Scheduling projects with variable-intensity activities: The case of dynamic earliness and tardiness costs

This paper addresses the problem of resource-constrained multi-project scheduling with variable-intensity activities. Four dynamic models, based on four types of precedence relations are presented to minimize dynamic earliness and tardiness of project activities. The first two models are designed to cope with start-to-end precedence relations via unit step functions and specially constructed penalty functions respectively. Conditions are derived for the case when an optimal solution of the second model with relaxed start-to-end precedence relations is the global optimal solution of the first model. The third and the fourth models are dealing with overlapping precedence relations based on a milestone approach and on start-to-start precedence relations with lags respectively. The relationship between the four models is studied and a lower bound on the objective function is proposed. An efficient time-decomposition approach is adopted for solving the last three models. This approach is used to guide an effective search for the solution of the first model.