IDEAS home Printed from https://ideas.repec.org/a/eur/ejesjr/64.html
   My bibliography  Save this article

Integer Programming Model for Two-Centered Double Traveling Salesman Problem

Author

Listed:
  • Mehmet Fatih Demiral

    (Department of Industrial Engineering, Faculty of Engineering and Architecture Mehmet Akif Ersoy University, Burdur, Turkey)

  • Åžen Halil

Abstract

Traveling Salesman Problem (TSP) is among the most popular combinatorial problems and has been widely studied with many extensions in the literature. There have been integer programming formulations and solution approaches for TSP and its variations. One of the most popular topics is the multiple TSP (m-TSP). It has been started to work on the last decades. Generally, m-TSP has a single depot and more than one tour. However, some types have more than one depot. Besides, if seeking, many encounter with double traveling salesman problem (d-TSP). As inferred from the literature, d-TSP is a variation of m-TSP in which two salespersons operate in parallel. They start and end either in a single or two depots. Apart from the literature, a new TSP model has been constructed in this study. The model analyzes the behaviors of traveling salesmen both in the main and secondary tour. Tours have been aggregated via single node existing in the secondary tour. In the application part, Simulated Annealing (SA) was used to optimize the traveling paths of salesmen. The objective parameters of both tours have been explored within a numerical example. According to them, several cost values have been found. The optimum parameters and costs of both tours are to be determined and some practical issues relevant to the behaviors of traveling salesmen have been given. Results suggest that alternative travel plans of traveling salesmen could be possible. Also, findings give hints about both tours and their characteristics.

Suggested Citation

  • Mehmet Fatih Demiral & Åžen Halil, 2021. "Integer Programming Model for Two-Centered Double Traveling Salesman Problem," European Journal of Economics and Business Studies Articles, Revistia Research and Publishing, vol. 2, May - Aug.
    • Handle: RePEc:eur:ejesjr:64
    DOI: 10.26417/ejes.v5i1.p80-86
    as

