Exact solution of one production scheduling problem

Abstract

In this study, one variant of multi-product scheduling problem is considered. The problem asks to find the optimal selection of a set of tasks to produce a given number of products in required amounts, to allocate the task on units, and to find the order of execution of tasks for each unit. The production rates for each task, the task-unit suitability matrix, and the sequence dependent changeover times for task pairs are given. For the one-unit problem, two combinatorial algorithms are proposed: a branch-and-bound algorithm and a parallel dynamic programming algorithm. The last one is implemented using the CUDA library for running on a Graphical Processing Unit (GPU). For the multiple-units problem, both approaches are combined in a branch-and-bound algorithm with bounds provided by the dynamic programming procedure. The algorithms are compared with CPLEX solver applied to the considered problem formulated as a mixed integer linear program. Although, the main limitation of using the proposed algorithms is a requirement of large amount of memory, the experiments showed their superior performance over CPLEX in terms of running time for rather large sized instances. The advantage of parallelization and using the GPU is also demonstrated.