Optimization Letters

, Volume 5, Issue 2, pp 259–272 | Cite as

New formulation for the high multiplicity asymmetric traveling salesman problem with application to the Chesapeake problem

  • Subhash C. SarinEmail author
  • Hanif D. Sherali
  • Liming Yao
Original Paper


This paper presents a new model for a special type of traveling salesman problem called the High Multiplicity Asymmetric Traveling Salesman Problem (HMATSP). The formulation adopts a flow-based subtour elimination structure and establishes its validity for this problem. Also, we present computational results to demonstrate the efficacy of our modeling approach. The model is then incorporated as a substructure in a formulation for the lot-sizing problem involving parallel machines and sequence-dependent setup costs, also known as the Chesapeake Problem, and related test problems are solved to optimality for the first time in the literature.


High multiplicity asymmetric traveling salesman problem Polynomial-length formulation Chesapeake problem Parallel machine scheduling Lot-sizing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, T., Muckstadt, J.A.: The CHES problems. Technical Paper, Chesapeake Decision Sciences, Inc., Providence (1989)Google Scholar
  2. 2.
    Belvaux G., Wolsey L.A.: Modeling practical lot-sizing problems as mixed integer programs. Manage. Sci. 47, 993–1007 (2001)CrossRefGoogle Scholar
  3. 3.
    Cosmadakis S.S., Papadimitriou C.H.: The traveling salesman problem with many visits to few cities. SIAM J. Comput. 13, 99–108 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Dantzig G., Fulkerson D., Johnson S.: Solution of a large scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Dastidar S.G., Nagi R.: Scheduling injection modeling operations with multiple resource constraints and sequence dependent setup times and costs. Comput. Oper. Res. 32, 2987–3005 (2005)CrossRefzbMATHGoogle Scholar
  6. 6.
    Fleischmann B.: The discrete lot-sizing and scheduling problem with sequence-dependent setup costs. Eur. J. Oper. Res. 75, 395–404 (1994)CrossRefzbMATHGoogle Scholar
  7. 7.
    Grigoriev A., van de Klundert J.: On the high multiplicity traveling salesman problem. Discrete Optim. 3, 50–62 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gupta D., Magnusson T.: The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times. Comput. Oper. Res. 32, 727–747 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Hasse K., Kimms A.: Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities. Int. J. Prod. Econ. 66, 159–169 (2000)CrossRefGoogle Scholar
  10. 10.
    Kang S., Malik K., Thomas L.J.: Lotsizing and scheduling on parallel machines with sequence-dependent setup costs. Manage. Sci. 45, 273–289 (1999)CrossRefGoogle Scholar
  11. 11.
    Meyr H.: Simultaneous lotsizing and scheduling on parallel machines. Eur. J. Oper. Res. 139, 277–292 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Sarin S.C., Sherali H.D., Bhootra A.: New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints. Oper. Res. Lett. 33, 62–70 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Sherali H.D., Sarin S.C., Tsai P.F.: A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints. Discrete Optim. 3, 20–32 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Wong, R.T.: Integer programming formulations of the traveling salesman problem. In: Proceedings of the IEEE International Conference on Circuits and Computers, Part I, pp. 149–152, New York (1980)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Subhash C. Sarin
    • 1
    Email author
  • Hanif D. Sherali
    • 1
  • Liming Yao
    • 1
  1. 1.Grado Department of Industrial and Systems EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations