Optimization of group incentive schemes

This paper considers the problem of motivating the reduction of project duration. The duration cuts of project works and the corresponding costs are given. A group incentive scheme is used to compensate for the costs. In this scheme, all works are partitioned into groups and a unified incentive scheme is applied for each group. Two types of unified incentive schemes are studied for groups, namely, linear and jump ones. The problem is to partition all project works into groups and choose an appropriate incentive scheme for each group by minimizing the total incentive fund. Solution algorithms are proposed based on determining the shortest path in the network. Special cases are also analyzed (partition with the minimum number of groups and partition with the maximum number of groups).