    Download full text from publisher

    File URL: https://revistia.com/index.php/ejes/article/view/2591
    Download Restriction: no
    File URL: https://revistia.com/files/articles/ejes_v2_i2_16/mehmet.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26417/ejes.v5i1.p80-86?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. anonymous, 1995. "Does the bouncing ball lead to economic growth?," Regional Update, Federal Reserve Bank of Atlanta, issue Jul, pages 1-2,4-6.
    2. Greenwood, Jeremy & Hercowitz, Zvi, 1991. "The Allocation of Capital and Time over the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1188-1214, December.
    3. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    4. Chen, Shu-Hua & Guo, Jang-Ting, 2013. "Progressive taxation and macroeconomic (In) stability with productive government spending," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 951-963.
    5. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    6. Campbell, John Y & Ludvigson, Sydney, 2001. "Elasticities of Substitution in Real Business Cycle Models with Home Protection," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 33(4), pages 847-875, November.
    7. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, April.
    8. Booth, Alison L., 2009. "Gender and competition," Labour Economics, Elsevier, vol. 16(6), pages 599-606, December.
    9. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    10. Paul A. Samuelson, 1959. "A Modern Treatment of the Ricardian Economy: I. The Pricing of Goods and of Labor and Land Services," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 73(1), pages 1-35.
    11. Turnovsky, Stephen J, 2004. "The Transitional Dynamics of Fiscal Policy: Long-Run Capital Accumulation and Growth," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(5), pages 883-910, October.
    12. Lakshmi Kanta Raut, 1992. "Effect of Social Security on Fertility and Savings: An Overlapping Generations Model," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 27(1), pages 25-43, July.
    13. Goodfriend, Marvin & McDermott, John, 1995. "Early Development," American Economic Review, American Economic Association, vol. 85(1), pages 116-133, March.
    14. Wei-Bin Zhang, 2014. "Multi-regional economic growth with public good and regional fiscal policies in a small-open economy," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 409-429, March.
    15. Chen, Shu-Hua & Guo, Jang-Ting, 2014. "Progressive taxation and macroeconomic (in)stability with utility-generating government spending," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 174-183.
    16. Morgan Kelly, 1997. "The Dynamics of Smithian Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(3), pages 939-964.
    17. Cazzavillan, Guido, 1996. "Public Spending, Endogenous Growth, and Endogenous Fluctuations," Journal of Economic Theory, Elsevier, vol. 71(2), pages 394-415, November.
    18. Hu, Yunfang & Ohdoi, Ryoji & Shimomura, Koji, 2008. "Indeterminacy in a two-sector endogenous growth model with productive government spending," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1104-1123, September.
    19. Lane, Philip R., 2001. "The new open economy macroeconomics: a survey," Journal of International Economics, Elsevier, vol. 54(2), pages 235-266, August.
    20. Theodore Palivos & Chong K. Yip & Junxi Zhang, 2003. "Transitional Dynamics and Indeterminacy of Equilibria in an Endogenous Growth Model with a Public Input," Review of Development Economics, Wiley Blackwell, vol. 7(1), pages 86-98, February.
    21. Glomm, Gerhard & Ravikumar, B., 1994. "Public investment in infrastructure in a simple growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(6), pages 1173-1187, November.
    22. Ilzetzki, Ethan & Mendoza, Enrique G. & Végh, Carlos A., 2013. "How big (small?) are fiscal multipliers?," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 239-254.
    23. P. A. Diamond, 1971. "Disembodied Technical Change in a Two-Sector Model," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 7, pages 53-60, Palgrave Macmillan.
    24. Antonio Ladrón-de-Guevara & Salvador Ortigueira & Manuel S. Santos, 1999. "A Two-Sector Model of Endogenous Growth with Leisure," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 609-631.
    25. Fernandez, Esther & Novales, Alfonso & Ruiz, Jesus, 2004. "Indeterminacy under non-separability of public consumption and leisure in the utility function," Economic Modelling, Elsevier, vol. 21(3), pages 409-428, May.
    26. Kelly, M., 1996. "The Dynamics of Smithian growth," Papers 96/9, College Dublin, Department of Political Economy-.
    27. Paul Gomme & Finn E. Kydland & Peter Rupert, 2001. "Home Production Meets Time to Build," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1115-1131, October.
    28. J. Ignacio Conde-Ruiz & Eduardo L. Giménez & Mikel Pérez-Nievas, 2010. "Millian Efficiency with Endogenous Fertility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 154-187.
