An Optimal Approach for Minimization of Total Costs in the Multi-mode Resource-constrained Project Scheduling Problem

In this paper, we introduce a new multimode project scheduling problem, taking into account finish-to-start precedence relations among project activities as well as renewable and nonrenewable resources constraints. We suppose renewable resources are hired and not accessible in all time intervals of a project. In other words, there is a presumed release date as well as a mandated due date for each renewable resource type such that no resource can be available before its release date. However the resources are allowed to be executed later than their due dates by remitting penalty costs based on the resource type. The objective is to minimize the entire costs of renewable and nonrenewable resources, called multi-mode resource-constrained project scheduling problem, minimization of total weighted resource tardiness penalty cost (MRCPSP-TWRTPC) where nonrenewable resource costs depend on the activity modes. In this paper, we present a branch and bound algorithm to deal with this extended type of MRCPSP. A numerical example is presented to describe our branch and bound approach in more details. Experimental results reveal the capability of the proposed algorithm in solving the problem in question particularly for the small and medium sized test functions.