On the nucleolus of the basic vehicle routing game

Mathematical Programming, Series B

Volumn 72, Issue 1, 1996, Pages 83-100

  Göthe Lundgren, Maud ^a   Jörnsten, Kurt ^b   Värbrand, Peter ^a  

^a LINKÖPING INSTITUTE OF TECHNOLOGY   (Sweden)

^b NORWEGIAN SCHOOL OF ECONOMICS   (Norway)

Author keywords

Co operative game theory; Constraint generation; Cost allocation; Vehicle routing problem

Indexed keywords

EID: 0042267452     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02592333     Document Type: Article

References (17)

1. E. Balas, "The prize collecting traveling salesman problem," Networks 19 (1989) 621-636.
2. M.L. Balinski and R.E. Quandt, "On an integer program for a delivery problem," Operations Research 12, (1964) 300-304.
3. L. Bodin, B. Golden, A. Assad and M. Ball, "Routing and scheduling of vehicles and crews: The state of the art," Computers & Operations Research 10 (1983) 62-212.
4. N. Christofides and S. Eilon, "An algorithm for the vehicle dispatching problem," Operational Research Quarterly 20 (1969) 309-318.
5. M. Desrochers, J. Desrosiers and M. Solomon, "A new optimization algorithm for the vehicle routing problem with time windows," Operations Research 40 (1992) 342-354.
6. I. Dragan, "A procedure for finding the nucleolus of a cooperative n person game," Zeitschrift für Operations Research 25 (1981) 119-131.
7. M. Dror, "Cost allocation: The traveling salesman, binpacking, and the knapsack," Applied Mathematics and Computation 35 (1990) 191-207.
8. M. Fischetti and P. Toth, "An additive approach for the optimal solution of the prize-collecting travelling salesman problem," in: B.L. Golden and A.A. Assad, (Eds.) Vehicle Routing: Methods and Studies, Studies in Management Science and Systems vol. 16, (North-Holland, Amsterdam, 1988) pp. 319-344.
9. P.C. Gilmore, R.E. Gomory, "A linear programming approach to the cutting stock problem," Operations Research 9 (1961) 849-859.
10. B.L. Golden and A.A. Assad, eds., Vehicle Routing: Methods and Studies, Studies in Management Science and Systems, Vol. 16 (North-Holland, Amsterdam, 1988).
11. A. Hallefjord, R. Helmig and K. Jörnsten, "Calculation of the nucleolus when the characteristic function is given implicitly: A constraint generation approach," Internal Report, Chr. Michelsen Institute, Bergen, Norway (1988).
12. A. Kopelowitz, "Computation of the kernels of simple games and the nucleolus of n person games," Research Memorandum No. 31, Department of Mathematics, The Hebrew University of Jerusalem (1967).
13. G. Laporte and S. Martello, "The selective travelling salesman problem, " Discrete Applied Mathematics 26 (1990) 193-207.
14. S. Martello and P. Toth, "An upper bound for the zero-one knapsack problem and a branch and bound algorithm," European Journal of Operational Research 1 (1977) 169-175.
15. M. Maschler, B. Peleg and L.S. Shapley, "Geometric properties of the kernel, nucleolus, and related solution concepts," Mathematics of Operations Research 4 (1979) 303-338.
16. D. Schmeidler, "The nucleolus of a characteristic function game," SIAM Journal on Applied Mathematics 17 (1969) 1163-1170.
17. A, Tamir, "On the core of a traveling salesman cost allocation game," Operations Research Letters 8 (1989) 31-34.