    29. Kamiguchi, Akira & Tamai, Toshiki, 2011. "Can productive government spending be a source of equilibrium indeterminacy?," Economic Modelling, Elsevier, vol. 28(3), pages 1335-1340, May.
    30. Alfred Greiner, 2007. "An Endogenous Growth Model With Public Capital And Sustainable Government Debt," The Japanese Economic Review, Japanese Economic Association, vol. 58(3), pages 345-361, September.
    31. Ms. Janet Gale Stotsky, 2006. "Gender and its Relevance to Macroeconomic Policy: A Survey," IMF Working Papers 2006/233, International Monetary Fund.
    32. Rupert, Peter & Rogerson, Richard & Wright, Randall, 1995. "Estimating Substitution Elasticities in Household Production Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 179-193, June.
    33. repec:bla:scandj:v:95:y:1993:i:4:p:607-25 is not listed on IDEAS
    34. James Albrecht & Anders Bjorklund & Susan Vroman, 2003. "Is There a Glass Ceiling in Sweden?," Journal of Labor Economics, University of Chicago Press, vol. 21(1), pages 145-177, January.
    35. Lourdes BENERÍA, 1999. "The enduring debate over unpaid labour," International Labour Review, International Labour Organization, vol. 138(3), pages 287-309, September.
    36. Uy, Timothy & Yi, Kei-Mu & Zhang, Jing, 2013. "Structural change in an open economy," Journal of Monetary Economics, Elsevier, vol. 60(6), pages 667-682.
    37. Pierre‐Richard Agénor, 2011. "Schooling and Public Capital in a Model of Endogenous Growth," Economica, London School of Economics and Political Science, vol. 78(309), pages 108-132, January.
    38. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    39. Chen, Been-Lon, 2006. "Public capital, endogenous growth, and endogenous fluctuations," Journal of Macroeconomics, Elsevier, vol. 28(4), pages 768-774, December.
    40. Zhang W.B., 2015. "Birth And Mortality Rates, Gender Division Of Labor, And Time Distribution In The Solow Growth Model," Revista Galega de Economía, University of Santiago de Compostela. Faculty of Economics and Business., vol. 24(1), pages 121-134.
    41. Jordi Galí & Tommaso Monacelli, 2005. "Monetary Policy and Exchange Rate Volatility in a Small Open Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 707-734.
    42. Vendrik, Maarten C. M., 2003. "Dynamics of a household norm in female labour supply," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 823-841, March.
    43. Jang‐Ting Guo & Sharon G. Harrison, 2008. "Useful Government Spending and Macroeconomic (In)stability under Balanced‐Budget Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(3), pages 383-397, June.
    44. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 103-126, October.
    45. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 989-1015, July.
    46. Glomm, Gerhard & Ravikumar, B., 1997. "Productive government expenditures and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 183-204, January.
    47. Turnovsky, Stephen J., 2000. "Fiscal policy, elastic labor supply, and endogenous growth," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 185-210, February.
    48. Jenny Chesters & Janeen Baxter, 2009. "Paid and Unpaid Work in Australian Households: Trends in the Gender Division of Labour, 1986-2005," Australian Journal of Labour Economics (AJLE), Bankwest Curtin Economics Centre (BCEC), Curtin Business School, vol. 12(1), pages 89-107.
    49. Zhang, Wei-Bin, 1993. "A woman's labor participation and economic growth : Creativity, knowledge utilization and family preference," Economics Letters, Elsevier, vol. 42(1), pages 105-110.
    50. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    51. Barro, Robert J & Becker, Gary S, 1989. "Fertility Choice in a Model of Economic Growth," Econometrica, Econometric Society, vol. 57(2), pages 481-501, March.
    52. Rupa Banerjee, 2008. "An Examination of Factors Affecting Perception of Workplace Discrimination," Journal of Labor Research, Springer, vol. 29(4), pages 380-401, December.
    53. Dong, Xiao-yuan & Zhang, Liqin, 2009. "Economic transition and gender differentials in wages and productivity: Evidence from Chinese manufacturing enterprises," Journal of Development Economics, Elsevier, vol. 88(1), pages 144-156, January.
    54. Tassel, Eric Van, 2004. "Household bargaining and microfinance," Journal of Development Economics, Elsevier, vol. 74(2), pages 449-468, August.
    55. Kollmann, Robert, 2001. "The exchange rate in a dynamic-optimizing business cycle model with nominal rigidities: a quantitative investigation," Journal of International Economics, Elsevier, vol. 55(2), pages 243-262, December.
    56. Zhang, Junxi, 2000. "Public services, increasing returns, and equilibrium dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 227-246, February.
    57. repec:bla:econom:v:70:y:2003:i:280:p:639-653 is not listed on IDEAS
    58. Gianluca Benigno & Pierpaolo Benigno, 2003. "Price Stability in Open Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 743-764.
