Minimizing makespan in a Flow Shop Sequence Dependent Group Scheduling problem with blocking constraint

Abstract

Flow Shop Sequence Dependent Group Scheduling (FSDGS) problems gathered much attention from the body of literature in recent years. Nevertheless, the combination of blocking constraint and Group Technology (GT) principles has not been faced by academics so far. The aim of the present paper is to propose an original meta-heuristic approach for minimizing makespan in a FSDGS problem with blocking constraint. To this end, a novel Parallel Self-Adaptive Genetic Algorithm (PSAGA) which adaptively varies the genetic parameters along the evolutionary mechanism was devised. Validation of the proposed metaheuristics was performed by means of the global optima generated by a proper mixed integer linear programming model. An extended experimental campaign, also supported by a specific statistical analysis, demonstrates the effectiveness of the proposed approach compared to other meta-heuristics arising from the relevant literature.

Introduction

Group Technology (GT) is a manufacturing philosophy aiming at increasing production efficiency by grouping parts and products with similar design or process requirements in order to reduce setup time and cost, simplify material flow and handling, rationalize design and standardize production processes (Ham et al., 1985). Whenever GT principles are applied in scheduling activities, a Group Scheduling (GS) problem arises. In GS problems, jobs belonging to the same group are processed sequentially with no interruption by jobs of other groups. A major setup is required on each machine when switching from one group to another, whereas setup times between jobs of the same group are usually negligible. With special reference to flow shop environments, the issue is commonly known as the Flow Shop Group Scheduling (FSGS) problem or, if setup time of groups are sequence-dependent, as the Flow Shop Sequence-Dependent Group Scheduling (FSDGS) problem.

FSGS and FSDGS problems typically arise in Cellular Manufacturing (CM) environments (Costa et al., 2014a, Costa et al., 2014b), where the shop floor is divided into smaller organizational units called manufacturing cells, each of which produces certain groups, or families, of jobs. However, such class of scheduling problems has been largely studied by literature with reference to many other practical applications, such as furniture production (Wilson et al., 2004), label sticker manufacturing (Lin and Liao, 2003), automotive paint and body shops (Salmasi et al., 2010), electronics industry (Gelogullari and Logendran, 2010).

In a comprehensive review about this topic, Neufeld et al. (2016) examined all the real-world implication of flow shop group scheduling problems, as well as the solution method proposed by the relevant literature. Metaheuristic algorithms are by far the most recurring optimization procedure for solving such a challenging issue. A pioneer metaheuristic approach was proposed by Vakharia and Chang (1990), who developed a Simulated Annealing (SA) algorithm for the FSGS problem in a manufacturing cell. Later, Skorin-Kapov and Vakharia (1993) demonstrated that a Tabu Search (TS) algorithm can reach better performances than SA for the same problem. The SA algorithm was also used by Sridhar and Rajendran (1994) to assess performances of a Genetic Algorithm (GA) specifically developed for the same problem. The comparison between TS and GA approaches was finally performed by Schaller (2000) who demonstrated as a properly adjusted Tabu Search algorithm may lead to better performance.

In order to fit the real-world industrial practice, the recent literature has been mainly focusing on flow shop group scheduling problems with sequence-dependent setup times. Franca et al. (2005) proposed a Genetic Algorithm and a Memetic Algorithm (MA) embedding a Local Search (LS) scheme for the FSDGS problem. Both algorithms used a compact representation of solutions and a hierarchically structured population where the number of possible neighbor solutions is limited by dividing the population into clusters. Bouabda et al. (2011) developed a cooperative optimization approach including a Genetic Algorithm and a Branch and Bound (BB) procedure, with the BB probabilistically integrated in the GA in order to enhance current solutions. Naderi and Salmasi (2012) formulated two different MILP models for the FSDGS problem under the total completion time minimization objective, as well as a metaheuristic procedure hybridizing GA and SA algorithms, called SGA, specifically developed for large-sized instances.

Costa et al. (2014b) developed a Mixed Integer Linear Programming (MILP) model and three GA-based metaheuristic algorithms for the FSDGS problem with skilled workforce assignment, proposing a trade-off analysis between manpower cost and makespan improvement. Nikjo and Zarook (2014) addressed a dynamic manufacturing cell scheduling problem with agreeable job release dates for each part family and setup times dependent on the sequence of part within families. The authors proposed and compared under several measures of performance two distinct approaches, namely a GA and a TS. Recently, Shahvari and Logendran (2016) addressed a bi-objective hybrid flow shop batching and scheduling problem with sequence-dependent family setup times, developing specific tabu search/path-relinking algorithms. Costa et al., 2017a, Costa et al., 2017b embedded a Biased Random Search (BRS) technique in a Genetic Algorithm to tackle the FDSGS problem under the makespan minimization objective, demonstrating the superiority of the proposed metaheuristic procedure in respect of the best performing algorithms recommended by literature. They also proved the effectiveness of their optimization procedure for the FSDGS problem with skilled workforce assignment and learning effect. Sabouni and Logendran (2018) addressed a flow-shop group scheduling problem in the assembly of Printed Circuit Boards (PCBs), proposing search algorithm and lower bounds for large-sized problems instances. Shahvari and Logendran (2018) studied a hybrid flow shop batch scheduling problem with sequence- and machine-dependent family setup times with the objective of simultaneously minimizing the weighted sum of the total weighted completion time and total weighted tardiness. They proposed robust meta-heuristics based on hybridization of local search and population-based structures along with the stage-based interdependency strategy to solve the research problem.

Despite the sizeable interest for group scheduling problems in industry, sequencing families of jobs in a flow shop environment under the blocking constraint has not received so much attention by literature, so far. To the best of our knowledge, Logendran and Sriskandarajah (1993), who studied a two-machine FSGS cellular manufacturing system, were the only one to provide a contribution to such a demanding issue. Nevertheless, blocking conditions widely exist in modern manufacturing and production environments, typically where buffer inventories are not allowed due to just-in-time strategies. When the blocking constraint is introduced in a flow shop manufacturing system, every completed job must remain on its current machine, preventing any other successive job from being processed, until the downstream machine is available (Pinedo, 2016). As shown by Martinez et al. (2006), blocking constraints are common to be encountered in manufacturing of metallic parts. In such contexts, shop floors are often arranged in cellular layouts, and therefore imply processing groups of jobs. Such consideration motivates the present research, which addresses the problem of minimizing makespan in an M machines flow shop sequence dependent group scheduling problem with blocking constraint.

This paper aims to investigate the Flow Shop Sequence-Dependent Group Scheduling problem with blocking constraint through a novel Self-Calibrating Genetic Algorithm (PSAGA). The main feature of the proposed algorithm consists of its ability in changing the genetic parameters according to an evolutionary scheme, which allows achieving a proper balance between exploration and exploitation, thus avoiding any time-consuming calibration analysis. In fact, besides the advantage in terms of quality of solutions, a relevant characteristic of the developed PSAGA lies in the fact that no preliminary tuning phase is needed, thus ensuring a fast and effective implementation.

The remainder of the paper is organized as follows. Section 2 provides a description of the FSDGS problem under blocking constraint. Section 3 illustrates the structure and the main operators of the proposed PSAGA. In Section 4, test problem instances and obtained results are shown. Finally, Section 5 concludes the paper.