.

Appendices

Appendix 1

See Tables 7 and 8.

Table 7 95 % Confidence intervals of performance ratios for batch assignment rules (in heuristics without local search)
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Table 8 95 % Confidence intervals of performance ratios for batch sequencing rules (in heuristics without local search)
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Appendix 2

See Tables 9 and 10

Table 9 Heuristic worst performance ratios without local search
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Table 10 Heuristic worst performance ratios with local search
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Cakici, E., Mason, S.J., Geismar, H.N. et al. Scheduling parallel machines with single vehicle delivery. J Heuristics 20, 511–537 (2014). https://doi.org/10.1007/s10732-014-9249-y

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  • DOI: https://doi.org/10.1007/s10732-014-9249-y

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