Advertisement

TOP

, Volume 26, Issue 1, pp 30–67 | Cite as

Optimization model for a production, inventory, distribution and routing problem in small furniture companies

  • Pedro L. Miranda
  • Reinaldo Morabito
  • Deisemara Ferreira
Original Paper

Abstract

Production and distribution are two key decisions in supply chain planning. In order to achieve an effective operational performance, it is important for these two decisions to be integrated, especially in supply chains with low inventory levels. In this paper, we propose a mixed integer programming model to integrate production, inventory, distribution and routing decisions in a single framework. The model was inspired by small Brazilian furniture companies and focuses on production and distribution decisions at an operational level. In particular, we consider a scenario in which only one production line and one vehicle, which makes multiple trips over the planning horizon, are available to produce items and deliver final products, respectively. We also take into account some features rarely considered in the literature, but commonly found in real-world applications, such as producing and stocking multiple items, distribution routes extending over one or more periods, multiple time windows and customers’ due dates. Computational tests on a set of randomly generated instances were carried out using a well-known optimization software and six relax-and-fix heuristics, which explore different criteria for partitioning and fixing variables. We also implemented two hybrid heuristics in which an initial solution is first constructed and then fed into the optimization software to improve it. The results showed that one relax-and-fix and the two hybrid heuristics performed better than the solver on the largest instances.

Keywords

Production, inventory, distribution routing problem Production routing problem Integrated production–distribution planning Furniture industry 

Mathematics Subject Classification

90B06 90C11 90C27 

Notes

Acknowledgements

The authors would like to thank the two anonymous reviewers for their useful comments and suggestions of revision.

