# An investigation of matrix generators for coverting time-cost trade-off data into mathematical programming format

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The purpose of this thesis is to demonstrate the development of the time-cost trade-off problem in mathematical programming format and to demonstrate the development of a matrix generator for the conversion of critical path data into mathematical programming format. The advent of large scale mathematical programming systems has made the solution of the time-cost trade-off problem feasible. These systems use special techniques which allow larger problems to be solved. Post- optimal procedures allow the analyst to determine the sensitivity of the model to various time-cost functions. Theoretically, the analyst faced with a project scheduling problem may bring the above techniques to bear on it. However, in practice such a formulation would be a tedious task. The matrix generator is proposed as a solution to this problem. The procedure used is to develop the mathematical programming formulation of the time-cost trade-off problem. The development includes linear, nonlinear convex, nonlinear non-convex, and penalty/bonus functions. Next the steps necessary to convert the data into mathematical programming format are considered. Finally, a sample problem is used to illustrate the procedure.