Abstract
In this study, we consider a resource constrained project scheduling problem with variable activity intensity. In this problem, the resource consumption of an activity is a variable and is proportional to the activity intensity. Based on the theory of Leontief production functions, Hackman and Leachman 【1989】 first introduce the concept of activity intensity. Leachman et al.【1990】 apply the theory of Leontief production functions to project scheduling problem and propose that the resource consumption is proportional to activity intensity, and the activity duration is the reciprocal of the activity intensity. Therefore, the activity intensity can be used to establish the relationship between resource consumption and activity duration in a resource constrained project scheduling problem. However, our literature survey reveals that only a few studies focused on this type of problem. These researchers used a nonlinear program or a mixed integer linear program to model the problem. If a heuristic approach is used, it cannot guarantee an optimal solution. Hence, we propose an approach that uses a linear program formulation. To use linear program, we have to take care of two problems. The first problem is that the actual relationship between intensity and duration is nonlinear convex function. In this study, we propose to use piece-wise linear curve to approximate the nonlinear convex curve. The second problem is that there are many feasible event sequences. An event sequence unique determines a set of resource constraints of its corresponding linear programming problem. Therefore, by solving all the linear programs of all the feasible event sequence, we can obtain the optimal solution of the resource constrained projected scheduling problem. Keywords: resource constrained project scheduling, variable intensity activities,linear programming, piece-wise linear curve