References

  1. Absi N, Archetti C, Dauzère-Pérès S, Feillet D (2014) A two-phase iterative heuristic approach for the production routing problem. Transp Sci 49(4):784–795. doi: 10.1287/trsc.2014.0523 CrossRefGoogle Scholar
  2. Adulyasak Y, Cordeau JF, Jans R (2014a) Formulations and branch-and-cut algorithms for multivehicle production and inventory routing problems. INFORMS J Comput 26:103–120CrossRefGoogle Scholar
  3. Adulyasak Y, Cordeau JF, Jans R (2014b) Optimization-based adaptive large neighborhood search for the production routing problem. Transp Sci 48(1):20–45CrossRefGoogle Scholar
  4. Adulyasak Y, Cordeau JF, Jans R (2015) Benders decomposition for production routing under demand uncertainty. Oper Res 63(4):851–867. doi: 10.1287/opre.2015.1401 CrossRefGoogle Scholar
  5. Adulyasak Y, Cordeau JF, Jans R (2015b) The production routing problem: a review of formulations and solution algorithms. Comput Oper Res 55:141–152. doi: 10.1016/j.cor.2014.01.011 CrossRefGoogle Scholar
  6. Amorim P, Belo-Filho M, Toledo F, Almeder C, Almada-Lobo B (2013) Lot sizing versus batching in the production and distribution planning of perishable goods. Int J Prod Econ 146(1):208–218. doi: 10.1016/j.ijpe.2013.07.001 CrossRefGoogle Scholar
  7. Amorim P, Parragh SN, Sperandio F, Almada-Lobo B (2014) A rich vehicle routing problem dealing with perishable food: a case study. TOP 22(2):489–508. doi: 10.1007/s11750-012-0266-4 CrossRefGoogle Scholar
  8. Araujo S, Arenales M, Clark A (2007) Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups. J Heuristics 13(4):337–358. doi: 10.1007/s10732-007-9011-9 CrossRefGoogle Scholar
  9. Archetti C, Bertazzi L, Paletta G, Speranza MG (2011) Analysis of the maximum level policy in a production–distribution system. Comput Oper Res 38(12):1731–1746. doi: 10.1016/j.cor.2011.03.002 CrossRefGoogle Scholar
  10. Armentano V, Shiguemoto A, Løkketangen A (2011) Tabu search with path relinking for an integrated production–distribution problem. Comput Oper Res 38(8):1199–1209. doi: 10.1016/j.cor.2010.10.026 CrossRefGoogle Scholar
  11. Armstrong R, Gao S, Lei L (2007) A zero-inventory production and distribution problem with a fixed customer sequence. Ann Oper Res 159(1):395–414. doi: 10.1007/s10479-007-0272-3 CrossRefGoogle Scholar
  12. Azi N, Gendreau M, Potvin JY (2007) An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. Eur J Oper Res 178(3):755–766. doi: 10.1016/j.ejor.2006.02.019 CrossRefGoogle Scholar
  13. Bard JF, Nananukul N (2009) Heuristics for a multiperiod inventory routing problem with production decisions. Comput Ind Eng 57(3):713–723. doi: 10.1016/j.cie.2009.01.020 CrossRefGoogle Scholar
  14. Bard JF, Nananukul N (2009b) The integrated production–inventory–distribution–routing problem. J Sched 12(3):257–280. doi: 10.1007/s10951-008-0081-9 CrossRefGoogle Scholar
  15. Bard JF, Nananukul N (2010) A branch-and-price algorithm for an integrated production and inventory routing problem. Comput Oper Res 37(12):2202–2217. doi: 10.1016/j.cor.2010.03.010 CrossRefGoogle Scholar
  16. Beamon BM (1998) Supply chain design and analysis: models and methods. Int J Prod Econ 55:281–294CrossRefGoogle Scholar
  17. Belhaiza S, Hansen P, Laporte G (2014) A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Comput Oper Eng 52(Part B):269–281. doi: 10.1016/j.cor.2013.08.010 CrossRefGoogle Scholar
  18. Beraldi P, Ghiani G, Grieco A, Guerriero E (2008) Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs. Comput Oper Res 35(11):3644–3656. doi: 10.1016/j.cor.2007.04.003 CrossRefGoogle Scholar
  19. Bertazzi L, Paletta G, Speranza MG (2005) Minimizing the total cost in an integrated vendor-managed inventory system. J Heuristics 11:393–419CrossRefGoogle Scholar
  20. Boudia M, Prins C (2009) A memetic algorithm with dynamic population management for an integrated production–distribution problem. Eur J Oper Res 195(3):703–715. doi: 10.1016/j.ejor.2007.07.034 CrossRefGoogle Scholar
  21. Boudia M, Louly M, Prins C (2007) A reactive GRASP and path relinking for a combined production–distribution problem. Comput Oper Res 34(11):3402–3419. doi: 10.1016/j.cor.2006.02.005 CrossRefGoogle Scholar
  22. Brahimi N, Aouam T (2016) Multi-item production routing problem with backordering: a MILP approach. Int J Prod Res 54(4):1076–1093. doi: 10.1080/00207543.2015.1047971 CrossRefGoogle Scholar
  23. Chandra P, Fisher ML (1994) Coordination of production and distribution planning. Eur J Oper Res 72:503–517CrossRefGoogle Scholar
  24. Chen HK, Hsueh CF, Chang MS (2009) Production scheduling and vehicle routing with time windows for perishable food products. Comput Oper Res 36(7):2311–2319. doi: 10.1016/j.cor.2008.09.010 CrossRefGoogle Scholar
  25. Chen ZL (2004) Integrated production and distribution operations: taxonomy, models, and review. In: Simchi-Levi D, Wu S, Shen ZJ (eds) Handbook of quantitative supply chain analysis: modeling in the e-business era, chap 17. Kluwer Academic Publishers, Boston, pp 711–745Google Scholar
  26. Chen ZL (2010) Integrated production and outbound distribution scheduling: review and extensions. Oper Res 58(1):130–148. doi: 10.1287/opre.1080.0688 CrossRefGoogle Scholar
  27. Chen ZL, Pundoor G (2006) Order assignment and scheduling in a supply chain. Oper Res 54(3):555–572. doi: 10.1287/opre.1060.0280 CrossRefGoogle Scholar
  28. Chen ZL, Vairaktarakis GL (2005) Integrated scheduling of production and distribution operations. Manag Sci 51(4):614–628. doi: 10.1287/mnsc.1040.0325 CrossRefGoogle Scholar
