Concurrent scheduling and lot sizing in a flexible flow shop environment considering intermediate and public buffers

Abstract

Due to the special position of the scheduling and lot sizing of flow shop scheduling systems in production centers, these issues have received a lot of attention in recent years. The problems of scheduling and lot sizing are among the most important and at the same time the most difficult problems related to production planning. One common assumption in these cases is the assumption of unlimited buffer capacity between different workstations. In real industrial environments, the buffer capacity between two consecutive stations may be limited due to the physical dimensions of the products and the lack of space. Limited buffer capacity may cause blocking. Blocking occurs when the buffer capacity is full and the previous machine cannot release the job it has completed. In such cases, this machine will hold the job until one of the jobs in the queue (buffer) is removed from the queue and its processing will begin on one of the machines at the next station. Due to the importance of this issue, in the present study the concurrent scheduling and lot sizing of the flexible flow shop scheduling problem considering buffer constraints between workstations and public buffer is investigated which is multi-period and multi-product and the capacity of the machines is also limited. Also, among the buffers, middle buffers have a higher priority to be filled than the public buffer. In order to realize this condition, a cost has been defined for sending jobs to the public buffer. For the mentioned problem, a Mixed Integer Non Linear Programing (MINLP) model is presented. The objective of this model is to minimize the production, maintenance and external supply costs. The General Algebraic Modeling System (GAMS) software is used to solve the model. Due to the complexity of the model and the NP- hardness of the proposed problem, the Hybrid Discrete Artificial Bee Colony (HDABC) is proposed to solve large-scale problems. In order to evaluate the performance of the proposed algorithm, numerical sample problems in different sizes are solved using this algorithm, the GAMS software as well as the genetic algorithm and the Simulated Annealing Algorithm-based Hopfield Neural Network algorithm (SAA–HNN) algorithm. Computational results demonstrate the effectiveness of the proposed algorithm for the considered problem.