Skip to main content
SpringerLink
Log in

MIP models for production lot sizing problems with distribution costs and cargo arrangement

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

This study presents mixed integer programming (MIP) models for production lot sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in the bins are considered. In general, these problems involve a trade-off between production, inventory and distribution costs. Lot sizing decisions should take into account production capacity and product demand constraints. Distribution decisions are related to the loading and transport of products in unit load devices. The MIP models are solved by the branch-and-cut method of an optimization package and the results show that these approaches have the potential to address different practical situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3

Similar content being viewed by others

References

  • Alvarez-Valdes R, Parreño F and Tamarif JM (2005). A branch-and-cut algorithm for the pallet loading problem. Computers and Operations Research 32(11): 3007–3029.

    Article  Google Scholar 

  • Amorim P, Belo-Filho M, Toledo FMB, Almeder C and Almada-Lobo B (2013). Lot sizing versus batching in the production and distribution planning of perishable goods. International Journal of Production Economics 146(1): 208–218.

    Article  Google Scholar 

  • Anily S and Tzur M (2006). Algorithms for the multi-item multi-vehicles dynamic lot sizing problem. Naval Research Logistics 53(2): 157–169.

    Article  Google Scholar 

  • Baumol WJ and Vinod HD (1970). An inventory theoretic model of freight transport demand. Management Science 16(7): 413–421.

    Article  Google Scholar 

  • Beasley JE (1985). An exact two-dimensional non guillotine cutting tree search procedure. Operations Research 33(1): 49–64.

    Article  Google Scholar 

  • Beasley JE (1990). OR-library: Distributing test problems by electronic mail. Journal of the Operational Research Society 41(11): 1069–1072.

    Article  Google Scholar 

  • Bertazzi L and Speranza MG (1999). Models and algorithms for the minimization of inventory and transportation costs: A survey. In: Speranza MG and Staehly P (eds). New Trends in Distribution Logistics. Lecture Notes in Economics and Mathematical Systems Vol. 480 Springer-Verlag: Berlin Heidelberg, pp 137–157.

    Chapter  Google Scholar 

  • Beullens P (2014). Revisiting foundations in lot sizing—Connections between Harris, Crowther, Monahan, and Clark. International Journal of Production Economics 155: 68–81.

    Article  Google Scholar 

  • Birgin EG, Lobato RD and Morabito R (2010). An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. Journal of the Operational Research Society 61(2): 306–320.

    Article  Google Scholar 

  • Brahimi N, Dauzere-Peres S, Najid NM and Nordi A (2006). Single item lot sizing problems. European Journal of Operational Research 168(1): 1–16.

    Article  Google Scholar 

  • Coffman EG, Garey MR and Johnson DS (1997). Approximation algorithms for bin packing: A survey. In: Hochbaum DS (ed). Approximation Algorithms for N-Hard Problems. PWS Publishing Company: Boston, MA, pp 46–93.

    Google Scholar 

  • de Matta R and Miller T (2004). Production and inter-facility transportation scheduling for a process industry. European Journal of Operational Research 158(1): 72–88.

    Article  Google Scholar 

  • Erengüç SS, Simpson NC and Vakharia AJ (1999). Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research 115(2): 219–236.

    Article  Google Scholar 

  • Fumero F and Vercellis C (1999). Synchronized development of production, inventory, and distribution schedules. Transportation Science 33(3): 330–340.

    Article  Google Scholar 

  • Glock CH, Grosse EH and Ries JM (2014). The lot sizing problem: A tertiary study. International Journal of Production Economics 155: 39–51.

    Article  Google Scholar 

  • Holmbom M and Segerstedt A (2014). Economic order quantities in production: From Harris to economic lot scheduling problems. International Journal of Production Economics 155: 82–90.

    Article  Google Scholar 

  • Jans R and Degraeve Z (2007). Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches. European Journal of Operational Research 177(3): 1855–1875.

    Article  Google Scholar 

  • Jans R and Degraeve Z (2008). Modelling industrial lot sizing problems: A review. International Journal of Production Research 46(6): 1619–1643.

    Article  Google Scholar 

  • Kaminsky P and Simchi-Levi D (2003). Production and distribution lot sizing in a two stage supply chain. IIE Transactions 35(11): 1065–1075.

    Article  Google Scholar 

  • Kantorovich LV (1960). Mathematical methods of organizing and planning production. Management Science 6(4): 366–422.

    Article  Google Scholar 

  • Karimi B, Ghomi S M T F and Wilson JM (2003). The capacitated lot sizing problem: A review of models and algorithms. OMEGA 31(5): 365–378.