  29. Chiang WC, Russell R, Xu X, Zepeda D (2009) A simulation/metaheuristic approach to newspaper production and distribution supply chain problems. Int J Prod Econ 121(2):752–767. doi: 10.1016/j.ijpe.2009.03.001 CrossRefGoogle Scholar
  30. Díaz-Madroñero M, Peidro D, Mula J (2015) A review of tactical optimization models for integrated production and transport routing planning decisions. Comput Ind Eng 88:518–535. doi: 10.1016/j.cie.2015.06.010 CrossRefGoogle Scholar
  31. Dillenberger C, Escudero LF, Wollensak A, Zhang W (1994) On practical resource allocation for production planning and scheduling with period overlapping setups. Eur J Oper Res 75(2):275–286. doi: 10.1016/0377-2217(94)90074-4 CrossRefGoogle Scholar
  32. Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Progr 91(2):201–213. doi: 10.1007/s101070100263 CrossRefGoogle Scholar
  33. Farahani P, Grunow M, Günther HO (2012) Integrated production and distribution planning for perishable food products. Flex Serv Manuf J 24(1):28–51. doi: 10.1007/s10696-011-9125-0 CrossRefGoogle Scholar
  34. Ferreira D, Morabito R, Rangel S (2009) Solution approaches for the soft drink integrated production lot sizing and scheduling problem. Eur J Oper Res 196(2):697–706. doi: 10.1016/j.ejor.2008.03.035 CrossRefGoogle Scholar
  35. Ferreira D, Morabito R, Rangel S (2010) Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants. Comput Oper Res 37(4):684–691. doi: 10.1016/j.cor.2009.06.007 CrossRefGoogle Scholar
  36. Fumero F, Vercellis C (1999) Synchronized development of production, inventory, and distribution schedules. Transp Sci 33(3):330–340. doi: 10.1287/trsc.33.3.330 CrossRefGoogle Scholar
  37. Geismar HN, Laporte G, Lei L, Sriskandarajah C (2008) The integrated production and transportation scheduling problem for a product with a short lifespan. INFORMS J Comput 20(1):21–33. doi: 10.1287/ijoc.1060.0208 CrossRefGoogle Scholar
  38. Goel A (2012) The minimum duration truck driver scheduling problem. EURO J Transp Logist 1(4):285–306. doi: 10.1007/s13676-012-0014-9 CrossRefGoogle Scholar
  39. Gramani M, França P, Arenales M (2009) A lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem. Int J Prod Econ 119(2):219–227. doi: 10.1016/j.ijpe.2009.02.011 CrossRefGoogle Scholar
  40. IBM ILOG CPLEX (2013) IBM ILOG CPLEX Optimization Studio: CPLEX user’s manual v.12.6, IBM CorporationGoogle Scholar
  41. James R, Almada-Lobo B (2011) Single and parallel machine capacitated lotsizing and scheduling: new iterative MIP-based neighborhood search heuristics. Comput Oper Res 38(12):1816–1825. doi: 10.1016/j.cor.2011.02.005 CrossRefGoogle Scholar
  42. Jans R, Degraeve Z (2008) Modeling industrial lot sizing problems: a review. Int J Prod Res 46(6):1619–1643. doi: 10.1080/00207540600902262 CrossRefGoogle Scholar
  43. Lei L, Liu S, Ruszczynski A, Park S (2006) On the integrated production, inventory, and distribution routing problem. IIE Trans 38(11):955–970. doi: 10.1080/07408170600862688 CrossRefGoogle Scholar
  44. Molina F, Morabito R, Araujo S (2016) MIP models for production lot sizing problems with distribution costs and cargo arrangement. J Oper Res Soc 67(11):1395–1407. doi: 10.1057/jors.2016.12 CrossRefGoogle Scholar
  45. Moons S, Ramaekers K, Caris A, Arda Y (2017) Integrating production scheduling and vehicle routing decisions at the operational decision level: a review and discussion. Comput Ind Eng 104:224–245CrossRefGoogle Scholar
  46. Mula J, Peidro D, Díaz-Madroñero M, Vicens E (2010) Mathematical programming models for supply chain production and transport planning. Eur J Oper Res 204(3):377–390. doi: 10.1016/j.ejor.2009.09.008 CrossRefGoogle Scholar
  47. Quadt D, Kuhn H (2007) Capacitated lot-sizing with extensions: a review. 4OR 6(1):61–83. doi: 10.1007/s10288-007-0057-1 CrossRefGoogle Scholar
  48. Rancourt ME, Cordeau JF, Laporte G (2013) Long-haul vehicle routing and scheduling with working hour rules. Transp Sci 47(1):81–107CrossRefGoogle Scholar
  49. Russell R, Chiang WC, Zepeda D (2008) Integrating multi-product production and distribution in newspaper logistics. Comput Oper Res 35(5):1576–1588. doi: 10.1016/j.cor.2006.09.002 CrossRefGoogle Scholar
  50. Sarmiento AM, Nagi R (1999) A review of integrated analysis of production–distribution systems. IIE Trans 31(11):1061–1074Google Scholar
  51. Savelsbergh M, Song JH (2008) An optimization algorithm for the inventory routing problem with continuous moves. Comput Oper Res 35(7):2266–2282. doi: 10.1016/j.cor.2006.10.020 CrossRefGoogle Scholar
  52. Shiguemoto AL, Armentano V (2010) A tabu search procedure for coordinating production, inventory and distribution routing problems. Int Trans Oper Res 17(2):179–195. doi: 10.1111/j.1475-3995.2009.00741.x CrossRefGoogle Scholar
  53. Toledo FMB, Armentano V (2006) A lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines. Eur J Oper Res 175(2):1070–1083. doi: 10.1016/j.ejor.2005.06.029 CrossRefGoogle Scholar
  54. Trigeiro WW, Thomas LJ, McClain JO (1989) Capacitated lot sizing with setup times. Manag Sci 35(3):353–366. doi: 10.1287/mnsc.35.3.353 CrossRefGoogle Scholar
  55. Vidal CJ, Goetschalckx M (1997) Strategic production–distribution models: a critical review with emphasis on global supply chain models. Eur J Oper Res 98(1):1–18CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Department of Production EngineeringFederal University of São CarlosSão CarlosBrazil
  2. 2.Department of Physics, Chemistry and MathematicsFederal University of São CarlosSorocabaBrazil

Personalised recommendations