Tolerance Approach to Sensitivity Analysis in Multiobjective Transportation Problem


  • Modern College of Arts, Science and Commerce, Department of Mathematics, Shivajinagar, Pune, 411005, India
  • Faculty of Civil Engg., College of Military Engineering, Department of Mathematics, Pune, 411 031, India


This paper represents ordinary sensitivity analysis and tolerance approach to sensitivity analysis in supply and demand values of the multiobjective transportation problem. Our proposed approach allows simultaneous and independent changes in the supply and demand values. The aim of this paper is to find the ranges for each supply and demand value within which the changes can occur without affecting the current basis of the best compromise solution. We have used the best compromise solution obtained using fuzzy programming technique for the postoptimality analysis of the multiobjective transportation problem. The approach is illustrated by a numerical example.


Multiobjective transportation problem, the best compromise solution, sensitivity analysis, tolerance analysis, fuzzy linear programming, membership function

Full Text:


H. Arsham, Postoptimality analyses of the transportation problem, J. Operational Res. Soc., (1992), 121–139.

H. Arsham and M. Oblak, Perturbation analysis of general lp models: A unified approach to sensitivity, parametric, tolerance, and more-for-less analysis, Mathematical and Computer Modelling, 13. (8)(1990), 79–102.

N. M. Badra, Sensitivity analysis of transportation problems, J. Appl. Sc. Research, 3. (8)(2007), 668–675.

A. K. Bit, M. P. Biswal and S S Alam, Fuzzy programming approach to multicriteria decision making transportation problem, Fuzzy sets and Systems, 50. (2)(1992), 135–141.

Dilip V. Deshpande and Stanley Zionts, Sensitivity analysis in multiple objective linear programming: changes in the objective function matrix, Multiple Criteria Decision Making Theory and Application, Springer, (1980), 26–39.

S. Doustdargholi, D Derakhshan Asl and V Abasgholipour, Sensitivity analysis of right hand-side parameter in transportation problem, Applied Mathematical Sciences, 3. (30)(2009), 1501–1511.

Carlo Filippi, A fresh view on the tolerance approach to sensitivity analysis in linear programming, European journal of operational research, 167. (1)(2005), 1–19.

R. Flavell and G. R. Salkin, An approach to sensitivity analysis, Journal of the Operational Research Society, 26. (4)(1975), 857–866.

Pierre Hansen, Martine Labbe and Richard E. Wendell, Sensitivity analysis in multiple objective linear programming: The tolerance approach, European J. Operational Research, 38. (1)(1989), 63–69.

Milan Hladik, Tolerance analysis in linear systems and linear programming, Optimization Methods and Software, 26. (3)(2011), 381–396.

Milan Hladik and Sebastian Sitarz, Maximal and supremal tolerances in multiobjective linear programming, European J. Operational Research, 228. (1)(2013), 93–101.

K. Kavitha and P. Pandian, Type II sensitivity analysis in degeneracy interval transportation problem, J. Innovative Research and Solutions, 1 (2015), 67–76.

Sebastian Sitarz, Approaches to sensitivity analysis in MOLP, International J. Information Tech. and Computer Sc., 6. (3)(2014), 54–60.

Richard E. Wendell, Using bounds on the data in linear programming: The tolerance approach to sensitivity analysis, Mathematical Programming, 29. (3)(1984), 304–322.

Richard E. Wendell, The tolerance approach to sensitivity analysis in linear programming, Management Science, 31. (5)(1985), 564–578.

Richard E. Wendell and Wei Chen, Tolerance sensitivity analysis: Thirty years later, Croatian Operational Research Review, 1. (1)(2010), 12–21.


  • There are currently no refbacks.