A mathematical model for the continuous time/resource trade-off problem

This paper presents an exact model for the resource-constrained project scheduling problem in situations involving continuous time/resource trade-off. The duration of an activity is treated as a continuous function of the resource requirements and duration reduction (crashing) is allowed. All resources considered are renewable. The objective is to determine an amount of resources allocated to an activity (as a percentage), a duration (amount of crashing), and a start time for each activity so that all constraints are obeyed and the project duration is minimized. Project scheduling of this type occurs in many fields, for instance to predict the resources and durations of activities in industrial processes. The proposed model has been inspired by the rectangle packing problems. A key feature of the model is that none of the typical models can cope with the continuous resource constraints.