    59. Edmonds, Eric V. & Pavcnik, Nina, 2006. "Trade liberalization and the allocation of labor between households and markets in a poor country," Journal of International Economics, Elsevier, vol. 69(2), pages 272-295, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei-bin ZHANG, 2020. "Corruption and Public Service in an Extended Solowian Growth Model with Endogenous Labor Supply," Journal of Economic Policy Researches, Istanbul University, Faculty of Economics, vol. 7(2), pages 1-20, July.
    2. Chen, Shu-Hua & Guo, Jang-Ting, 2014. "Progressive taxation and macroeconomic (in)stability with utility-generating government spending," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 174-183.
    3. Wei-Bin ZHANG, 2018. "Nonlinear Progressive Income Taxation And Inequalities In Income And Wealth Between Heterogeneous Households," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 17(2), pages 42-53.
    4. wei-bin zhang, 2017. "Business Cycles with Progressive Income Taxation," International Journal of Business and Management, International Institute of Social and Economic Sciences, vol. 5(2), pages 78-95, November.
    5. Eda Özdiler Küçük, 2017. "Adapting Legal Culture: Legislation and Interpretation in Tax Law," European Journal of Economics and Business Studies Articles, Revistia Research and Publishing, vol. 3, ejes_v3_i.
    6. Zhang, Wei-Bin, 2015. "Tourism, Trade, Externalities, And Public Goods In A Three-Sector Growth Model," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 6(1), pages 1-19.
    7. Wei-Bin ZHANG, 2014. "Gender Discrimination, Education and Economic Growth in a Generalized Uzawa-Lucas Two-Sector Model," Timisoara Journal of Economics and Business, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 7(1), pages 1-34.
    8. Wei-Bin Zhang, 2017. "How Do the Richest 1% Owns 50% of Wealth in a Small-Open Growth Model with Endogenous Wealth and Human Capital," Academicus International Scientific Journal, Entrepreneurship Training Center Albania, issue 15, pages 58-79, January.
    9. Shu-Hua Chen & Jang-Ting Guo, 2019. "Progressive taxation as an automatic destabilizer under endogenous growth," Journal of Economics, Springer, vol. 127(1), pages 47-71, June.
    10. Wei-Bin ZHANG, 2016. "Tourism and economic structural change with endogenous wealth and human capital and elastic labor supply," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(609), W), pages 103-126, Winter.
    11. Wei-Bin Zhang, 2016. "Gender-Differentiated Human Capital And Time Distributions In A Generalized Heckscher-Ohlin Model With Endogenous Physical Capital," Knowledge Horizons - Economics, Faculty of Finance, Banking and Accountancy Bucharest,"Dimitrie Cantemir" Christian University Bucharest, vol. 8(2), pages 112-132, June.
    12. Wei-Bin ZHANG, 2016. "Tourism and economic structural change with endogenous wealth and human capital and elastic labor supply," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(4(609), W), pages 103-126, Winter.
    13. Zhang W.B., 2015. "Birth And Mortality Rates, Gender Division Of Labor, And Time Distribution In The Solow Growth Model," Revista Galega de Economía, University of Santiago de Compostela. Faculty of Economics and Business., vol. 24(1), pages 121-134.
    14. Wei-Bin Zhang, 2016. "Population Growth And Preference Change In A Generalized Solow Growth Model With Gender Time Distributions," Oradea Journal of Business and Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 7-30, September.
    15. Wei-Bin Zhang, 2017. "Economic Development and Environmental Change with Endogenous Birth and Mortality Rates," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(1), pages 77-97, March.
    16. Wei-Bin ZHANG, 2014. "Human Capital, Wealth, and Renewable Resources," Expert Journal of Economics, Sprint Investify, vol. 2(1), pages 1-20.
    17. Shu‐Hua Chen & Jang‐Ting Guo, 2018. "On Indeterminacy and Growth under Progressive Taxation and Utility‐Generating Government Spending," Pacific Economic Review, Wiley Blackwell, vol. 23(3), pages 533-543, August.
    18. Wei-Bin Zhang, 2018. "Business Cycles, Growth, And Imported Energy In A Small-Open Growth Model," Oradea Journal of Business and Economics, University of Oradea, Faculty of Economics, vol. 3(2), pages 7-21, September.
    19. Zhang Wei-Bin, 2020. "Economic Development and International and Interregional Tourism," Economic and Regional Studies / Studia Ekonomiczne i Regionalne, Sciendo, vol. 13(4), pages 375-387, December.
    20. Shu‐Hua Chen & Jang‐Ting Guo, 2013. "On indeterminacy and growth under progressive taxation and productive government spending," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 46(3), pages 865-880, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eur:ejesjr:64. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Revistia Research and Publishing (email available below). General contact details of provider: https://revistia.com/index.php/ejes .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.