reverse flow

The Flexible Job shop Scheduling Problem (FJSP), as a Production Scheduling Problem (PSP), is generally an extension of the Job shop Scheduling Problem (JSP). In this paper, the FJSP with reverse flow consisting of two flows of jobs (direct and reverse) at each stage is studied; the first flow initiates in Stage 1 and goes to Stage C (the last stage), and the second flow starts with Stage c and ends up in Stage 1. The aim is to minimize the makespan of the jobs (the maximum completion time). A Mixed Integer Programming (MIP) is presented to model the problem and the Branch and Bound (B&B) method is used to solve the problem. A numerical small-size problem is presented to demonstrate the applicability, for which the Lingo16 software is employed for a solution. Due to the NP-hardness of the problem, a meta-heuristic, namely the Vibration Damping Optimization (VDO) algorithm with tuned parameters using the Taguchi method, is utilized to solve large-scale problems. To validate the results obtained using the proposed solution algorithm in terms of the solution quality and the required computational time, they are compared with those obtained by the Lingo 16 software for small-size problems. Finally, the performance of the proposed algorithm is compared with a Genetic Algorithm (GA) by solving some randomly generated larger-size test problems, based on which the results are analyzed statistically. Computational results confirm the efficiency and effectiveness of the proposed algorithm and show that the VDO algorithm performs well.

This paper discusses the modeling and solution of a flexible flow shop scheduling problem with forward and reverse flow (FFSP-FR). The purpose of presenting this mathematical model is to achieve a suitable solution to reduce the completion time (Cmax) in forward flow (such as assembling parts to deliver jobs to the customer) and reverse flow (such as disassembling parts to reproduce parts). Other important decisions taken in this model are the optimal assignment of jobs to each machine in the forward and reverse flow and the sequence of processing jobs by each machine. Due to the uncertainty of the important parameters of the problem, the Fuzzy Jiménez method has been used. The results of the analysis with CPLEX solver show that with the increase in the uncertainty rate, due to the increase in the processing time, the Cmax in the forward and reverse flow has increased. GA, ICA and RDA algorithms have been used in the analysis of numerical examples with a larger size due to the inability of the CPLEX solver. These algorithms are highly efficient in achieving near-optimal solutions in a shorter time. Therefore, a suitable initial solution has been designed to solve the problem and the findings show that the ICA with an average of 273.37 has the best performance in achieving the near-optimal solution and the RDA with an average of 31.098 has performed the best in solving the problem. Also, the results of the T-Test statistical test with a confidence level of 95% show that there is no significant difference between the averages of the objective function index and the calculation time. As a result, the algorithms were prioritized using the TOPSIS method and the results showed that the RDA is the most efficient solution algorithm with a utility weight of 0.9959, and the GA and ICA are in the next ranks. Based on the findings, it can be said that industrial managers who have assembly and disassembly departments at the same time in their units can use the results of this research to minimize the maximum delivery time due to the reduction of costs and energy consumption, even though there are conditions of uncertainty