Resource Tardiness Weighted Cost Minimization in Project Scheduling

In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem, the project is subject to renewable resources, each renewable resource is available for limited time periods during the project life cycle, and keeping the resource for each extra period results in some tardiness penalty cost. We introduce a branch and bound algorithm to solve the problem exactly and use several bounding, fathoming, and dominance rules in our algorithm to shorten the enumeration process. We point out parameters affecting the RCPSP-TWRTPC degree of difficulty, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using the customized algorithm and also CPLEX solver. We analyze the algorithm behavior with respect to the changes in instances degree of difficulty and compare its performance for different cases with the CPLEX solver. The results reveal algorithm efficiency

A Modified PSO Algorithm for Minimizing the Total Costs of Resources in MRCPSP

We introduce a multimode resource-constrained project scheduling problem with finish-to-start precedence relations among project activities, considering renewable and nonrenewable resource costs. We assume that renewable resources are rented and are not available in all periods of time of the project. In other words, there is a mandated ready date as well as a due date for each renewable resource type so that no resource is used before its ready date. However, the resources are permitted to be used after their due dates by paying penalty costs. The objective is to minimize the total costs of both renewable and nonrenewable resource usage. This problem is called multimode resource-constrained project scheduling problem with minimization of total weighted resource tardiness penalty cost (MRCPSP-TWRTPC), where, for each activity, both renewable and nonrenewable resource requirements depend on activity mode. For this problem, we present a metaheuristic algorithm based on a modified Particle Swarm Optimization (PSO) approach introduced by Tchomté and Gourgand which uses a modified rule for the displacement of particles. We present a prioritization rule for activities and several improvement and local search methods. Experimental results reveal the effectiveness and efficiency of the proposed algorithm for the problem in question