Benders decomposition for a period-aggregated resource leveling problem with variable job duration

We consider a special case of resource leveling problem with variable job duration and period-aggregated resource consumption. The objective function is to minimize the total extra resource cost required to complete all jobs before the hard project deadline. All jobs must be implemented without any preemption. The planning horizon is divided into periods, each period is characterized by an available level of resources of each type. For each job, resource consumption varies from one period to another. It is possible to control the speed of the job execution: if more resources are allocated to a job, then the job is executed faster if fewer resources are used, the job takes more time. A problem solution defines the start and end times for each job, but also its resource usage per period. On contrary to former models of this problem, our formulation allows an independent resource usage for each resource type. This approach can reach more flexible solutions with lower cost objective function value. We develop a Benders decomposition algorithm to solve this new formulation. Several enhancements are also implemented, such as the construction of effective bounds and multi-cut generation with the single search tree (Branch&Benders cuts). Numerical experiments on several sets of instances demonstrate the advantage of the algorithm in comparison with the basic model and a CPLEX built-in Benders decomposition.