Integrated Material Lot Sizing and Multi-Resource Leveling Models with Activity Splitting
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In the project management literature, project scheduling and material procurement problems are often studied separately and are addressed following a sequential approach. The few papers in the literature that integrated both problems assumed that materials are ordered and received prior to their needed activities. This research will contribute to the project management literature by developing mathematical models that integrate project scheduling and material lot sizing decisions when dealing with renewable and consumable resources having constant and variable consumption rates. The formulated models minimize renewable resource leveling related costs and material ordering and inventory associated costs for consumable resources. The models allow activity splitting to smooth the utilization of renewable resources and to optimally schedule the ordering of consumable resources. Both models with time independent and dependent rates of consumption are formulated as mixed integer linear programs. Sensitivity analysis is performed to assess the effect of varying the problem's parameters on the total project cost savings realized after the integration of leveling and ordering decisions. The results show that under certain values of the problem parameters, the integrated decision approach achieved significant cost savings compared to the sequential decision approach. While low holding costs resulted in low cost savings, high holding costs significantly boosted cost savings. Furthermore, the numerical results show that the time-variation of the resource utilization rates has an effect on cost savings. The results of the sensitivity analysis also show that reductions in both resource leveling and material ordering related costs are realized when non-critical activities are allowed to split. Among all input parameters analyzed, the ordering and holding costs had the greatest effect on the total project costs. However, for large values of the ordering and holding costs, cost savings from splitting are not significant. Thus, every cost element in the objective function has an effect on either total holding costs or resource leveling and a project manager has to consider both leveling related costs and material related costs at the same time in order to find the optimal and minimum project cost.