A honey bee swarm optimization algorithm for minimizing the total costs of resources in MRCPSP

In this paper, we solve an extended type of multimode project scheduling problem considering renewable and non-renewable resource constraints and finish-to-start precedence relations among project activities. We suppose that renewable resources are hired and are not accessible in the whole duration of the project. Therefore, there is an assigned ready date as well as a due date for each renewable resource type so that no resource can be rented before its ready date. But, the resources are allowed to be used after their due dates by incurring penalty costs. The aim is to minimize the whole charges of both renewable and nonrenewable resource usage. This problem is introduced by Khalilzadeh et al.⁷ as multi-mode resource-constrained project scheduling problem minimizing the net present value of entire weighted resource tardiness penalty costs (MRCPSP-DCTWRTPC) in which both renewable and nonrenewable resource restrictions rely on activity mode. The problem we proposed in this paper is the extended form of the problem introduced by Khalilzadeh et al.⁷ with considering the discounted cash flows of the resource costs. We call this problem multi-mode resource-constrained project scheduling problem, minimization of discounted cash flows of total weighted resource tardiness penalty cost (MRCPSP-DCTWRTPC). For this problem, we propose a novel meta-heuristic algorithm based on a Honey Bee Swarm Optimization (HBSO) approach together with a prioritization rule for project tasks and numerous improvement and local search procedures. Computational results prove the effectiveness and efficiency of the presented method.