PROJECT SCHEDULING WITH START-TIME DEPENDENT COST AND IMPRECISE DURATION

The goal of a project manager is generally to minimize the cost of the project and also to cope with uncertainty. This paper deals with the problem of project scheduling a set of activities satisfying precedence constraints in order to minimize the sum of the costs associated with the starting times of the activities in the network with imprecise activity durations, represented by means of interval or fuzzy numbers. So far this problem has been completely solved by several authors when the activities durations have crisp values. However, they do not consider the imprecision in activity durations in their models. Here the framework of possibility theory is proposed to solve this problem. In fuzzy arithmetic, usually, the interval calculations are used for the aim of complexity reduction and simplification. Thus the case of interval-valued durations is first addressed, and then extended to fuzzy intervals. A numerical example is used to illustrate the developed concept.