Activity couple with interdependent durations: Serial, parallel or partly overlapping scheduling?

This paper explores a problem of a hammock (sub-project) with two remaining activities, both eligible for execution. The activities can be scheduled in a serial mode, a parallel mode, or a partly overlapping mode. Each activity has alternative execution-modes that are related to the amount of budget allocated. We assume an interdependency between the activity time-cost trade-offs functions that are defined differently if the activities are scheduled separately, or if their schedule is overlapping. The aim is to determine, in the context of different objective functions and budget constraints, the optimal scheduling of the activities, with the appropriate allocation of budget to the activities. The paper presents a deterministic time-cost trade-offs model that takes into account the interdependency between the activity durations and enables decision makers to meet the above aim. Extension of the model and the analysis for the case where the activity durations are stochastic, are also examined. The paper reveals that when activity durations are stochastic, the optimal scheduling can be completely different from that of the deterministic case. Theoretical analysis and a case study provide numeric results that illustrate the difference between the deterministic and the stochastic solutions.