Resource constrained project scheduling and material ordering problem with discounted cash flows

Integration of project scheduling (PS) with materials ordering has received greater attention in the last three decades as an approach to ensure the profitability of a project. The fundamental concern of the material ordering integrated PS is to select the right supplier of the right material by placing an order at the right time so that the ordering, purchasing, and holding cost of the materials are minimized which finally maximizes the project's profitability. This study proposes a mathematical model and solution approach for a resource constrained project scheduling and material ordering problem with discounted cash flows (RCPS-MOP-DC). The mathematical model for this proposed RCPS-MOP-DC considers decisions regarding materials ordering, supplier selection, transportation and inventory of the raw materials. A mixed integer programming (MIP) model has been proposed for this RCPS-MOP-DC with the objective to maximize the project's net present value (NPV). A meta-heuristic approach by hybridizing genetic algorithm (GA) and immune algorithm (IA) is proposed as a potential solution approach for this RCPS-MOP-DC model. Performance of this hybridized GA and IA (IGA) approach is compared and contrasted with its constituent algorithms (GA and IA) to validate the effectiveness of this hybridization. Performance of the IGA is further improved by applying a forward-backward improvement (FBI) based local search technique. A restart mechanism is also incorporated in the algorithms which ensures diversity and helps to avoid becoming trapped in local optima. The Taguchi Design of Experiment (DOE) is used to investigate the impact of various parameters and to determine the appropriate parameter sets for the proposed algorithms. The performance of this proposed solution approach has been tested on varied self-generated RCPS-MOP-DC instances ranging from 30 to 120 activities. The results show that the hybrid IGA outperforms GA and IA in terms of the project's NPV.