Multi-Mode Project Scheduling with Limited Resource and Budget Constraints

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In this research paper, we figure out multi-mode project scheduling problem where resources are limited and project scheduling cost is fixed. An activity of the project may be executed by a resource in a chosen mode. These multi-modes are relying on project duration time, time lags to other activities and requirement of resources. A multi-mode resource constrained project scheduling problem can be formally prescribed by a number of activities-nodes with several modes that should be scheduled to minimize the project duration, subject to generalized precedence relations with limited resources. The most common exact approaches for solving these problems are based on branch-and-bound algorithm, linear programming and boolean satisfiability (SAT). We consider, Mixed Integer Linear Programming (MILP) for modeling and solving the project scheduling problem with limited resources, budget constraints and activity precedence relations. In this paper, we propose a mathematical model for finding its optimal solution. We jointly consider to make sure that, the project duration is minimized, while maintaining the budget limit and incorporate multiple types of computational resources. The performance evaluation results carried out in CPLEX optimization tool, show that the proposed model outperforms existing approaches in terms of project completion time and project cost.