A flexible job shop cell scheduling with sequence‐dependent family setup times and intercellular transportation times using conic scalarization method

Abstract

In this paper, we propose novel mathematical models involving both single‐ and biobjective functions that deal with a flexible job shop scheduling problem in cellular manufacturing environment by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence‐dependent family setup times, and recirculation. The problem has been known as NP‐hard. The proposed models have been tested and solved using Lingo 11.0 with minimization of makespan for the problems involving about 4 cells, 4 part families, 15 parts, and 12 machines. The most suitable model among the proposed single‐objective models is determined using the test results. Then, another objective function as total tardiness is added to this model. The obtained biobjective model is solved using the scalarization methods, the weighted sum method, ɛ‐constraint method, and conic scalarization method (CSM), in order to convert the mathematical model's objectives into a single‐objective function. By utilizing these scalarization methods, the Pareto effective solutions are generated for a specific test problem. The advantages of the CSM are demonstrated by considering the Pareto effective solutions.

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“…They presented a nonlinear 0-1 integer programming to minimize inter-cell material handling costs, the fixed costs of machines and workers, and the operating costs of machines and workers by taking into consideration multi-skilled machines and workers and operation sequence. Deliktas et al [49] proposed four nonlinear multi-objective models to handle a flexible job shop scheduling problem in a CM environment. They considered intercellular movements, intercellular transportation times, exceptional parts, sequence-dependent family setup times, and recirculationa part may visit more than once in a machine or work center.…”

A New Mathematical Model for the Integrated Solution of Cell Formation and Part Scheduling Problem

“…Halat and Bashirzadeh [15] have presented a mathematical model which has linear structure for CPS problem and used a concurrent approach to schedule jobs in cells. Deliktas et al [36] have presented new nonlinear multi objective models for flexible job shop scheduling problem in cellular environment. Mainly, exceptional parts, sequence dependent family setup times, intercellular transportation times and recirculation have been considered.…”

An effective algorithm for flexible assembly job‐shop scheduling with tight job constraints

“…Deliktaş et al. (2017) addressed FJSP in a cellular manufacturing environment by considering exceptional parts, intercellular moves, intercellular transportation times, sequence‐dependent family setup times, and recirculation. In addition, Nouri et al.…”

“…Gao examined the FJSP (Gao et al, 2015) and MO-FJSP (Gao et al, 2016a(Gao et al, , 2016b) using fuzzy processing time. Deliktaş et al (2017) addressed FJSP in a cellular manufacturing environment by considering exceptional parts, intercellular moves, intercellular transportation times, sequence-dependent family setup times, and recirculation. In addition, Nouri et al (2017) proposed a hybrid metaheuristics-based clustered holonic multiagent model for solving the FJSP, and some new upper bounds of four sets of well-known benchmarks are found.…”