Effect Of The Changes In The Weights On The Solution Of The Preemptive Weighted Linear Goal Programming Problems
M. O. Wankhade, H. S. Lunge
Key words: Linear Goal Programming, Preemptive weighted goal programming, achievement function.
Abstract: The purpose of this paper is to study the effect of the changes in the weights (w+ik, w-ik) of the deviational variables (ni, pi, ni+pi) in the achievement function of the Weighted Linear Goal Programming Problem (GPP). If the weights of the deviational variables associated with priority levels are increased/decreased Lee’s Modified Simplex method showed that an achievement level of unachieved priorities are decreased/increased respectively and the values of decision variables remain unchanged. While the standard simplex method showed that if the weights of the deviational variables are increased/decreased, an achievement level of the priorities are decreased/increased respectively, the values of decision variables remain unchanged for some weighting structures and there exist some other weighting structures for which the solution of GPP is changed. Thus Standard simplex method can be used for solution and sensitivity analysis of a particular class of WGPP.
 Charnes A. and Cooper W. (1977), “Goal programming and multiple objective optimizations. Part I”, European Journal of Operational Research, Vol. 1, 39-54.
 Ignizio J. P. and Romero C. (2003), “Goal programming”, Encyclopedia of information systems, Elsevier Science, vol. 2, 489-500.
 Iskander M. G. (2012), “A Suggested Approach for Solving Weighted Goal Programming Problem” American Journal of Computational and Applied Mathematics 2(2): 55-57
 Jones D. F. (2011), “A practical weight sensitivity algorithm for goal and multiple objective programming”, European Journal of Operational Research, 213, pp. 238-245.
 Jones D. F., Tamiz M. (2010), Practical Goal Programming, Springer, New York.
 Latinopoulos D. and Mylopoulos Y. (2005), “Optimal Allocation of Land And Water Resources In Irrigated agriculture by Means of Goal Programming: Application In Loudias River Basin” Global Nest Journal, Vol 7, No 3, Pp 264-273
 Lee S. M. (1972), “Goal programming for decision analysis”, Auerbach, Philadelphia.
 Romero C. (2004), “A general structure of achievement function for a goal programming model”, European Journal of Operational Research, 153, 3, 675-686.
 Tamiz M., Jones D. F, Romero C. (1998), “Goal programming for decision making: An overview of the current state-of-the- art”, European Journal of Operational Research 111, 569-581
 Timo Salmi: LINSOLVE software; University of Vassa.