Solving the Resource Constrained Project Scheduling Problem to Minimize the Financial Failure Risk

Abstract

In practice, a project usually involves cash in- and out- flows associated with each activity. This paper aims to minimize the payment failure risk during the project execution for the resource-constrained project scheduling problem (RCPSP). In such models, the money-time value, which is the product of the net cash in-flow and the time length from the completion time of each activity to the project deadline, provides a financial evaluation of project cash availability. The cash availability of a project schedule is defined as the sum of these money-time values associated with all activities, which is mathematically equivalent to the minimization objective of total weighted completion time. This paper presents four memetic algorithms (MAs) which differ in the construction of initial population and restart strategy, and a double variable neighborhood search algorithm for solving the RCPSP problem. An experiment is conducted to evaluate the performance of these algorithms based on the same number of solutions calculated using ProGen generated benchmark instances. The results indicate that the MAs with regret biased sampling rule to generate initial and restart populations outperforms the other algorithms in terms of solution quality. payment failure risk during the project execution. To achieve this goal, the money-time value, which is the product of the cash in-flow and the length from the time the cash received to the project makespan, can provide a financial evaluation of project cash availability. The cash availability of a project schedule is defined as the total money-time values associated with all activities. This financial metric does not consider discount rate, and it will provide a conservative estimate of cash in-flows during the project execution, since cash on hand will grow in value over time. In the proposed model, the cash in-flows are assumed to occur at the completion time of each activity, and the cash amounts can be used during the rest of project execution time. Hereafter, we shall refer to this model as the project cash availability maximization problem (PCAMP) for the resource constrained project scheduling problem (RCPSP). The PCAMP is mathematically equivalent to the RCPSP with the objective of minimizing total weighted completion time (also known as total weighted flow time). This problem is strongly NP-hard since its sub-problem, single machine scheduling with total flow time minimization objective subject