    Article  Google Scholar 

  • Lee WS, Han JH and Cho SJ (2005). A heuristic for a multi-product dynamic lot-sizing and shipping problem. International Journal of Production Economics 98(2): 204–214.

    Article  Google Scholar 

  • Melo RA and Wolsey LA (2010). Uncapacitated two-level lot-sizing. Operations Research Letters 38(3): 241–245.

    Article  Google Scholar 

  • Molina F, Morabito R and de Araujo SA (2013). Modelos matemáticos para problemas de dimensionamento de lotes com restrições de capacidade e custos de transporte. Gestão & Produção 20(3): 573–586.

    Article  Google Scholar 

  • Molina F, Santos MO, Toledo FMB and Araujo SA (2009). An approach using Lagrangean/surrogate relaxation for lot-sizing with transportation costs. Pesquisa Operacional 28(2): 269–288.

    Article  Google Scholar 

  • Morabito R and Pureza V (2009). Loading optimization. In: Raton B (ed) Erdogdu F (org). Optimization in Food Engineering. CRC Press—Taylor & Francis Group: Boca Raton, FL, pp 657–683.

    Google Scholar 

  • Nascimento MC, Resende MG and Toledo FM (2010). Grasp heuristic with path-relinking for the multiplant capacitated lot sizing problem. European Journal of Operational Research 200(3): 747–754.

    Article  Google Scholar 

  • Norden L and Velde S (2005). Multi-product lot-sizing a transportation capacity reservation contract. European Journal of Operational Research 165(1): 127–138.

    Article  Google Scholar 

  • Rizk N and Martel A (2001). Supply chain flow planning methods: A review of the lot-sizing literature. Working Paper DT-2001-AM-1, Université Laval, QC, Canada.

  • Robinson P, Narayananb A and Sahinc F (2009). Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms. Omega 37(1): 3–15.

    Article  Google Scholar 

  • Sambasivan M and Schmidt CP (2002). A heuristic procedure for solving multi-plant, multiitem, multi-period capacitated lot-sizing problems. Asia-Pacific Journal of Operational Research 19: 87–105.

    Google Scholar 

  • Sambasivan M and Yahya S (2005). A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers. Computers & Operations Research 32(3): 537–555.

    Article  Google Scholar 

  • Sarmiento AM and Nagi N (1999). A review of integrated analysis of production—Distribution systems. IIE Transactions 31(11): 1061–1074.

    Google Scholar 

  • Seliaman ME and Ahmad AR (2009). A generalized algebraic model for optimizing inventory decisions in a multi-stage complex supply chain. Transportation Research Part E 45(3): 409–418.

    Article  Google Scholar 

  • Stecke KE and Zhao X (2007). Production and transportation integration for a make-to-order manufacturing company with a commit-to-delivery business mode. Manufacturing & Service Operations Management 9(2): 206–224.

    Article  Google Scholar 

  • Thomas DJ and Griffin PM (1996). Coordinated supply chain management. European Journal of Operational Research 94(11): 1–15.

    Article  Google Scholar 

  • Vidal CJ and Goetschalckx M (1997). Strategic production-distribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research 98(1): 1–18.

    Article  Google Scholar 

  • Vroblefski M, Ramesh R and Zionts S (2000). Efficient lot-sizing under a differential transportation cost structure for serially distributes warehouses. European Journal of Operational Research 127(3): 574–593.

    Article  Google Scholar 

  • Wong JT (2010). The distribution processing and replenishment policy of the supply chain under asymmetric information and deterioration: Insight into the information value. Expert Systems with Applications 37: 2347–2353.

    Article  Google Scholar 

  • Xiao Y and Taaffe K (2010). Satisfying market demands with delivery obligations or delivery charges. Computers & Operations Research 37(2): 396–405.

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the two anonymous reviewers for their useful comments and suggestions. This research had the financial support of CNPq and FAPESP (Process number 2010/10133-0, 2014/01203-5 and 474782/2013-1).

Author information

Authors and Affiliations

  1. Universidade Federal do Triângulo Mineiro, Uberaba, Brazil

    Flavio Molina

  2. Universidade Federal de São Carlos, São Carlos, Brazil

    Reinaldo Morabito

  3. Universidade Estadual Paulista, São José do Rio Preto, Brazil

    Silvio Alexandre de Araujo

Authors
  1. Flavio Molina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinaldo Morabito
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Silvio Alexandre de Araujo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reinaldo Morabito.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Molina, F., Morabito, R. & de Araujo, S. MIP models for production lot sizing problems with distribution costs and cargo arrangement. J Oper Res Soc 67, 1395–1407 (2016). https://doi.org/10.1057/jors.2016.12

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2016.12

Keywords

Search

Navigation