Stochastic Bottleneck Multi-Resource Generalized Assignment Problem

The bottleneck multi-resource generalized assignment problem (B-MRGAP) is the assignment of jobs to capacitated resources (periods) of agents to minimize the maximum agent load. The problem of assigning the products (tasks) that a firm has to supply to its sub-industries considering more than one period is an example of B-MRGAP. In this problem, any change in product demands will also change the resource consumption amounts of the tasks in the sub-industries. Since changes in production quantities are common in many sectors, handling resource consumption quantities as stochastic rather than deterministic will lead to more realistic solutions. In this study, resource consumption amounts in B-MRGAP are handled as stochastic. To solve this problem, a two-stage stochastic programming model has been developed. The performance of the proposed method is demonstrated by using randomly generated test problems. When the test results were examined, it was seen that even in small-sized problems, handling the problem stochastically made a contribution. In addition, it was revealed that the contribution increased as the number of agents, the number of tasks, and the resource consumption variability increased.